Balanced Flow States Resulting from Penetrative, Slantwise Convection

Abstract Analytic solutions representing rectilinear flow in geostrophic and hydrostatic balance are constructed using the conformal mapping technique of Gill. Two types of mapping are used to characterize the state of a fluid after a parcel convects to a position of neutral buoyancy. The first mapping corresponds to the homogeneous intrusion in a rotating, stratified fluid studied by Gill. The second mapping describes an internal discontinuity of finite length, embedded in a fluid of uniform potential vorticity. In the idealized physical problem represented by these conformal transformations, an elliptical region of undisturbed fluid is considered to be “saturated” and in a state of unstable equilibrium. On perturbing the system, the saturated parcel convects to a new level distant from its initial position and is rendered homogeneous in absolute momentum and potential temperature by internal mixing. The resulting equilibrium configuration involves a two-dimensional fluid lens, which 1ocally distorts the...