GEOSTROPHIC ADJUSTMENT - FRONTOGENESIS AND ENERGY-CONVERSION

Nonlinear geostrophic adjustment is examined with a Boussinesq model. The motion is restricted to a two-dimensional channel in the horizonta l and vertical (x, z) plane; the fluid is in uniform rotation, is stab ly stratified, inviscid, and incompressible. The flows considered fall under two classes: zero and uniform potential vorticity flows. Steady geostrophic flow fields are determined from initial mass imbalances, represented by both symmetric and antisymmetric density anomalies that vary along the x axis. The distinguishing characteristic of these sol utions is the development of a front, defined as a zero-order disconti nuity in both density and geostrophic velocity at one or both vertical boundaries. Frontal formation occurs, as previously discovered by Ou for zero potential vorticity flow, when the initial horizontal density gradient is sufficiently large. The critical values are displayed for different cases in terms of the initial amplitude and initial scale o f the density anomaly. The conversion of initial potential energy into geostrophic kinetic Delta KE and potential Delta PE energies during a djustment is also derived. Ou's result that gamma = Delta KE/Delta PE = 1/2, independent of the initial scale is confirmed. It is shown, how ever, that gamma less than or equal to 1/2 for uniform potential vorti city flow. Large initial scales a(-1), large compared to the deformati on radius, have the largest values of gamma, approaching gamma = 1/2 a s a --> 0. This limit approaches the solution and energy ratio for zer o potential vorticity flow. The energy ratio associated with an antisy mmetric density anomaly is characterized by gamma --> 1/3 and a --> in finity: that is, the initial mass imbalance becomes a step function. I n the other case, when the initial disturbance is symmetric and vanish es with a --> infinity, gamma also vanishes. These results unify previ ous studies that have not provided the distinction between zero and un iform potential vorticity flows in examinations of the energy conversi on process. Yet the reason for this distinction has not been delineate d.