Vanishing transport noise enhances stability of stratified Couette flow in the 3D Boussinesq system

Source abstract

In this paper, we study the enhanced nonlinear stability of stably stratified Couette flow in the three-dimensional Boussinesq system driven by a common affine Stratonovich transport noise. Our main result shows that, for fixed $β>1/2$, suitably chosen noise amplitudes enlarge the range of perturbations for which we prove stability, even as they vanish with viscosity. For each fixed deterministic Sobolev perturbation satisfying the sufficient smallness conditions, the strong solution is global and obeys stability estimates on an event of prescribed high probability. No spatial localization or vanishing initial double means are required. The proof combines noise-induced mixing with coupled energy estimates to control nonlinear feedback and preserve the physical damping of the fast vertical velocity and temperature.