Coral reefs and vortices

It seems that counter-rotating vortices are everywhere. The September 2014 edition of the Proceedings of the (US) National Academy of Sciences has published a fascinating study which reveals that coral reefs actively create quasi-steady arrays of counter-rotating vortices.

Corals exist in a symbiotic relationship with algae, which live within the tissue of the coral, and photosynthesise the organic carbon used by the corals to build their calcium-carbonate skeletons. In return, the corals have to provide nutrients for the algae, and remove the excess oxygen produced by photosynthesis.

Until now, it's been assumed that corals were dependent upon molecular diffusion alone to achieve the necessary mass transport. A concentration boundary layer exists at the surface of the coral: the concentration of a molecular species produced by the coral (such as molecular oxygen, O₂) is highest at the surface of the coral, and a concentration gradient exists in the direction normal to the surface of the coral until the edge of the boundary layer is reached, where the concentration matches the ambient level. This concentration gradient drives outward molecular diffusion.

In the presence of an ambient flow, the boundary layer becomes thinner, increasing the steepness of the concentration gradient, and thereby enhancing the mass transfer rate. However, many parts of many coral reefs often experience periods of very low ambient flow, and there was evidence to believe that mass transfer rates were actually higher than could be explained by the ambient flow conditions. (Here there is a similarity with heat transfer within a bundle of nuclear fuel rods, where the rate of thermal mixing was higher than could be explained by turbulent diffusion and thermal conduction alone).

The research just published has revealed that the cilia (tiny hairlike entities) on the surface of the coral polyps are able to create a pattern of counter-rotating vortices which enhance mass transfer rates even in conditions of stagnant ambient flow (see image below). The counter-rotating vortices seem to be produced by the coordinated sweeping motion of the cilia, with one group of cilia sweeping in direction, and another group sweeping in the opposite direction.

The research revealed that the vortices are able to transport dissolved molecules by ~1mm in ~1sec, under conditions which would otherwise require ~1000secs to traverse the same distance by molecular diffusion alone.

It was also found that the location and shape of one such vortex was stable over the 90min period under which the concentration levels of oxygen were measured. The latter produced the image below, showing that one side of the vortex, flowing towards the surface of the coral, had ambient levels of oxygen, whilst the other side of the same vortex transports the oxygenated water away.