Impact of reynolds number and slip/no-slip boundary condition on stratification in a two-dimensional boussinesq system

Abstract Buoyancy-driven fluid flows, such as tornadoes, hurricanes, and Rayleigh-Bénard convection (e.g., boiling water), exhibit a fundamental feature known as stratification: hotter (lighter) fluid rises while colder (heavier) fluid sinks. This process is described by the Boussinesq equations. Motivated by real-world applications, this paper explores via the Boussinesq equations how stratification is influenced by the Reynolds number and different boundary conditions (slip and no-slip). It is well known that the dynamics of fluids with no-slip boundary conditions is still not well understood in the high Reynolds number regime. First, we rigorously establish the large Reynolds number limit of viscous Boussinesq flow with an explicit convergence rate under the stress-free boundary condition. Second, we present a linear stability analysis for perturbations near the hydrostatic equilibrium, the stationary eventual temperature profile. Third, numerical simulations reveal the stratification is faster under the higher Reynolds numbers and the slip boundary condition. In particular, we observe the boundary plume eruptions that facilitate stratification and the seesaw-like oscillations for the large Reynolds numbers.