How Swimmers Mix the Oceans

The mechanical energy added to the oceans by the wind and tides each amounts to some 10^12 Watts. That kind of power has a huge effect on the way that warm, cold, salty and fresh waters mix and climatologists are well aware of its importance in climate change models.

But what of living creatures in the oceans? Can the mechanical energy they produce have a significant effect on mixing? Oceanographers have pondered this question for over 40 years. Add up the amount of mechanical energy produced by the biomass in the oceans and you get a figure of just under 10^12 W.

By assuming that all this energy is delivered to the top 3 km of ocean, swimmers generate 0.2cm^-2/s of effective diffusivity which is about 1000 times more than the molecular value for heat.

That’s an enormous amount, comparable to the wind and the tides. It means that roughly a third of all ocean mixing is caused by the swimming motion of ocean-going creatures.

But these are very rough “top down” calculations which raises the question of how accurate they can be.

One way to find out is to compare the numbers with the results of another approach: to calculate the effect of a single swimmer on a test particle and then multiply.

Today, Jean-Luc Thiffeault at the University of Wisconsin and Stephen Childress at the Courant Institute of Mathematical Sciences in New York take a shot at this “bottom up” approach. They model the mixing caused by an individual swimmer by assuming it to be a cylinder or sphere and then calculating its effect on a test particle as it passes by.

They then repeat this calculation many thousands of times and watching what happens to the test particle. The result is an estimate of the effective diffusivity of the process which can be compared to the diffisivity calculated by the earlier “top down” approach

The results suggest that the question of biological mixing is far more complex than the earlier top-down approaches indicate. For example, Thiffeault and Childress calculate the effect of a 1cm sphere moving at about 1cm/s (their mathematical model of a krill) on a test particle and say this process has an effective diffusivity of x10^-5 cm^2/s. In other words, a couple of orders of magnitude less than is thermal molecular value and many orders of magnitude less than the top down value..

If that were the final conclusion, then this model would severely challenge the notion that swimmers significantly contribute to mixing in the oceans. But it is not.

Thiffeault and Childress point out that the result is hugely sensitive to small changes in the model, for example to the way the swimming “sphere” interacts and displaces a test particle. The model does not take into account the wake of the swimmer nor the possibility that swimmers congregate in shoals which would certainly increase the effective diffusivity. Together these effects could increase the effective diffusivity by many orders of magnitude.

But there are also factors such as the streamlined shape of many swimmers which minimises turbulence and could reduce effective diffusivity.

Thiffeault and Childress say all of these factors and others need to be taken into account in future models. It’s an ambitious task and the work has only just begun. In the meantime, the role of biological mixing in the ocean remains a fascinating open question.

Ref: arxiv.org/abs/0911.5511: Stirring by swimming bodies