Chapter 6 - Double-diffusion convection

Abstract

In the oceans, the buoyancy of water is controlled by two contributions: temperature and salt. The two quantities are diffused by different diffusion rates. Thus it leads to a problem of double diffusion An interesting possibility arising from competing effects of temperature and salt to the buoyancy was originally pointed by Stommel et al. (1956). They made this point by an interesting experimental demonstration: prepare a container (a vertical glass tube) filled halfway with cold fresh water (and marked by a color of ink) overlaid by hot salty water in such manner that the density of water is stably stratified. Then, gently insert an (inner) glass tube into this container deeper, fill it with the lower-level colored water. Close the top of this glass tube, and lift it up slowly. If this is done slowly enough, the temperature of the inner glass tube is equilibrated with that of the container. Thus, this fresh water gains buoyancy and begins to spontaneously flow out from the tube, like a fountain. Stern (1960), in turn, realized that a similar phenomenon can also occur in natural ocean due to the fact that the thermal diffusion is much more efficient than the diffusion of salinity. Thus, imagine that a small deformation is generated over an interface between the bottom polar cold fresh water and the surface tropical salty hot water. The polar fresh water would be heated up rapidly, and the fresh polar water would begin to raise further due to a generated positive buoyancy. This instability leads to a generation of narrow non-salty tube like structures called “salt fingers”. An opposite situation can also be considered: the salty hot water overlaid by the fresh cold water. In this case, a parcel of a salty hot water can be displaced upwards: the parcel loses its heat rapidly by diffusion, and negative buoyancy due to salt brings it backwards towards the initial position. A systematic linear stability analysis over a full range of nondimensional parameter is presented by following Baines and Gill (1969).