On the mathematical fluid dynamics of the atmospheric Walker circulation

Abstract

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