Dynamic Potential Vorticity Initialization and the Diagnosis of Mesoscale Motion

Abstract

Abstract A new method for diagnosing the balanced three-dimensional velocity from a given density field in mesoscale oceanic flows is described. The method is referred to as dynamic potential vorticity initialization (PVI) and is based on the idea of letting the inertia–gravity waves produced by the initially imbalanced mass density and velocity fields develop and evolve in time while the balanced components of these fields adjust during the diagnostic period to a prescribed initial potential vorticity (PV) field. Technically this is achieved first by calculating the prescribed PV field from given density and geostrophic velocity fields; then the PV anomaly is multiplied by a simple time-dependent ramp function, initially zero but tending to unity over the diagnostic period. In this way, the PV anomaly builds up to the prescribed anomaly. During this time, the full three-dimensional primitive equations—except for the PV equation—are integrated for several inertial periods. At the end of the diagnostic period the density and velocity fields are found to adjust to the prescribed PV field and the approximate balanced vortical motion is obtained. This adjustment involves the generation and propagation of fast, small-amplitude inertia–gravity waves, which appear to have negligible impact on the final near-balanced motion. Several practical applications of this method are illustrated. The highly nonlinear, complex breakup of baroclinically unstable currents into eddies, fronts, and filamentary structures is examined. The capability of the method to generate the balanced three-dimensional motion is measured by analyzing the ageostrophic horizontal and vertical velocity—the latter is the velocity component most sensitive to initialization, and one for which a quasigeostrophic diagnostic solution is available for comparison purposes. The authors find that the diagnosed fields are closer to the actual fields than are either the geostrophic or the quasigeostrophic approximations. Dynamic PV initialization thus appears to be a promising way of improving the diagnosis of balanced mesoscale motions.