Enhanced dissipation, Taylor dispersion, and inviscid damping of Couette flow in the Boussinesq system on the plane
Year: 2025
Type: article
Abstract: We consider the quantitative asymptotic stability of the stably stratified Couette flow solution to the 2D fully dissipative nonlinear Boussinesq system on R 2 with large Richardson number R > 1 / 4 , viscosity ν and density dissipation κ. For an initial perturbation ( ω in , θ in ) of size μ 1 / 2 + ϵ in a low-order anisotropic Sobolev space, for µ roughly min ( ν , κ ) ( 1 − O ( 1 / R ) ) and ν, κ comparable, we demonstrate asymptotic stability with explicit enhanced dissipation and Taylor dispersion rates of decay. We also give inviscid damping estimates on the velocity u and the density θ. This is the first result of its type for the Boussinesq system on the fully unbounded domain R 2 . We also translate some known linear results from T × R to R 2 , and we give an alternative theorem for the nonlinear result.
Source: Nonlinearity
Author: Ryan Arbon
Institution: University of California, Los Angeles
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,325
Funder: National Science Foundation
OpenAlex ID: W4415114668