Viscosity-enhanced bio-mixing of the oceans

Current Science

Volumn 98, Issue 8, 2010, Pages 1103-1108

  Subramanian, Ganesh ^a  

^a JAWAHARLAL NEHRU CENTRE FOR ADVANCED SCIENTIFIC RESEARCH   (India)

Author keywords

Darwinian drift; Force dipole; Ocean mixing; Viscosity; Zooplankton

Indexed keywords

EID: 77954024845     PISSN: 00113891     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. Katija, K. and Dabiri, J. O., A viscosity-enhanced mechanism for biogenic ocean mixing. Nature, 2009, 460, 624-627.
2. The new drift-induced mixing mechanism is the subject of an article in the 'Science section' of BBC news under the heading 'Jellyfish help to stir the oceans'; http://news.bbc.co.uk/2/hi/science/nature/8173384.stm
3. Munk, W. H., Abyssal recipes. Deep-Sea Res., 1966, 13, 707-730.
4. Schiermeier, Q., Churn, churn, churn. Nature, 2007, 447, 522-524.
5. Visser, A. W., Biomixing of the oceans. Science, 2006, 316, 838-839.
6. Dewar, W. K., Bingham, R. J., Iverson, R. L., Nowacek, D. P., St Laurent, L. C. and Wiebe, P. H., Does the marine biosphere mix the ocean? J. Mar. Res., 2006, 64, 541-561.
7. It must be kept in mind that the error bars accompanying such estimates are considerable, and it may well be that winds and tides are indeed enough to account for the observed oceanic circulation; hence, the usage of the term 'an apparent shortfall'
8. Kunze, E., Dower, J. F., Beveridge, I., Dewey, R. and Bartlett, K. P., Observations of biologically generated turbulence in a coastal inlet. Science, 2006, 313, 1768-1770.
9. Huntley, M. E. and Zhou, M., Influence of animals on turbulence in the sea. Mar. Ecol. Prog. Ser., 2004, 273, 65-79.
10. Here, we neglect the effect of interactions between organisms leading to collective motion and larger length scales. This is justified in the present context, since the Darwinian-drift mechanism being examined is proposed to operate at the level of a single swimming organism.
11. 6, the total biomass of a large aquatic mammal such as the sperm whale, about 14 MT, pales in comparison to an estimated zooplankton mass in excess of 30 GT, 2006.
12. Turner, J. S., Buoyancy Effects in Fluids, Cambridge University Press, Cambridge, 1973.
13. The transition from a laminar to a turbulent wake occurs at about a Reynolds number (Re) of about 1000. For the sake of simplicity, we will assume this to be true for both wakes of passive particles that exhibit a non-trivial momentum defect, and the momentumless wakes that characterize self-propelled non-accelerating neutrally buoyant swimmers.
14. Darwin, C. G., Note on hydrodynamics. Proc. Camb. Phil. Soc., 1953, 49, 342-354.
15. 25, the result relies on a particular 'ordering of the infinities'; the presence of a rigid boundary, even an infinitely remote one, fundamentally alters the drift volume on length scales much larger than the particle.
16. Eames, I., Belcher, S. E. and Hunt, J. C. R., Drift, partial drift and Darwin's proposition. J. Fluid Mech., 1994, 275, 201-223.
17. Benjamin, B. T., Note on added mass and drift. J. Fluid Mech., 1994, 169, 251-256.
18. Thiffeault, J. L. and Childress, S., Stirring by swimming bodies, 2009; http://arxiv.org/PS_cache/arxiv/pdf/0911/0911.5511v1.pdf
19. Batchelor, G. K., Introduction to Fluid Dynamics, Cambridge University Press, Cambridge, 1967.
20. Lighthill, M. J., Hydromechanics of aquatic animal propulsion. Annu. Rev. Fluid Mech., 1969, 1, 413-446.
21. Tennekes, H. and Lumley, J. L., A First Course in Turbulence, MIT Press, 1972.
22. It is worth mentioning that the force-dipole that appears in the Oseen equation is the one relevant on large length scales. For any finite Re, this need not be the same as the actual force-dipole exerted by the swimmer. This is because, unlike the force or torque, a symmetric force-dipole is not transmitted unchanged across fluid surfaces.
23. Leal, L. G., Laminar Flow and Convective Transport Processes, Butterworth-Heinemann, 1992.
24. The absence of a volumetric displacement for a dipole field may appear to contradict Darwin's original demonstration of a net displacement for a sphere in the potential flow limit in which case the disturbance velocity field is that of a potential dipole, and therefore, fore-aft symmetric. However, as already indicated, the drift in this latter instance is of the order of the particle volume, or in the present context, of the order of the swimmer size. The Oseen analysis is, however, valid on much larger length scales - those that contribute to efficient mixing. Thus, any volumetric drift of the order of the swimmer size is not included in the analysis. In particular, a similar analysis in the potential flow limit would correspond, at leading order, to an actual potential dipole singularity rather than a finite-sized sphere, the displaced volume then being zero.
25. It may also be shown the volume displaced by a force-dipole, in the limit Re → 0 grows linearly with time, much like the passive particle at finite Re; however, the smallest aquatic organisms of interest here, the zooplankton, tend to have Reynolds numbers of order unity.