On the mathematical fluid dynamics of the atmospheric Walker circulation

Abstract Starting from the general, governing equations for a viscous, compressible fluid, with an associated description of its thermodynamics, we outline asymptotic derivation based on thin-shell approximation. [The details appear in another publication.] This produces reduced system which retain all dynamics and thermodynamics steady atmosphere, approximation alone being basis construction solution. The leading order describes background state next provides simple set that can be used to investigate, example, Walker circulation, particular atmospheric flow is restricted neighbourhood Equator across Pacific Ocean. Our formulation this problem shows, explicitly detail, how pressure temperature gradients azimuthal direction drive circulation; extends usual physical arguments describe circulation. An initial investigation highlights rȏle variable eddy viscosity then, these observations, solution obtained detail velocity fields cell. In particular, present example profile streamlines along bounded above by tropopause. Further circulation are given, together identification heat sources motion. Finally, comment changes pattern arise during El Niño event.