Instabilities of a two-layer coupled front

We consider the linear instability of a two-layer fluid, whose mean state consists of a motionless lower layer and a surface layer confined between two parallel fronts. An inverted form occurs at many locations in the deep ocean, notably in the Denmark Strait overflow. Because of the vanishing surface layer depth, quasigeostrophy cannot hold, and primitive equations must be used. Two modes of long wave instability are found. The first, valid for intermediate values of the ratio of total fluid depth to surface layer depth, is analogous to a mode found for an isolated front in an otherwise similar geometry. The second mode is the extension to two layers of the mode already discovered for the same geometry but with an infinitely deep lower layer. Numerical extensions of these long wave results to shorter waves show that the former mode would be observed in practice. The theory is applied to laboratory results, and is in excellent agreement with observations.