INSTABILITY OF DENSITY FRONTS IN LAYER AND CONTINUOUSLY STRATIFIED MODELS

The instability of density fronts is investigated as a possible genera tion mechanism for the small-scale, wavelike patterns that are commonl y observed along upwelling fronts and filaments. Unstable-wave solutio ns are obtained in two linearized models: a 1 1/2-layer model, and a c ontinuously stratified model confined to the surface region of the oce an. In both systems the thickness of the upper region is held constant for the background state, the front being specified by allowing the t emperature field T within the region to vary zonally. The background s tate in the layer model consists of vertically oriented isotherms asso ciated with a depth-independent current, whereas in the continuously s tratified model it consists of steeply tilted isotherms and a vertical ly sheared current. Solutions are found both when the background veloc ity field V is zonally uniform and when it is zonally sheared. When V is weak and zonally uniform, approximate solutions are derived analyti cally for both models that are valid for low-frequency, low-wavenumber waves. These solutions demonstrate that the unstable waves in the two systems are dynamically related, both being representations of ageost rophic baroclinic instability. Numerical solutions corroborate the ana lytic results and extend their range of validity. Energetics analyses confirm that the energy source for the waves is the background potenti al energy associated with the zonally varying T field. When V is a zon ally sheared jet, the models still exhibit a band of instability, whic h is identifiable with ageostrophic baroclinic instability. The most u nstable wave in this band has a short wavelength, a frequency near f/2 , and a rapid growth rate consistent with observed features. The layer model also has a band of larger-scale waves that is a mixed, baroclin ic-barotropic instability; however, for a typical frontal structure th is band is weaker than the baroclinic band.