Abstract
For ocean currents with a very small aspect ratio, the geostrophic constraint (which balances pressure and the Coriolis force) is associated solely with the vertical component of Earth’s rotation. This component varies with latitude (and vanishes at the equator), and Fourier analysis is no longer sufficient to describe the waves.
Under the effect of differential rotation, geostrophic equilibrium gives way to wave-like dynamics, which are much slower than Poincaré waves and propagate from east to west. These waves, known as Rossby waves, play a key role in the persistence of large ocean vortices.
The mathematical analysis of Rossby waves is more complex because the wave operators have non-constant coefficients. The betaplan approximation (where the rotation vector is assumed to be a linear function of latitude) allows for an explicit calculation of the spectrum by reducing the problem to a harmonic oscillator and using the Hermite basis. In the general case, information is obtained only on the geometric propagation of the waves under the assumption of a scale separation between the wavelength and the characteristic scale of rotation variation.
