Flow estimate for the perpetual salt fountain

Abstract

STOMMEL et al. (1955) pointed out the perpetual salt founta as an interesting oceanographical curiosity that might possibly be used for pumping up nutrient-rich deep water to the surface for ocean farming applications. The fountain would work in a region where there is a salinity minimum below the warm surface layer of the ocean. STOMMEL et aL state, If a long tube were lowered from the surface to depth of low salinity water, and the deep water were slowly pumped to the surface through the tube, and the pump then disconnected, the water would continue to flow, by itself, forever. This remarkable phenomenon occurs because slow motion through the tube allows the water inside to attain the same temperature as the surrounding water. Its salinity, and hence density, is therefore less than that of its surroundings outside the tube, and hence the entire column of water inside the tube is buoyant with respect to the fluid outside at the same level. If the direction of pumping is reversed, so that the fluid initially goes downward, it will of course continue to flow downward forever on account of its excess in density over that of the water outside the tube. In order to estimate the rate of flow in the salt fountain, let us assume that a straight tube of length L extends slanting from the surface to a depth h in a horizontally stratified ocean. The vertical co-ordinate y is taken positive downward and zero at the surface, and 0 (y) and S (y) represent the temperature and salinity, respectively, of the ocean. Inside the tube the salinity is uniformly equal to S (h) for upward flow and the temperature is designated by 4' (Y), steady state being assumed. Taking the temperature inside the tube as a function only of y presupposes complete mixing in any horizontal layer and leads to a slight over-estimate of heat conduction and hence flow rate especially in the case of laminar flow, but this will not seriously affect the results. The water density inside and outside the tube is taken as a linear