Horizontal divergence, acceleration and curvature change, a diagnostic equation with applications

The horizontal divergence of an accelerating flow is discussed in the contexts of meandering currents and the formation of eddy-rings. The purpose is to help discern areas of upwelling and other dynamical features. Two interrelated hypotheses, representing two meso-scale versions of the turning vorticity equation (Chew, 1975), are formulated with the help of the Florida Current data of Schmitz (1969). The first is a generalization of the pioneer work of Bjerknes (1937) on the relation between horizontal divergence and curvature vorticity change. Along a meandering flow in the northern hemisphere, and away from the equator, the hypothesis predicts horizontal convergence where there is a rapid increase in centripetal acceleration, and horizontal divergence where the increase is in centrifugal force. In particular, in a meandering surface flow with a succession of cyclonic and anticyclonic turns, the hypothesis predicts a series of alternating upwelling and downwelling tongues.

The second hypothesis illuminates a study by Fuglister (1972) of the role of vertical motion in the formation and evolution of eddy-rings. Eddies, as cut-off meanders, are initially irregular in shape. According to this hypothesis, an eddy evolving into a ring with circular symmetry is entering a stage of non-divergence and hence a stage of stability.