Double diffusive convection

Double-diffusive convection is an important fluid dynamics topic that describes a form of convection driven by two different density gradients which have different rates of diffusion.^[1]

Convection in fluids is driven by density variation within them. These density variations may be caused by gradients in the composition of the fluid, or by differences in temperature (through thermal expansion). Thermal and compositional gradients can often diffuse with time, reducing their ability to drive the convection, and requiring that gradients in other regions of the flow exist in order for the convection to continue. A common example of double diffusive convection is in oceanography, where heat and salt concentrations exist with different gradients and diffuse at differing rates. An example that affects both of these variables is the input of cold freshwater from an iceberg.

Double diffusive convection is important in understanding the evolution of a number of systems that have multiple causes for density variations. These include convection in the Earth's oceans (as mentioned above), in magma chambers,^[2] and in the sun (where temperature and Helium diffuse at differing rates).

Two quite different types of fluid motion exist - and therefore are classified accordingly - depending on whether the stable stratification is provided by the density-affecting component with the lowest or the highest molecular diffusivity. If the stratification is provided by the component with the lower molecular diffusivity (for example in case of a stable salt-stratified ocean perturbed by a thermal gradient due to an iceberg), the stratification is called to be of "diffusive" type (see external link below), otherwise it is of "finger" type, occurring frequently in oceanographic studies as salt-fingers.^[3] These long fingers of rising and sinking water occur when hot saline water lies over cold fresh water of a higher density. A perturbation to the surface of hot salty water results in an element of hot salty water surrounded by cold fresh water. This element loses its heat more rapidly than its salinity because the diffusion of heat is faster than of salt; this is analogous to the way in which just unstirred coffee goes cold before the sugar has diffused to the top. Because the water becomes cooler but remains salty, it becomes denser than the fluid layer beneath it. This makes the perturbation grow and causes the downward extension of a salt finger. As this finger grows, additional thermal diffusion accelerates this effect.

See also

• Rayleigh number
• Prandtl number

References

1. ^ Mojtabi, A.; Charrier-Mojtabi, M.-C. (2000). "13. Double-Diffusive Convection in Porous Media". In Kambiz Vafai. Handbook of porous media. New York: Dekker. ISBN 9780824788865. http://books.google.com/?id=Oi3VWK0773MC&pg=PA559&dq=double+diffusive+convection&q=double%20diffusive%20convection. 
2. ^ Huppert, H E; Sparks, R S J (1984). "Double-Diffusive Convection Due to Crystallization in Magmas". Annual Review of Earth and Planetary Sciences 12 (1): 11. Bibcode 1984AREPS..12...11H. doi:10.1146/annurev.ea.12.050184.000303. 
3. ^ Stern, Melvin E. (1969). "Collective instability of salt fingers". Journal of Fluid Mechanics 35 (02): 209. Bibcode 1969JFM....35..209S. doi:10.1017/S0022112069001066. 

• Huppert, Herbert E.; Turner, J. Stewart (2006). "Double-diffusive convection". Journal of Fluid Mechanics 106: 299. Bibcode 1981JFM...106..299H. doi:10.1017/S0022112081001614. 

External links

• Double Diffusive Convection
• Oceanic Double-diffusion: Introduction
• Double Diffusion in Oceanography
• Diffusive-mode Double Diffusive Convection, Stability and Density-Driven Flows
• Stockman, H.W; Li, C.; Cooper, C.; 1997. Practical application of lattice-gas and lattice Boltzmann methods to dispersion problems. InterJournal of Complex Systems, manuscript no. 90.