Linear stability and stable modes of geostrophic fronts

A Rayleigh integral is used to prove that an unbounded geostrophic front of uniform potential vorticity is stable with respect to small perturbations of arbitrary wavelength. The ageostrophic theory developed in this study yields a stable, near-inertial, long trapped mode. Recent oceanic observations of the increase in the energy of the inertial peak in the vicinity of fronts support the existence of this inertial trapped mode. In addition the theory yields a geostrophic mode which is expected to become unstable when the potential vorticity is not uniform.