Stratified convection with multiple states

Abstract

A simplified box model of the cooling of a salt-stratified ocean is analyzed analytically and numerically. A large isothermal basin of salt water has a layer of fresh water at the surface. Beside this is a small basin, cooled from above and connected to the large basin by horizontal tubes at the top, middle and bottom. For small cooling rate, fresh water enters the small basin, is cooled and leaves through the middle tube. For greater cooling rate, the fresh water leaves the small basin through the middle and bottom tube. If the top tube is smaller than the deeper tubes and the fresh water layer is sufficiently shallow, flow in the middle tube reverses at a critical cooling rate. In this case, a mixture of salt and fresh water is cooled and leaves the bottom tube. Increased cooling produces much greater flow rate; consequentially temperature increases rather than decreases in the small basin. A relaxation heat flow condition results in multiple equilibria. One of the stable modes has fresh surface water descending in the small basin and flowing out through the middle and bottom tube. The other has a greater rate of flow of both fresh and salty water (through the middle tube) into the basin with the flow of mixed salty water out of the bottom tube. Implications for deep convection in the ocean are discussed.