The Nonlinear Stability of Density Fronts in the Ocean

Density and temeprature fronts are common features of the ocean. However, frontal dynamics are not quasi-geostrophic because the isopycnal deflections associated with fronts are large compared with the scale height of the hydrostatic geopotential. The frontal geostrophic model, developed by Cushman-Roisin et al.(1992) is generally used fro describing the dynamics of surface-density ocean fronts, whereas the two-layer frontal geostrophic model is used for fronts on a sloping continental shelf. This paper investigates the baroclinic nonlinear stability of surface-density ocean fronts and fronts on a sloping continental shelf using the two-layer frontal geostrophic model mentioned above. Nonlinear stability criteria for the two kinds of fronts are obtained using Arnol'd's (1965; 1969) variational principle and a prior estimate method. This is the first time a nonlinear stability criterion for surface ocean fronts has been established, furthermore, the results obtained for fronts on a sloping bottom are superior to any previous ones.