A class of layered mesoscale models is presented, relevant for oceanographic studies of baroclinic frontal instability and propagation of coherent structures. The models allow for finite thickness variations in the frontal layer and continuous stratification in the ambient layer(s). The governing equations are derived in a formal asymptotic reduction of the primitive equations, assuming subinertial dynamics and leading-order geostrophy. The resulting systems are not quasigeostrophic (QG), however, since they allow for vanishing thickness of the frontal layer.

The linear stability problem is solved for idealized and realistic steady basic states, in the presence of linearly sloping topography. Linear stability criteria suggest that introduction of ambient stratification reduces the size of the stable region in parameter space. Indeed, perturbation growth rates associated with the linearized equations are shown to increase with the stratification number, in agreement with previous laboratory experiments. For monotonic frontal profiles, increasing bottom topography tends to be a stabilizing influence when the topographic and frontal thickness gradients are of opposite sign. This trend is consistent with traditional QG stability results, however, the present models are better suited than QG theory to the description of true fronts, which intersect the topography or fluid surface. Dependence of the instability characteristics on the width and relative thickness of the associated current is also investigated.

Oceanographic and experimental applications of the frontal models are discussed, with particular emphasis on instability of the Denmark Strait Overflow and laboratory investigations of axisymmetric buoyancy fronts. Long-term numerical integration of the models demonstrates plume formation and ejection of coherent vortex features, in agreement with similar primitive-equation studies of coastal processes. In contrast to some previous studies, however, irregularities in the coastline or topography are not necessary for the onset of instability.