Convergence to Stratified Flow for an Inviscid 3D Boussinesq System

Abstract

We study the stability of special, stratified solutions of a 3d Boussinesq system describing an incompressible, inviscid 3d fluid with variable density (or temperature, depending on the context) under the effect of a uni-directional gravitational force. The behavior is shown to depend on the properties of an anisotropic dispersive operator with weak decay in time. However, the dispersive decay also depends on the strength of the gravity in the system and on the profile of the stratified solution, whose stability we study. We show that as the strength of the dispersion in the system tends to infinity, the 3d system of equations tends to a stratified system of 2d Euler equations with stratified density.

16 pages

References in corpus (2)

• Sharp decay estimates for an anisotropic linear semigroup and applications to the SQG and inviscid Boussinesq systems
• On the inviscid Boussinesq system with rough initial data

Cited by in corpus (8)

• On the Boussinesq equations with non-monotone temperature profiles
• On asymptotic stability of the 3D Boussinesq equations without thermal conduction
• Regularity results for viscous 3D Boussinesq temperature fronts
• Global Axisymmetric Euler Flows with Rotation
• Enhanced convergence rates and asymptotics for a dispersive Boussinesq-type system with large ill-prepared data
• Asymptotic stability of the 2D Boussinesq equations without thermal conduction
• On variable viscosity and enhanced dissipation
• Hidden asymptotics for the weak solutions of the strongly stratified Boussinesq system without rotation