A Non-Archimedean Approach to the Equations of Convection Dynamics

Abstract

A new formulation of the momentum equations in convection dynamics is presented, dividing the pressure into separate hydrostatic and dynamic components. In this formulation, termed non-Archimedean, convection is envisaged as developing through the horizontal gradient of a time-dependent hydrostatic pressure, rather than the customary buoyancy. It is shown that in the vertical momentum equation there is only one forcing term, viz., the vertical gradient of the dynamic pressure rather than the customary combination of perturbation-pressure gradient and buoyancy force. In the multi-dimensional case, the new formulation leaves the vorticity form of the momentum equation unchanged from that obtained in the customary approach. A diagnostic equation is presented for computing the dynamic pressure component.