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 environmental stratification. An internal front is shown to represent the equilibrium flow structure in the region initially occupied by the saturated parcel.
The model predicts mesoscale regions of descent below the tens. The fluid within the lens has zero absolute vorticity whereas strong cyclonic vorticity exists above the internal front. Solutions are obtained for undisturbed states of uniform potential vorticity either at rest or uniformly sheared with constant horizontal temperature gradient. It is inferred that moist boundary layer air ahead of some cold fronts may slantwise convect in narrow plumes just above the frontal surface and in the process greatly accelerate the formation of a lower tropospheric frontal discontinuity line compared to the dry, geostrophic deformation problem. The model may also be relevant to the dynamical forcing of mesoscale downdrafts associated with deep cumulonimbus convection—particularly when organized into bands (e.g., the convective polar airstream trough).
