PerspectiveOcean Science

Biomixing of the Oceans?

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Science  11 May 2007:
Vol. 316, Issue 5826, pp. 838-839
DOI: 10.1126/science.1141272

Every now and then, an idea comes along that is so appealing, it seems bad manners to challenge it. Biomixing—the action of swimming organisms in mixing the world's oceans—is one such idea that has gained recent purchase. If correct, biomixing has far-reaching consequences for our understanding of the oceans. But can swimming organisms actually achieve significant mixing? Central to this question is their mixing efficiency.

Biomixing is certainly an engaging notion. For instance, at the global scale, it suggests that billions of small organisms paddling away in the deep oceans stir cold deep water upward, thus contributing to global circulation (1) and climate. At more local scales, it suggests that schools of krill and other marine animals (2) plough the thermocline, mixing nutrient-rich water upward and thereby fertilizing their own feeding grounds. Swimming organisms do seem to dissipate substantial amounts of mechanical energy. There are even observations showing considerably elevated dissipation rates in the wake of a migrating school of krill (3). The case for biomixing thus seems to be compelling.

However, in these studies, the dissipation of mechanical energy is equated with mixing. Yet, most of the biomixing is purportedly achieved by small but numerous zoo-plankton with diameters of 1 cm or less. Can mechanical energy at these small scales achieve any substantial mixing (that is, increase the potential energy of the water column) before it is dissipated as heat?

Turbulence in the oceans is generated by a variety of mechanisms, including tides, winds, and swimming animals. It cascades energy from large scales to ever smaller scales, where it is eventually dissipated. Turbulence is effective in mixing because it is active over a range of scales; stretching and folding of the fluid at large scales facilitates molecular diffusion at smaller scales.

The efficiency of turbulence in mixing a stratified water column is expressed by γ, the ratio of the change in potential energy to the work done. Mixing efficiency is controlled by three parameters: the integral frequency L (the scale at which turbulent kinetic energy is imparted to the flow), the rate of turbulent energy dissipation ϵ (equivalent to the rate of work done), and the buoyancy length scale N (a measure of the stratification of the water column). The latter two parameters can be conveniently combined as the buoyancy length scale B = (ϵ/N3)½. Theoretical considerations (4, 5) and observations (6, 7) indicate that when L Embedded Image B, the mixing efficiency is at its maximum. However, when L < B, the mixing efficiency can be orders of magnitude less (see the figure).

The efficiency of mixing.

(Top) The turbulent kinetic energy generated by a swimming animal dissipates either as heat or in increasing the potential energy of a stratified water column. (Bottom) The mixing efficiency Γ (that is, the proportion of kinetic energy that goes into potential-energy increase) is a function of the integral length scale L and the buoyancy length scale B. For a swimming animal, L is the size of the animal itself. Small animals tend to be much less efficient at mixing than larger animals, depending on the ratio L/B. For animals of a given size (that is, L), mixing efficiency decreases as dissipation rate increases, either because individual animals swim faster or because they aggregate in denser assemblages.

The net dissipation rate due to an assemblage of swimming organisms depends on the power expended per individual and the number of individuals per unit volume (2). Thus, the dissipation rate ϵ of a school of krill—assuming a body length of 1 to 1.5 cm, a swimming speed of 5 to 10 cm s−1, and a number density of 5000 individuals m−3—is equal to 10−5 to 10, SUP>-4 W kg−1, consistent with observations (3). How much mixing does this represent?

An organism of a given body size λ cannot inject energy into a flow at length scales larger than itself. Thus L ≈ λ, consistent with observations for grid-generated turbulence (8). The buoyancy frequency for the surface ocean is typically 10−2 s−1 or less, so that the buoyancy length scale associated with the above measurements is 3 to 10 m, and the corresponding mixing efficiency Γ = 10−4 to 10−2. Hence, only 1% at most of the mechanical energy dissipated by the swimming school of krill and other marine animals actually goes into mixing. The dissipation rate measured in the wake of a dense assemblage of swimming organisms may indeed be considerably higher than that associated with oceanic turbulence, but it does not necessarily follow that the corresponding mixing is also proportionally higher.

The case for biomixing as an important component of the meridional overturning circulation is fraught with the same problem. Considering tides and winds alone, there is an apparent shortfall of ~1 TW in the energy budget driving this circulation (9, 10). The oceanic biosphere captures solar energy at a rate of ~63 TW (1, 11). If only a small percentage of this captured solar energy makes its way into mechanical energy of swimming, the energy budget can apparently be closed. One terawatt corresponds to an average dissipation rate of 10−9 W kg−1 in the deep oceans, where the buoyancy frequency is typically 10−3 s−1 or less (12). Thus, a mean buoyancy length scale for the deep ocean is 1 m or greater. However, most of the biomass of the oceans is concentrated in small organisms such as copepods (≈ 1 mm). The efficiency of these organisms in mixing is only 10−3. It is only when one comes to larger, but much less abundant, organisms, such as fish and marine mammals, that the mixing efficiency approaches its maximum.

Dissipation is the end product of turbulence. It is also the most readily measured turbulence parameter in the ocean. However, important aspects of turbulence—such as mixing—also depend on the larger scales of turbulent motion (13, 14). By whatever means one approaches the calculation of biomixing of the oceans, one will always be confronted by the fact that the mixing efficiency of small organisms is extremely low. Most of the mechanical energy they impart to the oceans is dissipated almost immediately as heat. There may be a case to be made for biomixing by larger animals on a local scale, but their relatively low abundance means that they are unlikely to be important contributors to global circulation.

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