Impact of the SST–wind stress coupling on the dynamics and stability of ocean current inside and outside SST frontal zones

Abstract

The robust relationship between the sea surface temperature (SST) and wind stress is used to examine the impact of the SST–wind stress coupling on the dynamics and stability of ocean currents inside and outside SST frontal zones based on the wave-activity equations for the semi-geostrophic (SG) and quasi-geostrophic (QG) models.The results show that the coupling has fundamentally different effects on the ocean current inside and outside SST fronts. Outside the frontal zones the coupling only redistributes the surface temperature perturbation but does not change the total pseudo-momentum and pseudo-energy. Therefore the QG pseudo-momentum and pseudo-energy are still conserved under the impact of the coupling, although the pseudo-energy is slightly modified. The stability conditions, more general than the ones obtained by Spall (2007), are obtained from the conservation of the wave-activities. Inside the SST frontal zones, however, the coupling, along with the nonlinear Ekman effect, destroys the conservation of the SG pseudo-momentum and pseudo-energy. Therefore no stability condition is available, indicating that the current inside the frontal zone may be unstabilized by the coupling or nonlinear Ekman transport effect. It is also found that different dynamical features inside and outside frontal zones cause the different modulation of the coupling strength. The drastic differences are closely associated with the different assumptions underlying QG and SG dynamics about the density/temperature gradient and isotropy of motions.The different impacts of the coupling are further illustrated analytically by comparing the normal mode growth rates for the SG and QG Eady models. The comparisons show that ocean current outside the SST frontal zone is stable under any normal mode disturbances when the coupling factor σQG<−U¯s where U¯s is the basic zonal flow at the surface, but it is unstable under certain normal modes when σQG>−U¯s. However the ocean current inside the frontal zone is always unstable under the influence of the SST–wind coupling or nonlinear Ekman effect. It is found that the negative coupling (when surface wind blows from cold water to warm water) tends to generate strong instability. In addition, the growing/decaying normal modes are non-dispersive and propagate only in one direction (eastward) outside the frontal zone, but they are dispersive and can propagate in both directions inside frontal zone.