Convection induced by cooling at one side wall in two-dimensional non-rotating fluid —applicability to the deep Pacific circulation—

In recognition that similarity in the density balance leads to resemblance in circulation between the two-dimensional non-rotating and three-dimensional rotating systems which have similar density stratification, we investigate convection induced by cooling at one side wall and heating at the sea surface by using a two-dimensional non-rotating model as idealized representation for the deep Pacific circulation. In the model, various vertical profiles are taken for the side wall cooling, which are assumed to correspond to the density structure of the Anatarctic Circumpolar Current. In a small diffusivity range, two important features are found to be robust against change in the vertical profile of the side wall cooling. One is that the density stratification is horizontally almost uniform. The other is that the balance in the density equation between the vertical advection and the vertical diffusion holds in the interior. Consequently, the vertical density balance, together with the equation of continuity, determines the circulation pattern for the prescribed vertical profile of the side wall cooling. The multi-layered meridional flow, which is expected to exist in the deep Pacific, is shown to form for certain vertical profiles of the side wall cooling.