Low Rossby limiting dynamics for stably stratified flow with Finite Froude number

Details Low Rossby limiting dynamics for stably stratified flow with Finite Froude number Low Rossby limiting dynamics for stably stratified flow with Finite Froude number

2011-02-08

arxiv.org/abs/1102.1744v1

Nonlinear Sciences

Chaotic Dynamics

Accepted to Journal of Fluid Mechanics, 35 pages, 6 figures

Scientific paper

In this paper we explore the fast rotation, nonhydrostatic limit of the rotating and stratified Boussinesq equations. We derive new reduced equations for the slow dynamics that describe Taylor-Proudman flows. One new aspect of the dynamics is a decoupling of the horizontal kinetic energy, described by 2D Navier-Stokes, from new dynamics that describe the coupling of vertical kinetic energy and buoyancy. We support the theory with high resolution numerical simulations of the full Boussinesq equations that, in this limit, reveal the spontaneous formation of Taylor-Proudman columns and their dynamics.

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