# Abstracts

## Idealised modelling of ocean circulation driven by conductive and hydrothermal fluxes at the seabed

Jowan M. Barnes, Miguel Morales Maqueda, Jeff A. Polton, Alex P. Megann (2018) Ocean Modelling, 122, 26-35, doi: 10.1016/j.ocemod.2017.12.005

Abstract

Geothermal heating is increasingly recognised as an important factor affecting ocean circulation, with modelling studies suggesting that this heat source could lead to first-order changes in the formation rate of Antarctic Bottom Water, as well as a significant warming effect in the abyssal ocean. Where it has been represented in numerical models, however, the geothermal heat flux into the ocean is generally treated as an entirely conductive flux, despite an estimated one third of the global geothermal flux being introduced to the ocean via hydrothermal sources. A modelling study is presented which investigates the sensitivity of the geothermally forced circulation to the way heat is supplied to the abyssal ocean. An analytical two-dimensional model of the circulation is described, which demonstrates the effects of a volume flux through the ocean bed. A simulation using the NEMO numerical general circulation model in an idealised domain is then used to partition a heat flux between conductive and hydrothermal sources and explicitly test the sensitivity of the circulation to the formulation of the abyssal heat flux. Our simulations suggest that representing the hydrothermal flux as a mass exchange indeed changes the heat distribution in the abyssal ocean, increasing the advective heat transport from the abyss by up to 35% compared to conductive heat sources. Consequently, we suggest that the inclusion of hydrothermal fluxes can be an important addition to course-resolution ocean models.

keywords: Abyssal circulation; Ocean modelling; Hydrothermal; Geothermal heating; Heat flux

This manuscript is available as a preprint PDF file.

## Lagrangian ocean analysis: Fundamentals and practices

Erik van Sebille, Stephen M. Griffies, Ryan Abernathey, Thomas P. Adams, Pavel Berloff, Arne Biastoch, Bruno Blanke, Eric P. Chassignet, Yu Cheng, Colin J. Cotter, Eric Deleersnijder, Kristofer Doos, Henri F. Drake, Sybren Drijfhout, Stefan F. Gary, Arnold W. Heemink, Joakim Kjellsson, Inga Monika Koszalka, Michael Lange, Camille Lique, Graeme A. MacGilchrist, Robert Marsh, C. Gabriela Mayorga Adame, Ronan McAdam, Francesco Nencioli, Claire B. Paris, Matthew D. Piggott, Jeff A. Polton, Siren Ruhs, Syed H.A.M. Shah, Matthew D. Thomas, Jinbo Wang, Phillip J. Wolfram, Laure Zanna, Jan D. Zika (2018) Ocean Modelling, 121, 49-75, doi: 10.1016/j.ocemod.2017.11.008

Abstract

Lagrangian analysis is a powerful way to analyse the output of ocean circulation models and other ocean velocity data such as from altimetry. In the Lagrangian approach, large sets of virtual particles are integrated within the three-dimensional, time-evolving velocity fields. Over several decades, a variety of tools and methods for this purpose have emerged. Here, we review the state of the art in the field of Lagrangian analysis of ocean velocity data, starting from a fundamental kinematic framework and with a focus on large-scale open ocean applications. Beyond the use of explicit velocity fields, we consider the influence of unresolved physics and dynamics on particle trajectories. We comprehensively list and discuss the tools currently available for tracking virtual particles. We then showcase some of the innovative applications of trajectory data, and conclude with some open questions and an outlook. The overall goal of this review paper is to reconcile some of the different techniques and methods in Lagrangian ocean analysis, while recognising the rich diversity of codes that have and continue to emerge, and the challenges of the coming age of petascale computing.

keywords: Ocean circulation; Lagrangian analysis; Connectivity; Particle tracking; Future modelling

This manuscript is open access.

## Kilometric scale modeling of the North West European Shelf Seas: Exploring the spatial and temporal variability of internal tides

K Guihou, JA Polton, J Harle, S Wakelin, E O'Dea, J Holt (2017) JGR, 122, doi: 10.1002/2017JC012960

Abstract

The North West European shelf-break acts as a barrier to the transport and exchange between the open ocean and the shelf seas. The strong spatial variability of these exchange processes is hard to fully explore using observations, and simulations generally are too coarse to simulate the fine-scale processes over the whole region. In this context, under the FASTNEt programme, a new NEMO configuration of the North West European Shelf and Atlantic margin at 1/60 degree (approx 1.8km) has been developed, with the objective to better understand and quantify the seasonal and interannual variability of shelf break processes. The capability of this configuration to reproduce the seasonal cycle in SST, the barotropic tide, and fine-resolution temperature profiles is assessed against a basin-scale (1/12 degree, approx 9km) configuration and a standard regional configuration (7 km resolution). The seasonal cycle is well reproduced in all configurations though the fine-resolution allows the simulation of smaller scale processes. Time-series of temperature at various locations on the shelf show the presence of internal waves with a strong spatio-temporal variability. Spectral analysis of the internal waves reveals peaks at the diurnal, semi-diurnal, inertial and quarter-diurnal bands, which are only realistically reproduced in the new configuration. Tidally induced pycnocline variability is diagnosed in the model and shown to vary with the spring neap cycle with mean displacement amplitudes in excess of 2m for 30% of the stratified domain. With sufficiently fine-resolution, internal tides are shown to be generated at numerous bathymetric features resulting in a complex pycnocline displacement superposition pattern.

keywords: internal tides; high-resolution modeling; observations; North-West European shelf; Numerical modeling; Continental shelf and slope processes; Time series experiments; Internal and inertial waves; Upper ocean and mixed layer processes

This manuscript is available as a preprint PDF file.

## Correcting surface wave bias in structure function estimates of turbulent kinetic energy dissipation rate

BD Scannell, TP Rippeth, JH Simpson, JA Polton, JE Hopkins (2017) JTECH, 34, 2257-02273, doi: 10.1175/JTECH-D-17-0059.1

Abstract

The combination of acoustic Doppler current profilers and the structure function methodology provides an attractive approach to making extended time series measurements of oceanic turbulence (the rate of turbulent kinetic energy dissipation epsilon) from moorings. However, this study shows that for deployments in the upper part of the water column, estimates of epsilon will be biased by the vertical gradient in wave orbital velocities. To remove this bias, a modified structure function methodology is developed that exploits the differing length scale dependencies of the contributions to the structure function resulting from turbulent and wave orbital motions. The success of the modified method is demonstrated through a comparison of epsilon estimates based on data from instruments at three depths over a 3-month period under a wide range of conditions, with appropriate scalings for wind stress and convective forcing.

keywords: Data processing; In situ oceanic observations; Measurements; Profilers, oceanic; Quality assurance/control

This manuscript is open access.

## Thermocline bulk shear analysis in the northern North Sea

S Chen, JA Polton, J Hu, J Xing (2016) Ocean Dynamics, 66, 499-508, doi: 10.1007/s10236-016-0933-3

Abstract

Thermocline bulk shear is investigated in the northern North Sea using historical observations. The conventional bulk shear is modified to define a thermocline bulk shear (TBS), in order to better represent the shear across the thermocline. The TBS computed by observed currents is decomposed into components at different frequency bands. The near-inertial TBS is the largest component. Its dominance is significant during the period of high wind. It is formed by the wind-driven near-inertial current which has a distinct phase shift (approx. 180 degrees) across the thermocline. A linear model is presented, which well simulates the observed near-inertial TBS, especially during the period of relatively strong wind. The semidiurnal TBS makes a secondary contribution to the total TBS. It is only slightly smaller than the near-inertial TBS when the wind is relatively weak. The large values of semidiurnal TBS are associated with semidiurnal currents which have a phase shift (approx. 30-40 degrees) or a magnitude difference (approx. 5 cm/s) across the thermocline. The low-frequency (<0.7 cpd) TBS also makes an episodic contribution to the total. Its variation coincides with the Ekman transport during the period of relatively strong wind. The low-frequency TBS is mainly formed by an Ekman-like clockwise spiraling of velocity with depth or a distinct magnitude difference in velocities between upper and lower layers.

keywords: Thermocline bulk shear; near-inertial; semidiurnal; North Sea

This manuscript is available as a preprint PDF file.

## Local inertial oscillations in the surface ocean generated by time-varying winds

S Chen, JA Polton, J Hu, J Xing (2015) Ocean Dynamics, 65, 1633-1641, doi: 10.1007/s10236-015-0899-6

Abstract

A new relationship is presented to give a review study on the evolution of inertial oscillations in the surface ocean locally generated by time-varying wind stress. The inertial oscillation is expressed as the superposition of a previous oscillation and a newly generated oscillation, which depends upon the time-varying wind stress. This relationship is employed to investigate some idealized wind change events. For a wind series varying temporally with different rates, the induced inertial oscillation is dominated by the wind with the greatest variation. The resonant wind, which rotates anti-cyclonically at the local inertial frequency with time, produces maximal amplitude of inertial oscillations, which grows monotonically. For the wind rotating at non-inertial frequencies, the responses vary periodically, with wind injecting inertial energy when it is in phase with the currents, but removing inertial energy when it is out of phase. The wind rotating anti-cyclonically with time is much more favorable to generate inertial oscillations than the cyclonic rotating wind. The wind with a frequency closer to the inertial frequency generates stronger inertial oscillations. For a diurnal wind, the induced inertial oscillation is dependent on latitude and is most significant at 30 degrees. This relationship is also applied to examine idealized moving cyclones. The inertial oscillation is much stronger on the right-hand side of the cyclone path than on the left-hand side (in the northern hemisphere). This is due to the wind being anti-cyclonic with time on the right-hand side, but cyclonic on the other side. The inertial oscillation varies with the cyclone translation speed. The optimal translation speed generating the greatest inertial oscillations is 2 m/s at the latitude of 10 degrees and gradually increases to 6 m/s at the latitude of 30 degrees.

keywords: inertial oscillations; wind; cyclone

This manuscript is available as a preprint PDF file.

## Improving understanding of shelf-sea exchange

K Guihou, JA Polton (2015) Ocean Challenge, 21(1), 26-27.

This manuscript is available as a PDF file.

## Langmuir Turbulence and Surface Heating in the Ocean Surface Boundary Layer

BC Pearson, ALM Grant, JA Polton, SE Belcher (2015) J. Phys. Oceanogr., 45, 2897-2911, doi: 10.1175/JPO-D-15-0018.1

Abstract

This study uses large-eddy simulation to investigate the structure of the ocean surface boundary layer (OSBL) in the presence of Langmuir turbulence and stabilizing surface heat fluxes. The OSBL consists of a weakly stratified layer, despite a surface heat flux, above a stratified thermocline. The weakly stratified (mixed) layer is maintained by a combination of a turbulent heat flux produced by the wave-driven Stokes drift and downgradient turbulent diffusion. The scaling of turbulence statistics, such as dissipation and vertical velocity variance, is only affected by the surface heat flux through changes in the mixed layer depth. Di- agnostic models are proposed for the equilibrium boundary layer and mixed layer depths in the presence of surface heating. The models are a function of the initial mixed layer depth before heating is imposed and the Langmuir stability length. In the presence of radiative heating, the models are extended to account for the depth profile of the heating.

This manuscript is open access.

## Behaviour influences larval dispersal in shelf sea gyres: Nephrops norvegicus in the Irish Sea

J Phelps, JA Polton, AJ Souza, LA Robinson (2015) Mar. Ecol.-Prog. Ser., 518, 177-191, doi: 10.3354/meps11040

Abstract

The western Irish Sea seasonal gyre is widely thought to play an important role in the local retention of resident larvae. This mechanism could be particularly crucial for the larvae of the heavily fished crustacean Nephrops norvegicus (L.), as their sediment requirements highly restrict where they are able to settle. Recent research suggests that the gyre may be becoming less retentive due to changes in atmospheric forcing; thus it is now crucial to understand how the gyre influences larval dispersal. This investigation addresses the hypothesis that shelf sea gyres reinforce larval retention, using a biophysical model with vertical migration, habitat selection and temperature-dependent pelagic larval duration (PLD) configured to match the behaviour of N. norvegicus larvae. The results suggest that the gyre does increase the likelihood that passive larvae remain within the western Irish Sea when the larvae remain fixed at the depth of peak gyral flow. However, retention rates are significantly lower when vertical migration is introduced, and there is no evidence that the gyre promotes larval retention amongst either vertically migrating larvae, or larvae that require muddy sediments for successful settlement. In contrast, vertical migration is shown to be favourable for local retention in the eastern Irish Sea. PLD varies by a factor of 2 according to release date and location. The simulations suggest that whilst some highly limited and almost entirely unidirectional larval exchange may occur, the distinct sites largely rely upon local recruitment.

keywords:3D numerical modeling; Connectivity; Decapod crustaceans; Gyre; Irish Sea; Larval dispersal; Nephrops norvegicus; Zooplankton

This manuscript is open access.

## Modelling Large-Scale CO2 Leakages in the North Sea

J Phelps, JC Blackford, JT Holt, JA Polton (2015) International Journal of Greenhouse Gas Control, 38, 210-220. doi: 10.1016/j.ijggc.2014.10.013

Abstract

A three dimensional hydrodynamic model with a coupled carbonate speciation sub-model is used to simulate large additions of CO2 into the North Sea, representing leakages at potential carbon sequestration sites. A range of leakage scenarios are conducted at two distinct release sites, allowing an analysis of the seasonal, inter-annual and spatial variability of impacts to the marine ecosystem. Seasonally stratified regions are shown to be more vulnerable to CO2 release during the summer as the added CO2 remains trapped beneath the thermocline, preventing outgasing to the atmosphere. On average, CO2 injected into the northern North Sea is shown to reside within the water column twice as long as an equivalent addition in the southern North Sea before reaching the atmosphere. Short-term leakages of 5000 tonnes CO2 over a single day result in substantial acidification at the release sites (up to -1.92 pH units), with significant perturbations (greater than 0.1 pH units) generally confined to a 10 km radius. Long-term CO2 leakages sustained for a year may result in extensive plumes of acidified seawater, carried by major advective pathways. Whilst such scenarios could be harmful to marine biota over confined spatial scales, continued unmitigated CO2 emissions from fossil fuels are predicted to result in greater and more long-lived perturbations to the carbonate system over the next few decades.

keywords:Carbon capture and storage; CCS; North Sea; CO2; Shelf sea; pH

This manuscript is open access.

## Features of near-inertial motions observed on the northern South China Sea shelf during the passage of two typhoons

S Chen, J Hu, JA Polton (2015) Acta Oceanologica Sinica, 34(1), 38-43, doi: 10.1007/s13131-015-0594-y

Abstract

Features of near-inertial motions on the shelf (60 m deep) of the northern South China Sea were observed under the passage of two typhoons during the summer of 2009. There are two peaks in spectra at both sub-inertial and super-inertial frequencies. The super-inertial energy maximizes near the surface, while the sub-inertial energy maximizes at a deeper layer of 15 m. The sub-inertial shift of frequency is induced by the negative background vorticity. The super-inertial shift is probably attributed to the near-inertial wave propagating from higher latitudes. The near-inertial currents exhibit a two-layer pattern being separated at mid-depth (25-30 m), with the phase in the upper layer being nearly opposite to that in the lower layer. The vertical propagation of phase implies that the near-inertial energy is not dominantly downward. The upward flux of the near-inertial energy is more evident at the surface layer (above 17 m). There exist two boundaries at 17 and 40 m, where the near-inertial energy is reflected upward and downward. The near-inertial motion is intermittent and can reach a peak of as much as 30 cm/s. The passage of Typhoon Nangka generates an intensive near-inertial event, but Typhoon Linfa does not. This difference is attributed to the relative mooring locations, which is on the right hand side of Nangka's path (leading to a wind pattern rotating clockwise with time) and is on the left hand side of Linfa's path (leading to a wind pattern rotating anti-clockwise with time).

keywords:near-inertial motions; typhoon; South China Sea

This manuscript is available as a preprint PDF file.

## Tidally induced mean flow over bathymetric features: a contemporary challenge for high-resolution wide-area models

Jeff A. Polton (2015), Geophysical and Astrophysical Fluid Dynamics, 109:3, 207-215, doi:10.1080/03091929.2014.952726

Abstract

Huthnance [Estuarine CoastalMar. Sci. 1973, 1, 89-99] is reviewed, whereby an oscillating tide over bathymetric features induces a mean flow generally along isobaths. The effect is a superposition of Coriolis and frictional processes. These are discussed with the intention of elucidating the processes for a more general readership. Induced velocities of order several cm s^{-1} are expected around the UK shelf seas. The effect is dynamically significant over bathymetric scales of order a few kilometres and has previously been of most interest to dynamicists studying processes on this scale. However, with the increase in computing power, appropriate scales can be simulated in shelf-wide regional models and in next generation operational models. It is demonstrated that this small-scale effect is likely to be important for shelf-wide regional models and that a spatial resolution of at least 1.8km is recommended for shelf sea simulations.

keywords:Regional model; Resolution; Tides; Tidal residual; Bathymetry; Tidal excursion

This manuscript is open access.

## Observations of a diapycnal shortcut to adiabatic upwelling of Antarctic Circumpolar Deep Water

J Mead Silvester, Y-D Lenn, JA Polton, TP Rippeth, M Morales-Maqueda (2014) Geophys. Res. Lett., 41(22), 7950-7956,
doi: 10.1002/2014GL061538

Abstract

In the Southern Ocean, small-scale turbulence causes diapycnal mixing which influences important water mass transformations, in turn impacting large-scale ocean transports such as the Meridional Overturning Circulation (MOC), a key controller of Earth's climate. We present direct observations of mixing over the Antarctic continental slope between water masses that are part of the Southern Ocean MOC. A 12 h time series of microstructure turbulence measurements, hydrography, and velocity observations off Elephant Island, north of the Antarctic Peninsula, reveals two concurrent bursts of elevated dissipation of O(10E-6) W/kg, resulting in heat fluxes about 10 times higher than basin-integrated Drake Passage estimates. This occurs across the boundary between adjacent adiabatic upwelling and downwelling overturning cells. Ray tracing to nearby topography shows mixing between 300 and 400 m is consistent with the breaking of locally generated internal tidal waves. Since similar conditions extend to much of the Antarctic continental slope where these water masses outcrop, diapycnal mixing may contribute significantly to upwelling.

This manuscript is open access.

## Assessment of coastal density gradients near a macro-tidal estuary: Application to the Mersey and Liverpool Bay

M.J. Howarth, C.A. Balfour, Rose J.J. Player, Jeff A. Polton (2014), Cont. Shelf Res., 87, 73-83. doi:10.1016/j.csr.2013.11.016

Abstract

Density gradients in coastal regions with significant freshwater input are large and variable and are a major control of nearshore circulation. However their measurement is difficult, especially where the gradients are largest, close to the coast, with significant uncertainties because of a variety of factors - time and spatial (horizontal and vertical) scales are small, tidal currents are strong and water depths shallow. Whilst temperature measurements are relatively straightforward, measurement of salinity (the dominant control of spatial variability for density) can be less reliable in turbid coastal waters. The nearshore density gradients in Liverpool Bay are investigated using an integrated multi-year data set from an in situ buoy, instrumented ferry and HF radar. The ferry is particularly useful for estimating coastal density gradients since measurements are made right from the mouth of Mersey, where gradients are on average $3 \times 10^{-4} kg m^{-4}$. Using measurements at the single in situ site by the Mersey Bar, 17 km from land, density gradients can be estimated from the tidal excursion or by using ferry data; both giving average values of $5 \times 10^{-5} kg m^{-4}$. Nine years of surface salinity measurements there show no evidence of predominant periodicities, although there is a weak annual cycle, and no consistent relation with storms or floods, leading to the conclusion that the majority of the Mersey plume, for most of the time, lies closer to the English shore than the Mersey Bar. Liverpool Bay's circulation is the dominant factor, with wind forcing tending to reinforce it for wind speeds greater than $5-10 m s^{-1}$. Near bed currents are consistently shoreward and near surface currents northward.

keywords: Mersey plume; Liverpool Bay; Salinity; Ferrybox; HF radar

This manuscript is available as a PDF file.

## Can Drake Passage observations match Ekman's classic theory?

Jeff A. Polton, Y.-D. Lenn, S. Elipot, T.K. Chereskin, J. Sprintall (2013), J. Phys. Oceanogr., 43, p1733-1740. doi:10.1175/JPO-D-13-034.1

Abstract

Ekman's theory of the wind-driven ocean surface boundary layer assumes a constant eddy viscosity and predicts that the current rotates with depth at the same rate as it decays in amplitude. Despite its wide acceptance, Ekman current spirals are difficult to observe. This is primarily because the spirals are small signals that are easily masked by ocean variability and cannot readily be separated from the geostrophic component. This study presents a method for estimating ageostrophic currents from shipboard acoustic Doppler current profiler data in Drake Passage and finds that observations are consistent with Ekman's theory. By taking into account the sampling distributions of wind stress and ageostrophic velocity, the authors find eddy viscosity values in the range of 0.08-0.12 $m^2 s^{-1}$ that reconcile observations with the classic theory in Drake Passage. The eddy viscosity value that most frequently reconciles observations with the classic theory is 0.094 $m^2 s^{-1}$, corresponding to an Ekman depth scale of 39 m.

This manuscript is open access.

## The vertical structure of time-mean estuarine circulation in a shallow, rotating, semi-enclosed coastal bay: A Liverpool Bay case study with application for monitoring.

Jeff A. Polton, Matthew R. Palmer, and M. John Howarth (2013), Cont. Shelf Res., 59, p115-126, doi:10.1016/j.csr.2013.03.004

Abstract

A reduced physics Ekman boundary layer solution is developed to infer the vertical structure of time-mean circulation in a shallow tidal environment when the horizontal density and surface slope gradients are misaligned. This generalisation of the classic Heaps (1972) model shows that the time-mean depth weighted flow, or the residual circulation, is usefully constrained by knowledge of the surface velocity, instead of freshwater flux, and the horizontal density gradient. The generalised model is applied to Liverpool Bay. In regions where the Ekman depth scale is less than half the mean fluid depth the residual circulation is well modelled by a water column of uniform density, constant eddy viscosity and linear bottom drag. Lateral variability in long-term mooring observations of depth varying residual flow are attributed to the misalignment of sea surface slope and haline controlled density gradients. A method to infer 3D time-average residual currents in regions of misaligned freshwater density and sea surface slope gradients is presented. The method blends CTD survey data with HF radar surface currents and simulation estimates of viscosity and friction. It is validated against ADCP data in Liverpool Bay. It is speculated that this method could be applied more generally, to correct model biases, as part of a coastal monitoring system.

This manuscript is available as a PDF file.

## Hydrodynamic Timescales in a Hyper-tidal Region of Freshwater Influence

Phelps, J.J.C., J.A. Polton, A.J. Souza, L.A. Robinson (2013), Hydrodynamic timescales in a hyper-tidal region of freshwater influence, Cont. Shelf Res., 63, p13-22, doi:10.1016/j.csr.2013.04.027

Abstract

This study uses a three-dimensional hydrodynamic model to investigate transport timescales in Liverpool Bay, a shallow hyper-tidal Region of Freshwater Influence (ROFI) with a density-driven baroclinic residual circulation. Flushing time, residence time and age are evaluated, providing rigorously defined parameters to describe the rate of offshore freshwater transport and basin replenishment. Additional challenges encountered when assessing these timescales in a tidally mixed regime are highlighted by idealised models. Climatological river gauge data reveals that the numerous local rivers contribute an average of $203 m^3 s^{-1}$ of freshwater to Liverpool Bay. Based upon the mean salinity distribution, this would suggest a flushing time of approximately 136 days. The mean residence time of the region is approximately 103 days although small concentrations of water are retained over several years due to vigorous tidal mixing. Age in the region is highly variable with regular oscillations caused by tidal advection, whilst long term fluctuations are governed by river flow rates. The mean age gradient is directed offshore, approximately parallel to both the salinity gradient and the major axis of the tidal ellipse, with basin wide average magnitude of 6 days km^{-1}$. It is shown that salinity may be used to estimate the age of freshwater, which is not directly observable in practice.a This manuscript is available as a PDF file. ## Variable behavior in pycnocline mixing over shelf seas Palmer, M.R., J.A. Polton, M.E. Inall, T.P. Rippeth, J.A.M. Green, J. Sharples, and J.H. Simpson (2013), Variable behavior in pycnocline mixing over shelf seas, Geophys. Res. Lett., 40, doi: 10.1029/2012GL054638 Abstract Vertical mixing, driven by turbulence in the ocean, underpins many of the critical interactions that allow life on earth to flourish since vertical buoyancy flux maintains global overturning circulation and vertical nutrient fluxes are critical to primary production. Prediction of the ocean system is therefore dependent on accurate simulation of turbulent processes that, by their very nature, are chaotic. A growing evidence base exists that provides insight into these complex processes and permits investigation of turbulence relative to better determined, and therefore predictable, parameters. Here we examine three time series of the dissipation rate of turbulent kinetic energy ($\epsilon$) in 'stability space'. We reveal an ordered structure within the mean distribution of e that compares well to a variety of proposed models of oceanic turbulence. The requirement for differing site-specific tuning and only partial success however raises questions over 'missing physics' within such models and the validity of measurement techniques. This manuscript is available as a PDF file. ## Modelling temperature and salinity in Liverpool Bay and the Irish Sea: sensitivity to model type and surface forcing Clare K. O'Neill, Jeff A. Polton, Jason T. Holt and Enda J. O'Dea (2012), Ocean Sci., 8, 903-913. DOI:10.5194/os-8-903-2012 Abstract Three shelf sea models are compared against observed surface temperature and salinity in Liverpool Bay and the Irish Sea: a 7 km NEMO (Nucleus for European Modelling of the Ocean) model, and 12 km and 1.8 km POLCOMS (Proudman Oceanographic Laboratory Coastal Ocean Modelling System) models. Each model is run with two different surface forcing datasets of different resolutions. Comparisons with a variety of observations from the Liverpool Bay Coastal Observatory show that increasing the surface forcing resolution improves the modelled surface temperature in all the models, in particular reducing the summer warm bias and winter cool bias. The response of surface salinity is more varied with improvements in some areas and deterioration in others. The 7 km NEMO model performs as well as the 1.8 km POLCOMS model when measured by overall skill scores, although the sources of error in the models are different. NEMO is too weakly stratified in Liverpool Bay, whereas POLCOMS is too strongly stratified. The horizontal salinity gradient, which is too strong in POLCOMS, is better reproduced by NEMO which uses a more diffusive horizontal advection scheme. This leads to improved semi-diurnal variability in salinity in NEMO at a mooring site located in the Liverpool Bay ROFI (region of freshwater influence) area. This manuscript is available as a PDF file. ## A global perspective on Langmuir turbulence in the ocean surface boundary layer Belcher, S.E., Grant, A.L.M., Hanley, K.E., Fox-Kemper, B., Van Roekel, L., Sullivan, P.P., Large, W.G., Brown, A., Hines, A., Calvert, D., Rutgersson, A., Pettersson, H., Bidlot, J.-R., Janssen, P.A.E.M., Polton, J.A. (2012), Geophys. Res. Lett., 39, L18605. Abstract The turbulent mixing in thin ocean surface boundary layers (OSBL), which occupy the upper 100m or so of the ocean, control the exchange of heat and trace gases between the atmosphere and ocean. Here we show that current parameterizations of this turbulent mixing lead to systematic and substantial errors in the depth of the OSBL in global climate models, which then leads to biases in sea surface temperature. One reason, we argue, is that current parameterizations are missing key surface-wave processes that force Langmuir turbulence that deepens the OSBL more rapidly than steady wind forcing. Scaling arguments are presented to identify two dimensionless parameters that measure the importance of wave forcing against wind forcing, and against buoyancy forcing. A global perspective on the occurrence of wave-forced turbulence is developed using re-analysis data to compute these parameters globally. The diagnostic study developed here suggests that turbulent energy available for mixing the OSBL is under-estimated without forcing by surface waves. Wave-forcing and hence Langmuir turbulence could be important over wide areas of the ocean and in all seasons in the Southern Ocean. We conclude that surface-wave-forced Langmuir turbulence is an important process in the OSBL that requires parameterization. keywords: Langmuir turbulence; global diagnostics; ocean surface boundary layer. This manuscript is available as a PDF file. ## Remote sensing of seasonal stratification dynamics in the southern Irish Sea C. Neil, A. Cunningham, D. McKee, Jeff A. Polton (2012), Remote Sensing of Environment, 127, 288-297. Abstract In early summer, a well-defined front forms at the southern boundary of Irish Sea between thermally stratified and tidally mixed waters. The Proudman Oceanographic Laboratory Coastal Ocean Modelling System (POLCOMS) was used to predict the location of this front, and data from the MODIS Aqua sensor was used to derive a five-year time series of red-waveband remote sensing reflectance (Rrs667) and sea surface temperature (SST) for two representative areas on either side of the frontal region. Pronounced annual cycles in Rrs667 and SST were observed at both locations, with summer minima in Rrs667 being roughly coincident with SST maxima. Previous studies have shown that Rrs667 in the Irish Sea is mainly determined by near-surface concentrations of suspended mineral particles. The annual cycles in reflectance therefore indicate that vertical mixing of the water column in winter supplies fine particles to the surface layer which settle out in calmer summer conditions. While the temporal resolution achievable by remote sensing in a single year was limited by the high incidence of cloud cover, monthly averaged data for the whole five-year period revealed differences of the order of one month in the timing of the reflectance cycle on the mixed and stratified sides of the front. This difference produced transient patterns of reflectance in early summer (and occasionally in autumn) in which sharp contrasts coincided with the location of the tidal front predicted by the POLCOMS model. We conclude that optical remote sensing in shelf seas can provide information not only on changing concentrations of optically significant materials, but also on the location and timing of dynamical processes such as seasonal front formation, and note that such information is of potential value for tuning and validating numerical models of shelf sea ecosystems. keywords: Irish Sea mixing; Tidal front; Optical remote sensing This manuscript is available as a PDF file. ## Scales and structure of frontal adjustment and freshwater export in a region of freshwater influence. Joanne Hopkins and Jeffrey A. Polton (2012), Ocean Dynamics . DOI: 10.1007/s10236-011-0475-7. Abstract Sea surface temperature satellite imagery and a regional hydrodynamic model are used to investigate the variability and structure of the Liverpool Bay thermohaline front. A statistically based water mass classification technique is used to locate the front in both data sets. The front moves between 5 and 35 km in response to spring-neap changes in tidal mixing, an adjustment that is much greater than at other shelf-sea fronts. Superimposed on top of this fortnightly cycle are semi-diurnal movements of 5-10 km driven by flood and ebb tidal currents. Seasonal variability in the freshwater discharge and the density difference between buoyant inflow and more saline Irish Sea water give rise to two different dynamical regimes. During winter, when cold inflow reduces the buoyancy of the plume, a bottom-advected front develops. Over the summer, when warm river water provides additional buoyancy, a surface-advected plume detaches from the bottom and propagates much larger distances across the bay. Decoupled from near-bed processes, the position of the surface front is more variable. Fortnightly stratification and re-mixing over large areas of Liverpool Bay is a potentially important mechanism by which freshwater, and its nutrient and pollutant loads, are exported from the coastal plume system. Based on length scales estimated from model and satellite data, the erosion of post-neap stratification is estimated to be responsible for exporting approximately 19% of the fresh estuarine discharge annually entering the system. Although the baroclinic residual circulation makes a more significant contribution to freshwater fluxes, the episodic nature of the spring-neap cycle may have important implications for biogeochemical cycles within the bay. keywords: Spring-neap; Thermohaline front; Freshwater export; Stratification; Coastal; Shelf sea This manuscript is available as a PDF file. ## Physical and dynamical oceanography of Liverpool Bay Jeff A. Polton, Matthew R. Palmer, and M. John Howarth (2011), Ocean Dynamics. DOI: 10.1007/s10236-011-0431-6 Abstract The UK National Oceanography Centre (NOC) has maintained an observatory in Liverpool Bay since August 2002. Over 8 years of observational measurements are used in conjunction with regional ocean modelling data to describe the physical and dynamical oceanography of Liverpool Bay and to validate the regional model, POLCOMS. Tidal dynamics and plume buoyancy govern the fate of the fresh water as it enters the sea, as well as the fate of its sediment, contaminants and nutrient loads. In this context, an overview and summary of Liverpool Bay tidal dynamics are presented. Freshwater forcing statistics are presented showing that on average the bay receives$233 m^3 s^{-1}$. Though the region is salinity controlled, river input temperature is shown to significantly modulate the plume buoyancy with a seasonal cycle. Stratification strongly influences the region's dynamics. Data from long term moored instrumentation is used to analyse the stratification statistics that are representative of the region. It is shown that for$65\%$of tidal cycles the region alternates between being vertically mixed and stratified. Plume dynamics are diagnosed from the model and are presented for the region. The spring-neap modulation of the plume's westward extent, between$3.5 ^\circ W$and$4^\circ W$, is highlighted. The rapid eastward erosion of the plume during spring tides is identified as a potentially important freshwater mixing mechanism. Novel climatological maps of temperature, salinity and density from the CTD surveys are presented and used to validate numerical simulations. The model is found to be sensitive to the freshwater forcing rates, temperature and salinities. The existing CTD survey grid is shown to not extend sufficiently near the coast to capture the near coastal and vertically mixed component the plume. Instead the survey grid captures the westward spreading, shallow and transient, portion of the plume. This transient plume feature is shown in both the long term averaged model and observational data as a band of stratified fluid stretching between the mouth of the Mersey towards the Isle of Man. Finally the residual circulation is discussed. Long term moored ADCP data are favourably compared with model data, showing the general northward flow of surface water and southward trajectory of bottom water. keywords: Liverpool Bay; Climatology; ROFI; plume dynamics; coastal dynamics; coastal oceanography; shelf sea; model validation This manuscript is available as a PDF file. ## A strain induced freshwater pump in the Liverpool Bay ROFI Matthew R. Palmer, and Jeff A. Polton (2011), Ocean Dynamics. DOI:10.1007/s10236-011-0430-7 Abstract Liverpool Bay is a region of freshwater influence (ROFI) which receives significant freshwater loading from a number of major English and Welsh rivers. Strong tidal currents flow perpendicular to a persistent freshwater induced horizontal density gradient to produce strain induced periodic stratification (SIPS). Recent work (Palmer, 2010; Verspecht et al, 2010) has identified significant modification to tidal ellipses in Liverpool Bay during stratification due to an associated reduction in pycnocline eddy viscosity. Palmer (2010) identified that this modification results in asymmetry in flow in the upper and lower layers capable of permanently transporting freshwater away from the Welsh coastline via a SIPS pumping mechanism. Observational data from a new set of observations from the Irish Sea Observatory site B confirms these results; the measured residual flow is 4.0 cm/s to the north in the surface mixed layer and 2.4 cm/s to the south in the bottom mixed layer. A realistically forced 3-D hydrodynamic ocean model POLCOMS succeeds in reproducing many of the characteristics of flow and vertical density structure at site B and is used to estimate the transport of water through a transect WT that runs parallel with the Welsh coast. Model results show SIPS is the dominant steady state, occurring for 78.2% of the time while enduring stratification exists only 21.0% of the year and enduring mixed periods, less than 1%. SIPS produces a persistent offshore flow of freshened surface water throughout the year. The estimated net flux of water in the surface mixed layer is 327 km^3/y of which 281 km^3/y is attributable to SIPS periods. While the freshwater component of this flux is small the net flux of freshwater through WT during SIPS is significant; the model estimates 1.69 km^3/y of freshwater to be transported away from the coast attributable to SIPS periods equivalent to 23% of annual average river flow from the four catchment areas feeding Liverpool Bay. The results show SIPS pumping to be an important process in determining the fate of freshwater and associated loads entering Liverpool Bay. keywords: Liverpool Bay; Coastal Observatory; SIPS; ROFI; tidal straining; plume dynamics; coastal oceanography; POLCOMS This manuscript is available as a PDF file. ## A Hybrid Spectral/Finite-difference Large-eddy Simulator of Turbulent Processes in the Ocean. Andres E. Tejada-Martinez, Chester E. Grosch, Ann E. Gargett, Jeff A. Polton, Jerome A. Smith, Jennifer A. MacKinnon (2009). Ocean Modelling. 30, pp115-142. Abstract A three-dimensional numericalmodel for large-eddy simulation (LES) of oceanic turbulent processes is described. The numerical formulation is comprised of a spectral discretization in the horizontal directions and a high order compact finitedifference discretization in the vertical direction. Time-stepping is accomplished via a second order accurate fractional step scheme. LES subgrid-scale (SGS) closure is given by a traditional Smagorinsky eddy viscosity parametrization for which the model coefficient is derived following similarity theory in the near-surface region. Alternatively, LES closure is given by the dynamic Smagorinsky parametrization for which the model coefficient is computed dynamically as a function of the flow. Validation studies are presented demonstrating the temporal and spatial accuracy of the formulation for laminar flows with analytical solutions. Further validation studies are described involving direct numerical simulation (DNS) and LES of turbulent channel flow and LES of decaying isotropic turbulence. Sample flow problems include surface Ekman layers and wind driven shallow water flows both with and without Langmuir circulation (LC), generated by wave effects parameterized via the well-known Craik-Leibovich (C-L) vortex force. In the case of the Ekman layers, the surface viscous boundary layer is not resolved and instead parameterized with the Smagorinsky models previously described. The validity of the dynamic Smagorinsky model (DSM) for parameterizing the surface boundary layer is assessed and a modification to the surface stress boundary condition based on log-layer behavior is introduced improving the performance of the DSM. Furthermore, in Ekman layers with wave effects, the implicit LES grid filter leads to LC subgrid-scales requiring ad-hoc modeling via an explicit spatial filtering of the C-L force in place of a suitable SGS parameterization. This manuscript is available as a PDF file. ## A wave averaged energy equation: Comment on "Global Estimates of Wind Energy Input to Subinertial Motions in the Ekman-Stokes Layer" by Bin Liu, Kejian Wu and Changlong Guan. Jeff A. Polton (2009), J. Oceanogr. Soc. Japan 65(5), pp. 665-668. Abstract In a recent paper, Liu et al. (2007) formulate an expression for how surface gravity waves modify the Ekman layer energy budget. They then diagnose the effect in the world oceans using available data. This comment addresses the formulation of the energy equation that is fundamental to their study. This manuscript is available as a PDF file. ## Rapid generation of high-frequency internal waves beneath a wind and wave forced oceanic surface mixed-layer Jeff A. Polton, Jerome A. Smith, J. A. MacKinnon, and Andres E. Tejada-Martinez (2008), Geo. Phys. Res. Lett., 35, L13602, doi:10.1029/2008GL033856. Abstract High-frequency internal waves generated by Langmuir motions over stratified water may be an important source of turbulent mixing below the surface mixed-layer. Large eddy simulations of a developing mixed-layer and inertial current are employed to investigate this phenomena. Uniform surface wind stress and parallel Stokes drift wave forcing rapidly establishes a turbulent mixed-layer flow, which (as the inertial motion veers off the wind) generates high-frequency internal waves in the stratified fluid below. The internal waves evolve such that their vector phase velocity matches the depth-averaged mixed-layer velocity that rotates as an inertial oscillation. The internal waves drain energy and momentum from the mixed-layer on decay time-scales that are comparable to those of near-inertial oscillations. The high-frequency waves, which are likely to be trapped in the transition layer, may significantly contribute to mixing there and thus provide a potentially important energy sink for mixed-layer inertial motions. This manuscript is available as a PDF file. ## Langmuir Turbulence and deeply penetrating jets in an unstratified mixed layer Jeff A. Polton and Stephen E. Belcher (2007), JGR-Oceans, 112, C09020, doi:10.1029/2007JC004205, Abstract The influence of surface waves and an applied wind stress are studied in an ensemble of large eddy simulations to investigate the nature of deeply penetrating jets into an unstratified mixed layer. The influence of a steady monochromatic surface wave propagating parallel to the wind direction is parameterized using the wave filtered Craik-Leibovich equations. Tracer trajectories and instantaneous downwelling velocities reveal classic counter-rotating Langmuir rolls. The associated downwelling jets penetrate to depths in excess of the wave's Stokes depth scale,$\delta_s$. Qualitative evidence suggests the depth of the jets is controlled by the Ekman depth scale. Analysis of turbulent kinetic energy (tke) budgets reveals a dynamical distinction between Langmuir turbulence and shear-driven turbulence. In the former tke production is dominated by Stokes shear and a vertical flux term transports tke to a depth where it is dissipated. In the latter tke production is from the mean shear and is locally balanced by dissipation. We define the turbulent Langmuir number$La_t=(v_*/U_s)^{0.5}$($v_*$is the ocean's friction velocity and$U_s$is the surface Stokes drift velocity) and a turbulent anisotropy coefficient$R_t=\overline{w'^2} / ( \overline{u'^2} + \overline{v'^2} )$. The transition between shear-driven and Langmuir turbulence is investigated varying external wave parameters$\delta_s$and$La_t$and by diagnosing$R_t$and the Eulerian mean and Stokes shears. When either$La_t$or$\delta_s\$ are sufficiently small the Stokes shear dominates the mean shear and the flow is preconditioned to Langmuir turbulence and the associated deeply penetrating jets.

This manuscript is available as a PDF file.

## Overturning cells in the Southern Ocean and subtropical gyres

Jeff A. Polton and David P. Marshall (2007), Ocean Sci., 3(1), 17-30.

Abstract

The circulation of the subtropical gyres can be decomposed into a horizontal recirculation along contours of constant Bernoulli potential and an overturning circulation across these contours. While the geometry and topology of Bernoulli contours is more complicated in the subtropical gyres than in the Southern Ocean, these subtropical overturning circulations are very much analogous to the overturning cell found in the Southern Ocean. This analogy is formalised through an exact integral constraint, including the rectified effects of transient eddies. The constraint can be interpreted either in terms of vertical fluxes of potential vorticity, or equivalently as an integral buoyancy budget for an imaginary fluid parcel recirculating around a closed Bernoulli contour. Under conditions of vanishing buoyancy and mechanical forcing, the constraint reduces to a generalised non-acceleration condition, under which the Eulerian-mean and eddy-induced overturning circulations exactly compensate. The terms in the integral constraint are diagnosed in an eddy-permitting ocean model in both the North Pacific subtropical gyre and the Southern Ocean. The extent to which the Eulerian-mean and eddy-induced overturning circulations compensate is discussed in each case.

This manuscript is available as a PDF file.

## Control of large-scale ocean heat transport by small-scale mixing

Paola Cessi, W. R. Young and Jeff A. Polton (2006), J. Phys. Oceanogr., 36, 1877-1894.

Abstract

The equilibrium of an idealized flow driven at the surface by wind stress and rapid relaxation to nonuniform buoyancy is analyzed in terms of entropy production, mechanical energy balance, and heat transport. The flow is rapidly rotating, and dissipation is provided by bottom drag. Diabatic forcing is transmitted from the surface by isotropic diffusion of buoyancy. The domain is periodic so that zonal averaging provides a useful decomposition of the flow into mean and eddy components. The statistical equilibrium is characterized by quantities such as the lateral buoyancy flux and the thermocline depth; here, scaling laws are proposed for these quantities in terms of the external parameters. The scaling theory predicts relations between heat transport, thermocline depth, bottom drag, and diapycnal diffusivity, which are confirmed by numerical simulations. The authors find that the depth of the thermocline is independent of the diapycnal mixing to leading order, but depends on the bottom drag. This dependence arises because the mean stratification is due to a balance between the large-scale wind-driven heat transport and the heat transport due to baroclinic eddies. The eddies equilibrate at an amplitude that depends to leading order on the bottom drag. The net poleward heat transport is a residual between the mean and eddy heat transports. The size of this residual is determined by the details of the diapycnal diffusivity. If the diffusivity is uniform (as in laboratory experiments) then the heat transport is linearly proportional to the diffusivity. If a mixed layer is incorporated by greatly increasing the diffusivity in a thin surface layer then the net heat transport is dominated by the model mixed layer.

This manuscript is available as a PDF file.

## The Role of Wave-Induced Coriolis-Stokes Forcing on the Wind-Driven Mixed Layer

Jeff A. Polton, David M. Lewis, and Stephen E. Belcher (2005), J. Phys. Oceanogr., 34(4), 444-457.

Abstract

The interaction between the Coriolis force and the Stokes drift associated with ocean surface waves leads to a vertical transport of momentum, which can be expressed as a force on the mean momentum equation in the direction along wave crests. How this Coriolis-Stokes forcing affects the mean current profile in a wind-driven mixed layer is investigated using simple models, results from large-eddy simulations, and observational data. The effects of the Coriolis-Stokes forcing on the mean current profile are examined by reappraising analytical solutions to the Ekman model that include the Coriolis-Stokes forcing. Turbulent momentum transfer is modeled using an eddy-viscosity model, first with a constant viscosity and second with a linearly varying eddy viscosity. Although the Coriolis-Stokes forcing penetrates only a small fraction of the depth of the wind-driven layer for parameter values typical of the ocean, the analytical solutions show how the current profile is substantially changed through the whole depth of the wind-driven layer. It is shown how, for this oceanic regime, the Coriolis-Stokes forcing supports a fraction of the applied wind stress, changing the boundary condition on the wind-driven component of the flow and hence changing the current profile through all depths. The analytical solution with the linearly varying eddy viscosity is shown to reproduce reasonably well the effects of the Coriolis-Stokes forcing on the current profile computed from large-eddy simulations, which resolve the three-dimensional overturning motions associated with the turbulent Langmuir circulations in the wind-driven layer. Last, the analytical solution with the Coriolis-Stokes forcing is shown to agree reasonably well with current profiles from previously published observational data and certainly agrees better than the standard Ekman model. This finding provides evidence that the Coriolis-Stokes forcing is an important mechanism in controlling the dynamics of the upper ocean.

This manuscript is available as a PDF file.

## Understanding the Structure of the Subtropical Thermocline

Jeff A. Polton and David P. Marshall (2003), J. Phys. Oceanogr., 33(6), 1240-1249.

Abstract

Closing a gyre with a western boundary current imposes a constraint on its vertical structure that requires there to be no net vertical flux of potential vorticity through any closed pressure contour in steady state. This constraint resembles the traditional similarity balance for the internal thermocline, with additional terms representing friction in the western boundary current and convection in the mixed layer. The terms in the integral constraint are diagnosed in a planetary geostrophic ocean model and are used to understand the coexistence of ventilated and internal thermoclines within the subtropical gyre.

This manuscript is available as a PDF file.

## An International Perspective on Graduate Education in Physical Oceanography

Holger Brix, James L. Hench, Helen L. Johnson, T. M. Shaun Johnston, Jeff A. Polton, Moninya Roughan and Pierre Testor (2003), Oceanography, 16(3), 128-133.

Abstract

During the inaugural Physical Oceanography Dissertation Symposium in June 2002 we found that the graduate school experience varied markedly amongst the 20 international participants. The diversity of backgrounds led to lively discussion about the differences between physical oceanography programs. Here we review the length, content, and quality of education for graduate programs in Australia, France, Germany, the UK, and the U.S. We also comment on the financial, social, and scientific status of graduate students in these countries. Graduate programs in physical oceanography face the challenge of introducing students to the wide range of tools and techniques which define the field, ranging from observational work and remote sensing, through dynamical theory and laboratory experiments, to numerical modeling. While individual character largely determines the success of the Ph.D. experience, a graduate education in physical oceanography should include the following factors to best serve students in their future career: solid mentorship, regular department level progress checks, course work, summer schools, field work, practice in communication skills, scientific and social integration, international exchange, and stable and sufficient funding. We propose a model four year physical oceanography graduate degree structure, distilled from the best aspects of international physical oceanography programs.

This manuscript is available as a PDF file.

Jeff A. Polton (2002), Weather, 57(7), 255-258.

This manuscript is available as a PDF file.

## Understanding the Vertical Structure of the Subtropical Thermocline

Jeff A. Polton (2002), PhD thesis, Reading, UK.

Abstract

Current understanding of the vertical structure of the subtropical thermocline is broadly based on one of two competing theories: the diffusive thermocline theory where diapycnal mixing balances downward advection, or the ventilated thermocline theory where the surface conditions are advected into the interior. Neither of these theories include an active western boundary current, assuming that it does not significantly influence the thermocline stratification in closing the circulation. Closing the gyre with a western boundary current, however, imposes a strong constraint on the vertical structure, which can be conveniently interpreted as an integral constraint on potential vorticity fluxes. In particular, the vertical flux of potential vorticity through any steady-state closed Bernoulli contour must be zero. In a planetary geostrophic ocean, the integral constraint is a balance between vertical fluxes of potential vorticity associated with vertical advection, buoyancy forcing, and dissipative friction. The integral constraint recovers the diffusive and ventilated thermocline theories and further highlights that friction, manifest in the western boundary current, can be essential in closing the balance. The integral constraint is extended for application in an eddy-permitting ocean simulation. An additional potential vorticity flux attributed to eddies is shown to effectively replace the frictional flux and acts to either oppose the advective or the buoyancy potential vorticity fluxes in the western boundary current region, where the model effectively captures mesoscale variability. These results show that the western boundary current is active in closing the gyre-scale circulation and quantifies, in terms of potential vorticity fluxes, the role of dissipative western boundary current processes in maintaining the subtropical thermocline. Furthermore, the diagnostics developed in this thesis, which show that eddies can affect the stratification of the subtropical gyre, could be used, in eddy-resolving data, to diagnose the extent of the eddy influence.

This manuscript is available as a PDF file.