The spectra of the oscillating shear flows

2009/09/18 by С. А. Гуда, Sergey Guda, Guda, Sergey
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #physics.flu-dyn

paper · pdf · doi:10.48550/arxiv.0909.3436

10 pages, 4 figures

arxiv created 2009/09/18 · openalex publication_date 2009/09/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the spectral problems for the spatially periodic flows of inviscid incompressible fluid. The basic flows under consideration are the shear flows whose profiles oscillate on high frequencies. For such flows, we present asymptotic expansions of the unstable eigenvalues in the case when the limit spectral problem has multiple eigenvalues.

Related

• Spectral instability of symmetric shear flows in a two-dimensional channel
• Bifurcations of viscous boundary layers in the half space
• Bifurcations of viscous shear flows in a strip
• The transition to instability for stable shear flows in inviscid fluids
• The unstable spectrum of the Navier-Stokes operator in the limit of vanishing viscosity