Oceanic Velocity Gradients

Abstract

This paper is a theoretical and experimental investigation of the nature of oceanic velocity gradients.Starting with the equations of motion, equations governing the dynamic behavior of velocity gradients alongwith a first integral are derived. These nine equations are partitioned differently than in a previous derivation by Carstoiu so as to simplify the physical interpretation. It is pointed out that solutions to the gradientequations overspecify the equations of motion. This leads to the development of compatibilityconditionsfor the solutions. These conditions generalize similar equations used in elasticity. The general gradientequations are applied to two-dimensional horizontal flow. This application demonstrates the role that thewind field and bottom topography can play in generating velocity gradients. Free solutions to the linearizedgradient equations are discussed. The solutions show that inertial gravitational waves can be present in thegradient fields. A summary of observations of velocity gradients is given. Although the observations weremade in different locales and by different procedures, the range in values is surprisingly small. These dataare also used to evaluate the relative sizes of some of the various terms in the gradient equations. The dominant terms are the ones involving Coriolis while the jS terms are the least significant. The data also suggestthat the geostrophic vorticity formula is not a reliable approximation in strong current regimes.