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Stability of viscous three-dimensional stratified Couette flow via dispersion and mixing

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arxiv 2402.15312 v1 pith:DRUUBU3I submitted 2024-02-23 math.AP physics.flu-dyn

Michele Coti Zelati , Augusto Del Zotto , Klaus Widmayer This is my paper · ORCID
classification math.APphysics.flu-dyn
keywords gravitycouetteflowmixingstabilitystratifiedviscousacts
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abstract

This article explores the stability of stratified Couette flow in the viscous $3d$ Boussinesq equations. In this system, mixing effects arise from the shearing background, and gravity acts as a restoring force leading to dispersive internal gravity waves. These mechanisms are of fundamentally different nature and relevant in complementary dynamical regimes. Our study combines them to establish a bound for the nonlinear transition threshold, which is quantitatively larger than the inverse Reynolds number $\nu$, and increases with stronger stratification resp. gravity.

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  1. Transition threshold of Couette flow for 2D Boussinesq equations

    math.AP 2025-06 accept novelty 6.0 of 10

    The stability threshold α=1/3 for 2D Boussinesq-Couette flow holds for unequal viscosity and thermal diffusivity, with H^{s+1/2} regularity for s>3/2.

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