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arXiv · 2607.29598

Oscillatory shear flows and a new 2D self-sustaining process

Theo A. Lewy·Rich R. Kerswell
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Abstract

A new self-sustaining process (SSP) is identified in an oscillating spatially-homogeneous shear flow using a nonlinear Kelvin mode model. This SSP consists of energetic spanwise-invariant 1D `sheets' and weaker spanwise-dependent 2D fluctuations. It is instantaneously 2D, with a time-dependent invariant direction in the flow-cross-shear plane, and has a varicose symmetry. The sheets oscillate in time and are linearly unstable generating fluctuations which then nonlinearly self-interact to reinforce the sheets. The linear instability of the sheet is shown to be due to a lift-up mechanism acting in tandem with `push-forward', which arises due to the `streamwise' shear of the sheets. As the Reynolds number $Re\rightarrow\infty$, both asymptotics and numerics show SSP lower branches with fluctuation velocity $|\boldsymbol{u}'|\sim Re^{-1/2}$. Implications are discussed for oscillatory wall-bounded flows.

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Theo A. Lewy, Rich R. Kerswell. 2026-07-31. Oscillatory shear flows and a new 2D self-sustaining process. https://arxiv.org/abs/2607.29598

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