Oceanic internal waves forced by a latitude-independent wind field tra
velling eastward at speed U is investigated, extending the hydrostatic
f-plane model of Kundu & Thomson (1985). The ocean has a well-mixed s
urface layer overlying a stratified interior with a depth-dependent bu
oyancy frequency N(z), and f can vary with latitude. Solutions are fou
nd 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 de
pth-independent N, the trailing waves are found to have large frequenc
ies, and the vertical acceleration partial derivative w/partial deriva
tive t is important (that is the dynamics are non-hydrostatic) if the
frequency omega is larger than a few times (Nf)1/2. The wake contains
waves associated with all vertical modes, in contrast to hydrostatic d
ynamics in which slowly moving line fronts do not generate trailing wa
ves of low-order modes. It is argued that slowly moving wind fields ca
n provide an explanation for the frequently observed broad peak in the
spectrum of vertical motion at a frequency somewhat smaller than N, a
nd of the vertical coherence of the associated waves in the upper ocea
n. 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 lambda(y) = 2pi/betat as predicted by D'Asaro (1989), in a
ddition to the zonal wavelength lambda(x) due to translation of the wi
nd. The two effects combine to cause a greater horizontal inhomogeneit
y, so that energy from the surface layer descends quickly, travelling
equatorward and downward. Since waves at any point arrive from differe
nt 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 vertic
ally 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-or
der modes after 30 days of integration. As U decreases, the larger ban
dwidth of frequency increases the intermittency, and the larger bandwi
dth of vertical wavenumber decreases the vertical correlation. A super
position 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 respons
ible for the generation of a large fraction of internal waves in the o
cean at all depths. The main effect of nonlinearity and mean flow may
be to shape the internal wave spectra to a omega-2 form.