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

摘要

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