2024/01/28 by Dongfen Bian, Bian, Dongfen, Emmanuel Grenier +1 · 1 citation
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Boundary (topology) #Boundary layer #Convection #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Geology #Geometry #Instability #Materials science #Mathematical analysis #Mathematics #Mechanics #Nusselt number #Petrology #Physics #Prandtl number #Reynolds number #Shear (geology) #Turbulence #Turbulent Prandtl number #Vibration and Dynamic Analysis
paper · pdf · doi:10.48550/arxiv.2401.15679
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2024/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to the study of the nonlinear instability of shear layers and of Prandtl's boundary layers, for the incompressible Navier Stokes equations. We prove that generic shear layers are nonlinearly unstable provided the Reynolds number is large enough, or equivalently provided the viscosity is small enough. We also prove that, generically, Prandtl's boundary layer analysis fails for initial data with Sobolev regularity. In both cases we give an accurate description of the first instability which arises. In some cases a secondary instability appears, leading to several sublayers and to an unexpected complexity of the flow.