A noneddy resolving, time-dependent, nonlinear theory of the large-scale ocean circulation is presented. The variability in this theory occurs as a response to variability in forcing. Baroclinic and barotropic evolution is computed using a two-layer, quasigeostrophic, wind-driven model. Both analytical and numerical solutions are obtained. Attention is focussed on the low-frequency, basin scale fluctuations of the wind. Based on these restrictions, the various modes of response are separated by means of a multiple time scale analysis. The barotropic response is found to be effectively instantaneous, and a relatively simple advection equation is shown to govern the baroclinic response. Analytical solutions of the baroclinic equation are obtained under the assumption that the time scales of the wind variability are short compared to the cross-basin baroclinic wave propagation time. Numerical solutions are obtained in more general cases. The baroclinic large-scale response is fundamentally nonlinear in that baroclinic waves propagate in the presence of the Sverdrup flow, which is itself time dependent. This nonlinearity results in at least two effects. First, the characteristics of wave propagation are significantly altered from pure zonality. This leads to the formation of homogenized zones, within which directly forced thermocline variability vanishes. Second, thermocline fluctuations are produced which have variance at frequencies other than those of the forcing. Consequently, forcing the model with an annually varying wind stress yields contributions to the thermocline spectrum at one year and all its superharmonics (i.e., 6 months, 4 months, 3 months, etc.). The amplitude of the superharmonics increases with distance from the eastern boundary. Mean baroclinic circulation on the scale of the thermocline waves is also found. The above features are predicted by analytical theory and confirmed by numerical experimentation. Observations of the geographical distribution of thermocline variability in the North Pacific and North Atlantic Oceans and of first mode variance at "inadmissible" planetary wave frequencies are discussed in light of the theory.
Dewar, William K.. 1989. "A nonlinear, time-dependent thermocline theory." Journal of Marine Research 47, (1). https://elischolar.library.yale.edu/journal_of_marine_research/1920