Energetics of Linear Geostrophic Adjustment

Abstract

Abstract The potential and kinetic energy spectra following geostrophic adjustment of a barotropic fluid are determined as functions of the spectrum of arbitrary initial sea level or velocity. Remarkably, the functional dependences between initial and final spectra, and the general conclusions reached are independent of whether spatial variation in the initial field is permitted in either one or both horizontal directions. For initial sea level displacements, the potential and kinetic energy spectra obtained for the adjusted state are respectively shown to be low- and band-pass filtered versions of the initial potential energy spectrum. The maximum kinetic energy, ΔE, is obtained for initial displacements of wavelength k0−1 equal to the deformation radius, a, and is equal to 1/3 of the change in potential energy, ΔP, from initial to adjusted state. The value of ⅓ for ΔE/ΔP is also found for steplike initial displacements for which no horizontal scale is defined. However, in general ΔE/ΔP is shown to be de...