Nonmodal amplification of
disturbances in channel flows of viscoelastic fluids
Satish Kumar
University of Minnesota, USA
Whether and how channel flows of viscoelastic fluids with weak levels of
inertia and initially small-amplitude perturbations can transition to elastic
turbulence is a fundamental yet unsettled issue in non-Newtonian fluid
mechanics. Standard (modal) linear
stability analysis typically predicts that these flows are stable in the absence
of inertia. However, initially
small-amplitude perturbations can undergo considerable transient (nonmodal)
amplification due to the non-normal nature of the linearized problem. Such amplification may put the flow into a
regime where nonlinear terms are no longer negligible, thereby triggering a
transition to elastic turbulence. This
talk will provide an overview of the basic ideas of nonmodal amplification,
elucidate their relevance to viscoelastic channel flows, and present some
recent results showing that polymer-stress fluctuations due to a spatially
localized time-periodic disturbance can be amplified by an order of magnitude
while there is only negligible amplification of velocity fluctuations. This
stress amplification is highly localized in space and may be relevant for
understanding recent experimental observations (by P. Arratia and co-workers)
of elastic turbulence in microchannel flows of viscoelastic fluids (G.
Hariharan, M. R. Jovanovic, and S. Kumar, J. Non-Newtonian Fluid Mech. 291
(2021) 104514).
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