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On surface drift currents in the ocean

Published online by Cambridge University Press:  19 April 2006

Norden E. Huang
Norden E. Huang
Affiliation:
NASA Wallops Flight Center, Wallops Island, Virginia 23337
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Abstract

A new model of surface drift currents is constructed using the full nonlinear equations of motion. This model includes the balance between Coriolis forces due to the mean and wave-induced motions and the surface wind stresses. The approach used in the analysis is similar to the work by Craik & Leibovich (1976) and Leibovich (1977), but the emphasis is on the mean motion rather than the small-scale time-dependent part of the Langmuir circulation. The final result indicates that surface currents can be generated by both the direct wind stresses, as in the classical Ekman model, and the Stokes drift, derived from the surface wave motion, in an interrelated fashion depending on a wave Ekman number E defined as \[ E = \Omega/\nu_ek^2_0, \] where Ω is the angular velocity of the earth's rotation, νe, the eddy viscosity and k0, the wavenumber of the surface wave at the spectral peak. When E [Lt ] 1, the Langmuir mode dominates. When E [Gt ] 1, inertial motion results. The classical Ekman drift current is a special case even under the restriction E ≃ 1. On the basis of these results, a new model of the surface-layer movements for future large-scale ocean circulation studies is presented. For this new model both the wind stresses and the sea-state information are crucial inputs.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 91 , Issue 1 , 9 March 1979 , pp. 191 - 208
Copyright
© 1979 Cambridge University Press

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References

Assaf, G., Gerard, R. & Gordon, A. L. 1971 Some mechanisms of oceanic mixing revealed in aerial photographs. J. Geophys. Res. 76, 6550–6572.Google Scholar
Bashkirov, G. S. 1959 Turbulence and certain marine hydrological phenomena. Scientific Papers of OIIMF Gidroteknika 20.
Benilov, A. Yu. 1973 Generation of ocean turbulence surface waves. Izv. Atmos. Ocean Phys. 9, 293–303.Google Scholar
Bowden, K. F. 1950 The effect of eddy viscosity on ocean waves. Phil. Mag. (7), 41, 907–917.Google Scholar
Bowden, K. F. 1967 Stability effect on turbulent mixing in tidal currents. Phys. Fluids 10, 278–280.Google Scholar
Bowden, F. K., Howe, M. R. & Tait, R. I. 1970 A study of the heat budget over a seven day period at an oceanic station. Deep Sea Res. 17, 401–411.Google Scholar
Brennecke, W. 1921 Die Ozeanographischen arbeiten der Deutschen Antarktischen Expedition 1911–1912. Arch. dtsch Seewarte 39, 206.Google Scholar
Businger, J. A. 1966 Transfer of momentum and heat in the planetary boundary layer. Proc. Symp. Arctic Heat Budget Atmos. Circulation, Rand Corp., pp. 305–332.
Bye, J. A. T. 1967 The wave-drift current. J. Mar. Res. 25, 95–102.Google Scholar
Craik, A. D. & Leibovich, S. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73, 401–426.Google Scholar
Csanady, G. T. 1972 Frictional currents in the mixed layer at the sea surface. J. Phys. Oceanog. 2, 498–508.Google Scholar
Csanady, G. T. 1976 Mean circulation in shallow seas. J. Geophys. Res. 81, 5389–5399.Google Scholar
Defant, A. 1932 Die Gezeiten und inneren Gezeitenwellen des Atlantischen Ozeans. Wiss. Erg. Deut. Atlantische Expedition Meteor. 1925–1927, 7, 318.Google Scholar
Dinklage, L. E. 1888 Die Oberflächenstromungen im südwestlichen Teil der Ostsee und ilue Abhängigkeit von Winde. Ann. Hydr. Mar. Met. 16, 1–18.Google Scholar
Dobrokonskii, S. V. 1947 Eddy viscosity in the surface layer of the ocean and waves. Dokl. Akad. Nauk SSSR 58, 7.Google Scholar
Dobrokonskii, S. V. & Lesnikov, B. M. 1975 A laboratory study of the dynamic characteristic of drift currents in the presence of wind-driven waves. Izv. Atmos. Ocean Phys. 11, 942–950.Google Scholar
Durst, C. S. 1924 The relationship between current and wind. Quart. J. Roy. Met. Soc. 50, 113.Google Scholar
Ekman, V. W. 1905 On the influence of the earth's rotation on ocean-currents. Arkiv. Math. Astr. Ocean Phys., vol. 2, no. 11.
Ekman, V. W. 1953 Results of a cruise on board the “Armauer Hansen” in 1930 under the leadership of Bjorn Helland—Hansen studies on ocean currents. Geofys. Publ. 19, 106–122.Google Scholar
Faller, A. J. 1964 The angle of windrows in the ocean. Tellus 16, 363–370.Google Scholar
Fjeldstad, J. E. 1929 Ein Beitrag zur Theorie der wincerzenten Meereströmungeen. Gerlands Bietr. Geophys. 23, 237–247.Google Scholar
Fjeldstad, J. E. 1936 Results of tidal observations. Norwegian North Polar Exped. with the Mand 1918–1925 Sci. Results 4, (4), 88.Google Scholar
Forch, C. 1909 Über die bezeihungen zwischen Wind und Strom in Europaischen Mittelmeer. Ann. Hydr. Mar. Met. 37, 435.Google Scholar
Gallé, P. H. 1910 Zur Kenntius der Meeresströmungen. Mededeelingen en Verhandelingen, Utrecht 9, 1–102.Google Scholar
Hasselmann, K. et al. 1973 Measurements of wind-wave growth and swell decay during joint North Sea Wave Project (JONSWAP). Deut. Hydrogr. Z. Suppl. A 8 (12), 1–95.Google Scholar
Hasselmann, K., Ross, D. B., Müller, P. & Sell, W. 1976 A parametric wave prediction model. J. Phys. Oceanog. 6, 200–228.Google Scholar
Hoeber, H. 1972 Eddy thermal conductivity in the upper 12 m of the tropical Atlantic. J. Phys. Oceanog. 2, 303–304.Google Scholar
Huang, N. E. 1971 Derivation of Stokes drift for a deep-water random gravity wave field. Deep-Sea Res. 18, 255–259.Google Scholar
Hunkins, K. 1966 Ekman drift currents in the Arctic Ocean. Deep-Sea Res. 13, 607–620.Google Scholar
Ianniello, J. P. & Garvine, R. W. 1975 Stokes transport by gravity waves for application to circulation models. J. Phys. Oceanog. 5, 47–50.Google Scholar
Ichiye, T. 1964 On a dye diffusion experiment off Long Island. Lamont Geol. Obs. Tech. Rep. CU-2663–10.Google Scholar
Ichiye, T. 1967 Upper ocean boundary-lay or flow determined by dye diffusion. Phys. Fluids Suppl. 10, S270–277.Google Scholar
Jacobsen, J. P. 1913 Beitrag zur Hydrographie der Dänischen Gewässer. Komm. f. Havunders Medd., Ser. Hydr. 2 (2), 94.Google Scholar
Kármán, T. von 1930 Mechanische Ähnlichkeit und Turbulenz. Machr. Ges. Wiss. Göttingen, Math-Phys. Klasse 1, 58–76.Google Scholar
Katz, B., Gerard, R. & Costin, M. 1965 Response of dye tracers to sea surface conditions. J. Geophys. Res. 70, 5505–5513.Google Scholar
Kenyon, K. E. 1970 Stokes transport. J. Geophys. Res. 75, 1133–1135.Google Scholar
Kitaigorodskii, S. A. 1960 On the computation of the thickness of the wind mixing layer in the ocean. Izv. Geophys. Ser. 3, 425–431.Google Scholar
Kitaigorodskii, S. A. & Miropolsky, Yu. Z. 1968 Turbulent-energy dissipation in the ocean surface layer. Izv. Atmos. Ocean. Phys. 4, 647–659.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. C. R. Acad. Aci. URSS 30, 299–303.Google Scholar
Korvin-Kroukovsky, B. V. 1972 Pure drift current and mass transport in coexistent waves. Deut. Hydro. Z. 25, 1–13.Google Scholar
Kuftarkov, Yu. M. & Fel'zenbaum, A. I. 1976 A generalization of the theory of the main ocean thermocline. Isv. Atmos. Ocean Phys. 12, 648–656.Google Scholar
Kullenberg, G. 1971 Vertical diffusion in shallow waters. Tellus 23, 129–135.Google Scholar
Kullenberg, G. 1976 On vertical mixing and energy transfer from the wind to the water. Tellus 28, 159–165.Google Scholar
Leibovich, S. 1977 On the evolution of the system of wind drift currents and Langmuir circulations in the ocean. Part 1. Theory and averaged current. J. Fluid Mech. 79, 715–743.CrossRefGoogle Scholar
Leibovich, S. & Radhakrishnan, K. 1977 On the evolution of the system of wind drift currents and Langmuir circulations in the ocean. Part 2. Structure of the Langmuir vortices. J. Fluid Mech. 80, 481–507.CrossRefGoogle Scholar
Mamayev, O. I. 1958 The influence of stratification on vertical turbulent mixing in the sea. Izv. Geophys. Ser. 1, 870–875.Google Scholar
Mildner, P. 1932 Über die reibung einer speziellen Luftmasse in dem untersten Schichte der Atmosphäre. Beit. Phys. Freien Atmos 19, 151–158.Google Scholar
Miyake, M., Donelau, M., McBean, G., Paulson, C., Badgley, F. & Leavitt, E. 1970 Comparison of turbulent fluxes over water determined by profile and eddy correlation techniques. Quart. J. Roy. Met. Soc. 96, 132–137.Google Scholar
Mohn, H. 1883 The North Ocean, its depths, temperature and circulation. Norwegian North Atlantic Expedition 1876–1878, Christiana 2 (2), 117.Google Scholar
Monin, A. S. & Oboukhov, A. M. 1954 Basic turbulent mixing laws in the atmospheric surface layer. Trudy Geofiz. Inst. Akad. Nauk SSSR 24, 163–187.Google Scholar
Monin, A. S. & Yaglom, A. M. 1971 Statistical Fluid Mechanics. MIT Press.
Munk, W. H. & Anderson, E. R. 1948 Notes on a theory of the thermocline. J. Mar. Res. 7, 276–295.Google Scholar
Nan'niti, T. 1964 Some observed results of oceanic turbulence. In Studies on Oceanography (ed. K. Yoshida), pp. 211–215. University of Washington Press.
Nansen, F. 1902 The oceanography of the North Polar Basin. Norwegian North Polar Exp. 1893–96, Sci. Res. 3, 357.Google Scholar
Neumann, G. 1939 Triftströmungen an der Oberfläche bei “Adlergrund Feuerschiff.” Ann. d. Hydr. u. Marit. Meteor. 67, 82.Google Scholar
Neumann, G. & Pierson, W. J. 1964 Principles of Physical Oceanography. Prentice-Hall.
Ostapoff, F. & Worthem, S. 1974 The intradiurnal temperature variation in the upper ocean layer. J. Phys. Oceanog. 4, 601–612.Google Scholar
Palmén, E. 1930 Untersuchungen über die Strömungen in den Finnland umgebenden Meiren. Soc. Sci. Fenn. Comm. Phys.-Math. 5, 12.Google Scholar
Palmén, E. 1931 Zur Bestimmung des Triftstromes aus Terminbeobachtungen. J. Conseil. Int. 6, 3.Google Scholar
Phillips, O. M. 1958 The equilibrium range in the spectrum of wind-generated waves. J. Fluid Mech. 4, 426–434.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Prümm, D. 1974 Height dependence of diurnal variations of wind velocity and water temperature near the air-sea interface of the tropical Atlantic. Boundary-Layer Meteorol 6, 341–347.Google Scholar
Rossby, C. G. 1932 A generalization of the theory of the mixing length with applications to atmospheric and oceanic turbulence. MIT Met. Papers 1, 4.Google Scholar
Rossby, C. G. & Montgomery, R. B. 1935 The layer of frictional influence in wind and ocean currents. Papers in Phys. Oceanog. & Met. 3, 101.Google Scholar
Rossby, C. G. & Montgomery, R. B. 1936 On the momentum transfer at the sea surface. Papers in Phys. Oceanog. & Met. 4, 30.Google Scholar
Shemdin, O. H. 1972 Wind-generated current and phase speed of wind waves. J. Phys. Oceanog. 2, 411–419.Google Scholar
Smith, E. H. 1931 Arctic ice with special reference to its distribution to the North Atlantic Ocean. The Marion-Exped. 1928, Bull., vol. 19, no. 3.
Smith, J. E. (ed.) 1968 Torrey Canyon Pollution and Marine Life. Cambridge University Press.
Stern, M. E. 1975 Ocean Circulation Physics. New York: Academic Press.
Stommel, H. 1954 Serial observations of drift currents in the central North Atlantic Ocean. Tellus 6, 203–214.Google Scholar
Suda, K. 1926 On the dissipation of energy in the density current. Geophys. Mag. 10, 131–243.Google Scholar
Sutcliffe, W. H., Baylor, E. R. & Menzel, D. 1963 Sea surface chemistry and Langmuir circulation. Deep-Sea Res. 10, 233–242.Google Scholar
Sverdrup, H. U. 1926 Dynamics of tides on the North Siberian shelf, results from the Mand expedition. Geofys. Publ. 4 (5), 75.Google Scholar
Sverdrup, H. U. 1928 Die Eisdrift im Weddelmeer. Ann. Hydrograph. Mar. Met. 56, 265–274.Google Scholar
Swinbank, W. C. 1964 The exponential wind profile. Quart. J. Roy. Met. Soc. 90, 119.Google Scholar
Thomas, J. H. 1975 A theory of steady wind-driven currents in shallow water with variable eddy viscosity. J. Phys. Oceanog. 5, 136–142.Google Scholar
Thorade, H. 1914 Die Geschwindigkeit von Trifströmungen und die Ekmansche Theorie. Ann. d. Hydrogr. u. Mar. Meteor. 42, 379–391.Google Scholar
Thorade, H. 1928 Gerzeitenuntersuchungen in der Deutschen Bucht der Nordsee. Arch. dtsche Seewarte 46 (3), 1–85.Google Scholar
Tomczak, G. 1964 Investigations with drift cards to determine the influence of the wind on surface currents. In Studies on Oceanography (ed. K. Yoshida), pp. 129–139. University of Washington Press.
Van Dorn, W. 1953 Wind stress over water. J. Mar. Res. 12, 249–276.Google Scholar
Webster, C. A. G. 1964 An experimental study of turbulence in a density stratified shear flow. J. Fluid Mech. 19, 221–245.Google Scholar
Witten, A. J. & Thomas, J. H. 1976 Steady wind driven currents in a large lake with depth-dependent eddy viscosity. J. Phys. Oceanog. 6, 85–92.Google Scholar
Witting, R. 1909 Zur Kenntnis des vom Winde erzengten Overflächenstromes. Ann. d. Hydr. u. Marit. Meteor. 37, 193–202.Google Scholar
Wright, J. W. & Keller, W. C. 1971 Doppler spectra in microwave scattering from wind waves. Phys. Fluids 14, 466–474.Google Scholar
Wu, J. 1968 Laboratory studies of wind—wave interactions. J. Fluid Mech. 34, 91–111.Google Scholar
Wu, J. 1975 Wind-induced drift currents. J. Fluid Mech. 68, 49–70Google Scholar
Wüst, G. 1955 Stromgeschwindigkeiten in Tiefen-und Bodenwasser des Atlantischen Ozeans. Deep-Sea Res., Papers in Marine Biology and Oceanography, pp. 373–397.
Yamamoto, G. & Shimasuki, A. 1966 Turbulence transfer in diabatic conditions. J. Mer. Soc. Japan, 44, 301–307.Google Scholar