The energy conversion ratio, γ, is shown to be bounded below by 0 and above by 1/2 in the two-dimensional linear geostrophic adjustment of a continuously stably stratified, incompressible, inviscid non-Boussinesq fluid. ''Two-dimensional'' refers to problems in which the initial isopycnal displacement field is an arbitrary function of the vertical (parallel to the rotation axis) and a single horizontal coordinate. By using Fourier analysis techniques, the paper also identified classes of initial isopycnal displacement profiles for which the adjustment process leads to γ > 1/3. Finally, an expression for γ is derived when the initial isopycnal displacement profile is three dimensional.
Grimshaw, Roger H., Andrew J. Willmott, and Peter D. Killworth. 1998. "Energetics of linear geostrophic adjustment in stratified rotating fluids." Journal of Marine Research 56, (6). https://elischolar.library.yale.edu/journal_of_marine_research/2304