Baroclinic instability of buoyancy‐driven coastal density currents

Coastal density currents induced by buoyancy supply along an upper coast are studied in a three‐dimensional numerical model. Scaling analysis of the governing equations reveals that when the vertical eddy diffusivity is small, the horizontal Ekman number E h = A h ƒ/(g'Q e ) 2/3 is the crucial parameter determining the structures of the current, where A h is the horizontal eddy viscosity, Q e is the discharge rate per unit length along the coast, g ' is the reduced gravity constant, and ƒ is the Coriolis parameter. Based on numerical experiments with A h and Q e varied as external parameters, a critical E h ( E hc ) is found between 0.354 and 0.566. The density current develops unstably below this value. In cases where E h < E hc , excessive accumulation of fresh water causes sudden density changes near the coast, which eventually breaks down the quasi‐steady balance of the current and triggers small‐scale disturbances in the long‐shore direction. The large‐scale unstable waves induced by these disturbances have length scales of the order of 100 km and an e ‐folding time of several days. Study of the energetics revealed that the unstable waves grow via the baroclinic process, and as they develop into the finite‐amplitude stage, an energy transfer from the eddy field to the mean field accelerates the density current near the coast and induces an oppositely flowing mean flow offshore. These induced flows are important in the detachment process of the fully developed unstable eddies.