The Wavenumber–Frequency Content of Resonantly Excited Equatorial Waves

Abstract The theoretical resonant excitation of equatorial inertia–gravity waves and mixed Rossby–gravity waves is examined. Contrary to occasionally published expectations, solutions show that winds that are broadband in both zonal wavenumber and frequency do not in general produce peaks in the wavenumber–frequency spectrum of sea surface height (SSH) at wavenumbers associated with vanishing zonal group velocity. Excitation of total wave energy in inertia–gravity modes by broadband zonal winds is virtually wavenumber independent when the meridional structure of the winds does not impose a bias toward negative or positive zonal wavenumbers. With increasing wavenumber magnitude |k|, inertia–gravity waves asymptote toward zonally propagating pure gravity waves, in which the magnitude of meridional velocity υ becomes progressively smaller relative to the magnitude of zonal velocity u and pressure p. When the total wave energy is independent of wavenumber, this effect produces a peak in |υ|2 near the wavenumber where group velocity vanishes, but a trough in |p|2 (or SSH variance). Another consequence of the shift toward pure gravity wave structure is that broadband meridional winds excite inertia–gravity modes progressively less efficiently as |k| increases and υ becomes less important to the wave structure. Broadband meridional winds produce a low-wavenumber peak in total wave energy leading to a subtle elevation of |p|2 at low wavenumbers, but this is due entirely to the decrease in the forcing efficiency of meridional winds with increasing |k|, rather than to the vanishing of the group velocity. Physical conditions that might alter the above conclusions are discussed.