Oceanic internal waves forced by a latitude-independent wind field travelling eastward at speed U is investigated, extending the hydrostatic f-plane model of Kundu & Thomson (1985). The ocean has a well-mixed surface layer overlying a stratified interior with a depth-dependent buoyancy frequency N(z), and f can vary with latitude. Solutions are found by decomposition into vertical normal modes. Problems discussed are (i) the response to a slowly moving line front, and (ii) the response in a variable f ocean.For the slowly moving line front assuming a depth-independent N, the trailing waves are found to have large frequencies, and the vertical acceleration ∂w/∂t is important (that is the dynamics are non-hydrostatic) if the frequency ω is larger than a few times (Nf)½. The wake contains waves associated with all vertical modes, in contrast to hydrostatic dynamics in which slowly moving line fronts do not generate trailing waves of low-order modes. It is argued that slowly moving wind fields can provide an explanation for the frequently observed broad peak in the spectrum of vertical motion at a frequency somewhat smaller than N, and of the vertical coherence of the associated waves in the upper ocean.To study lower-frequency internal waves, the hydrostatic constant-f model of Kundu & Thomson is extended to variable f. Various sections through such a flow clearly illustrate the development of a meridional wavelength λy = 2π/βt as predicted by D'Asaro (1989), in addition to the zonal wavelength λx due to translation of the wind. The two effects combine to cause a greater horizontal inhomogeneity, so that energy from the surface layer descends quickly, travelling equatorward and downward. Since waves at any point arrive from different latitudes, spectra no longer consist of discrete peaks but are more continuous and broader than those in the constant-f model. The waves are more intermittent because of the larger spectral width, and vertically less correlated in the thermocline because of a larger bandwidth of vertical modes. The vertical correlation in the deep ocean, however, is still high because the response is dominated by one or two low-order modes after 30 days of integration. As U decreases, the larger bandwidth of frequency increases the intermittency, and the larger bandwidth of vertical wavenumber decreases the vertical correlation. A superposition of travelling wind events intensifies the high-frequency end of the spectrum; a month-long travelling series of realistic strength can generate waves with amplitudes of order 4 cm/s in the deep ocean.It is suggested that propagating winds and linear dynamics are responsible for the generation of a large fraction of internal waves in the ocean at all depths. The main effect of nonlinearity and mean flow may be to shape the internal wave spectra to a ω-2 form.
Perturbative linearization of super-Yang-Mills theories in general gauges
