A numerical study of low reynolds number 2-dimensional convective adjustment

Abstract

Abstract We use a 2-dimensional non-hydrostatic model on the vertical plane to examine the nature of convective adjustment. In the first part of the study, we investigate the mixing of an initial unstably stratified 2-layer fluid with molecular viscosities. The linear growth rates compare well to those obtained using an analytic model. The stratification of the convectively adjusted state is sensitive to the Prandtl number (Pr, the ratio of the eddy viscosity to thermal diffusivity). This is important as the instantaneous convective adjustment used in coarse resolution ocean circulation models corresponds to Pr→0, while the case of immiscible fluids corresponds to the limit of large Pr. Mixing in the ocean as well as in our numerical model are both characterized by a finite value of Pr. In the second part of the study, we scale up to ocean scales with a more realistic surface forcing and turbulent viscosities. The implications of our results for instantaneous convective adjustment are discussed.