Solution of the linear thermocline equations driven by wind stress and thermohaline forcing

Abstract

In this paper, new steady‐state solutions of the linearized thermocline equations satisfying prescribed fluxes of heat and salt at the base of the surface Ekman layer, are presented for a semi‐infinite ocean of constant depth. A decomposition into vertical modes is used to solve the problem. The solution is first determined in terms of a derivative of the unknown density at the surface and this derivative is then determined from an integral equation arising from applying the surface thermohaline boundary conditions. Solutions forced by wind stress alone, and by wind stress and thermohaline forcing are considered. The wind‐driven solution exhibits a temperature field with many realistic features, such as largest meridional gradients in the sub‐polar gyre, and the latitudinal spreading of isotherms towards the eastern boundary. The wind‐driven salinity field increases towards the poles, contrary to the observed annual mean salinity field. The stability of the sub‐tropical gyre is enhanced, whilst the sub‐polar gyre is de‐stabilized. With the addition of the thermohaline forcing the deficiencies of the salinity field associated with the wind‐driven solution are largely corrected, whilst the solution retains a reasonable representation of the climatological temperature field. Temperature and salinity anomaly fields relative to the Levitus climatology, calculated from the Met. Office Forecasting Ocean Assimilation Model, are shown to be qualitatively similar to the anomaly fields derviedfrom the model discussed in this paper. This result serves to underline the message that the combination of wind and surface buoyancy forcing are essential when modelling the large‐scale temperature and salinity fields using the thermocline equations.