Analytical Solutions for Circular Eddies of the Reduced-Gravity, Shallow-Water Equations

Abstract

New analytical, circular eddy solutions of the nonlinear, reduced-gravity, shallow-water equations in a rotating system are presented. While previous analytical solutions were limited to the description of pulsons, which are oscillating, frontal, warm-core eddies with paraboloidic shape and linear velocity components, the new solutions describe more general radial structures of eddy shape and azimuthal velocity. In particular, the new solutions, which contain as a subset the circular pulson solution, also allow for the description of circular, frontal, warm-core eddies with small azimuthal velocities at their periphery and/or with motionless cores, which are frequently observed characteristics of warm-core eddies in the World Ocean.