Linear inviscid damping and enhanced viscous dissipation of shear flows\n by using the conjugate operator method

2018/04/23 by Emmanuel Grenier, Grenier, Emmanuel, Toan T. Nguyen +5 · 2 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics and Turbulent Flows #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1804.08291

openalex publication_date 2018/04/23 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We study the large time behavior of solutions to two-dimensional Euler and\nNavier-Stokes equations linearized about shear flows of the mixing layer type\nin the unbounded channel mathbbT \× \ℝ. Under a simple\nspectral stability assumption on a self-adjoint operator, we prove a local form\nof the linear inviscid damping that is uniform with respect to small viscosity.\nWe also prove a local form of the enhanced viscous dissipation that takes place\nat times of order \ν^-1/3, \ν being the small viscosity. To prove these\nresults, we use a Hamiltonian approach, following the conjugate operator method\ndeveloped in the study of Schr "odinger operators, combined with a\nhypocoercivity argument to handle the viscous case.\n

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