An Expression for Effective Buoyancy in Surroundings with Horizontal Density Gradients

Abstract

An expression is obtained for effective buoyancy per unit volume in inviscid anelastic flow with surrounding horizontal density variations. Effective buoyancy is defined here as the statically forced part of the locally nonhydrostatic, upward pressure-gradient force because this is the part of the net vertical force that is both absolute (i.e., independent of an arbitrary base state) and dependent solely on variations in the specific weight of the air?hydrometeor mixture. For the case where the domain is the half space z > 0 above flat ground, effective buoyancy ?(x) at a given field point x is given by ?(x) = ?∞?∞ ?∞?∞ ?∞?∞ [g2H?T(x?)]/(4π|x ? x?|) dx? d? d?, where g?T is the total weight of air and hydrometeors per unit volume, the x? ≡ (x?, ?, ?) are source points, 2H is the horizontal Laplacian with respect to x?, and 2H?T(x?, ?, ??) ≡ ?2H?T(x?, ?, ?).