A class of layered mesoscale models is presented, relevant for oceanographic studies of baroclinicfrontal instabilities and propagation of coherent structures. The models allow for finite thicknessvariations in the frontal layer and continuous stratification in the ambient layer(s). The governingequations are derived in a formal asymptotic reduction of the primitive equations, assumingsubinertial 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 thepresence of linearly sloping topography. Linear stability criteria suggest that introduction of ambientstratification reduces the size of the stable region of parameter space. Indeed, perturbation growthrates associated with the linearized equations are shown to increase with the stratification number,in agreement with previous laboratory experiments. For monotonic frontal profiles, the bottomtopography tends to be a stabilizing influence when the interfacial and bottom slopes are of thesame sign. This trend is consistent with traditional QG stability results, however, the present modelsare better suited than QG theory to the description of true fronts, which intersect the topography orfluid surface. Dependence of the instability characteristics on the width and relative thickness of theassociated current is also investigated.
Oceanographic and experimental applications of the frontal models are discussed, withparticular emphasis on instability of the Denmark Strait Overflow and laboratory investigations ofaxisymmetric buoyancy fronts. Long-term numerical integration of the models demonstrates plumeformation and ejection of coherent vortex features, in agreement with similar primitive-equationstudies of coastal processes. In contrast to some previous studies, however, irregularities in thecoastline or topography are not necessary for the onset of instability. |
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