FEATURE DIFFERENTIAL FLUXES OF HEAT AND SALT: IMPLICATIONS FOR CIRCULATION AND ECOSYSTEM MODELING By Barry Ruddick What Are Differential Fluxes, and Conventional turbulent mixing, for eddy diffusivity for salt. Heat is also car- Why Might They Matter? which heat, salt, and density diffusivities ried downward by the fingers, but to a are equal and positive, reduces contrasts lesser extent because it is short-circuited THE SALTS DISSOLVED in the world's in density. In contrast, double diffusion by lateral diffusion. The heat contrast is oceans have profound effects, from the can increase density contrasts, and this is also reduced, but not to zero. Note that large scale, where evaporation-precipita- the key to understanding many of its the potential energy of the salt field is tion patterns have the opposite buoyancy oceanic consequences: the possibility of lowered, and that of the temperature field effect to thermal forcing, to the mi- mixing without an external source of ki- is raised. The surprising thing is discov- croscale, where molecular diffusion of netic energy, formation of regular series ered when we add up the contributions of heat is 70 times faster than that of salt. It of layers, the strange effects on vertical heat and salt to the density profiles--the has often been assumed that this differ- motion and stretching that modulate ther- ence can only matter at the smallest mohaline circulation, and even lateral scales, so that heat and salt are mixed in mixing over thousands of kilometers via exactly the same way by turbulence. thermohaline intrusions. However, the different molecular diffusiv- The best-known example of double- ities are the basis for a variety of phenom- diffusion is that of salt fingers, which ena known as double-diffusion, and these occur spontaneously when warm, salty can lead to important differences between water (green in Fig. 1, with the red dots heat and salt fluxes, with consequences representing heat) overlies cooler, fresher for much larger scales. In particular, water (blue in Fig. 1).* Consider what happens to a downward finger like per- Density fluxes the "wrong way": Kp < 0. turbation of the interface between the green and blue. The increased surface area offers an opportunity for enhanced Profiles S(z) T(z) p(z) Barry Ruddick, Department of Oceanography, heat exchange by molecular diffusion, Dalhousie University, Halifax, N.S., B3H 4Jl which cools off the warm, salty water. Canada. Since the molecular salt diffusivity is 70 times smaller, the "green finger" be- * Most of the Central Waters of the subtropical oceans is stratified in this sense, due to surface comes more dense, and therefore falls heating and evaporation. downward. The cooler, fresher blue Salt Flux Heat Flux Density Flux water receives the heat, becomes less ? This situation may be visualized surprisingly dense, and rises. The net effect is a Fig. 1: The mechanism of salt fingers. easily by filling a conveniently sized tank with room- growing field of nearly vertical fingers in Finger-like perturbations allow en- temperature fresh water, dissolving a pinch of floures- cein salts in a cup or two of water that is nearly boil- which vertical advection of salt by the hanced molecular diffusion of heat (red ing temperature. The hot flourescein mixture is than fingers is the most important feature. The dots) between warm salty water and cold carefully floated on the top of the fresh water by pour- vertical motion is enabled by the lateral fresh water. The warm salty water be- ing onto a piece of floating cardboard. As the top layer diffusion of heat between the fingers, but comes cooler and more dense, and sinks. cools by heat loss to the air, conditions become perfect requires the density difference of the salt The converse occurs to the cold fresh for the formation of relatively large heat-flourescein fingers, which can be made visible via a slit projector field to drive it.? water. The macroscale effect of salt fin- light source. I am indebted to two theoreticians, When we consider what happens in a gers is a downward flux of salt in the fin- George Veronis and Oliver Kerr, for pointing this out laboratory tank over time scales of -1 h, gers, and a smaller downward flux of to me. A movie of this and other laboratory demon- we find that the salt is carried downward heat. The density flux is also downward, strations can be found PO demos web page, accessable which enhances the density contrast be- through the Dalhousie Oceanography home page. by the fingers and the top-to-bottom con- <http:www.pbys.ocean.dal.ca/Da/Ocean_Home.html> trast is reduced to nearly zero--a positive tween layers. 122 OCEANOGRAPHY'gO1. 10, NO. 3°1997 density of the upper layer (which was in the region above the layer creates a lighter than the lower one to begin with) gradient region with diffusive sense strat- decreases, mostly due to loss of salt, and ification (warm salty underlying cooler the converse occurs to the lower layer. fresher). As the thermal boundary layer The flux of density is downward (i.e., up grows, the gradient region eventually be- the density gradient), which constitutes comes unstable, either to the overstable the net release of potential energy that oscillations or to Rayleigh convection. drives the salt fingering. The differences The region then breaks down and forms a in density are actually increased over new convecting layer, and molecular heat time--in other words, a negative eddy diffusion above this layer starts the diffusivity for density! process anew. The resulting series of lay- When warmer saltier water underlies Fig. 2: The self-propelled Cartesian ers separated by sharp interfaces is called cool, fresh water, as often occurs in sub- diver. a diffusive thermocline staircase, often polar waters, a different form of instabil- found in subpolar regions of the ocean, ity, called diffusive convection, can and in geothermally heated saline lakes. occur. Consider the motion of a small quantitatively about differential turbulent The heat and salt fluxes across the inter- fluid parcel (simulated by a Cartesian mixing, and so it won't be discussed fur- faces are thought to be via molecular dif- Diver in Fig. 2)~: in such a field. If the ther here. fusion, whereas the fluxes are carried diver is perturbed downward into warmer Are Double-Diffusive Fluxes Ever through the layers by convection (Fig. 3). water, it will gain heat from its surround- Large Enough to Matter? The downward salt flux by salt fingers ings and become lighter. This will make The phenomena of salt fingers and dif- can form layers in a similar fashion, by it rise in the density gradient to cooler fusive convection are together known as fluxing density into a stable stratification, levels, where it loses the heat, becomes "double-diffusive convection" (Turner and reducing the density gradient to the heavier, and falls. The time lag required 1973). When double-diffusion was first point of convection. for thermal diffusion changes an ordinary discovered, the fact that it is a form of It is possible (although very incom- buoyancy oscillation into an overstable "self-driven" turbulence that extracts the plete) to view layer formation in terms of growing oscillation, as was observed by potential energy of the salt field (in the a negative eddy diffusivity for density. Shirtcliffe (1967). The bobbing fluid par- case of fingers) or the temperature field (in The diffusion equation describes the evo- cel acts as a shuttle bus for the heat, the case of diffusive convection) caused lution of the density field, and with a pos- transferring it upward, while the small speculation that double-diffusive fluxes itive diffusivity K, tells us that small per- molecular diffusion of salt keeps the salt might be quite large. The quiet, efficient, turbations decay with increasing time: flux from becoming large. The net result and steady nature of double-diffusion is upward heat and salt fluxes (positive made oceanographers think that it could eddy diffusivities) and a downward den- 0t Oz ~zz be the "tortoise" compared with the ener- sity flux, again with a negative eddy dif- getic but intermittent "hare" of internal However, substituting -K for K is the fusivity for density. The result of this wave mixing. In this section we examine same as substituting -t for t. The diffu- growing oscillation can be a breakdown how double-diffusive fluxes are enhanced sion equation is therefore unstable for of smooth stratification into layers, as de- by the formation of layers, how laboratory negative K, so that perturbations will scribed in the next section. measurements have been successfully ver- grow with time. The upgradient fluxes Gargett (1988) has raised the possibil- ified in the ocean to quantify diffusive pile up into the perturbations and cause ity that the different molecular diffusivi- fluxes, and how the case seems to be them to grow. ties of heat and salt can result in different much more complicated for salt fingers. eddy diffusivities for heat and salt in stratified turbulence (hence the term "dif- Layer Formation \p(z) ferential fluxes" in the title of this arti- Huppert and Linden (1979) demon- S(z) T(z) \ Unstable cle). The resulting buoyancy flux and its strated one mechanism that causes a \Density convergence could lead to many of the smooth salt stratification to break down Gradient phenomena described below, even when into a series of well-mixed layers sepa- ~ T and S are stably stratified and there is rated by high-gradient "steps." This was no direct source of potential energy for important because continuous profiles of mixing. However, not much is known T and S from the newly invented Con- ductivity Temperature Depth profiler (CTD) often showed coincident steps and layers in both T and S that were dubbed $ The self-propelled diver is demonstrated on the PO demos web page, accessable through the "thermohaline staircases," and Huppert Dalhousie Oceanography home page <http://www.