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On wave-current interaction theories of Langmuir circulations

Published online by Cambridge University Press:  19 April 2006

S. Leibovich
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, N.Y. 14853

Abstract

The Craik–Leibovich (CL) equations for Langmuir circulations are shown to be an Eulerian approximation to an exact theory of the generalized Lagrangian mean (GLM) due to Andrews and McIntyre. Derivation of the CL equations using the GLM formalism is decisively simpler than the original method. The CL theory is then compared to other wave–current interaction theories of Langmuir circulations, notably those of Garrett and of Moen.

Type
Research Article
Copyright
© 1980 Cambridge University Press

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References

Andrews, D. G. & McIntyre, M. E. 1978 An exact theory of nonlinear waves on a Lagrangianmean flow. J. Fluid Mech. 89, 609646.Google Scholar
Bretherton, F. P. 1971 The general linearized theory of wave propagation. Lectures in Applied Mathematics, vol. 13, 61102. American Mathematical Society.
Craik, A. D. D. 1970 A wave-interaction model for the generation of windrows. J. Fluid Mech. 41, 801821.Google Scholar
Craik, A. D. D. 1977 The generation of Langmuir circulations by an instability mechanism. J. Fluid Mech. 81, 209223.Google Scholar
Craik, A. D. D. & Leibovich, S. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73, 401426.Google Scholar
Faller, A. J. 1978 Experiments with controlled Langmuir circulations. Science 201, 618620.Google Scholar
Garrett, C. J. R. 1976 Generation of Langmuir circulations by surface waves - a feedback mechanism. J. Mar. Res. 34, 117130.Google Scholar
Hasselmann, K. 1970 Wave-driven inertial oscillations. Geophys. Fluid Dyn. 1, 463502.Google Scholar
Huang, N. E. 1979 On the surface drift currents in the ocean. J. Fluid Mech. 91, 191208.Google Scholar
Leibovich, S. 1977a 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, 715743.Google Scholar
Leibovich, S. 1977b Convective instability of stably stratified water in the ocean. J. Fluid Mech. 82, 561585.Google Scholar
Leibovich, S. & Paolucci, S. 1980 The Langmuir circulation instability as a mixing mechanism in the upper ocean. J. Phys. Oceanogr. (to appear).Google 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, 481507.CrossRefGoogle Scholar
Leibovich, S. & Ulrich, D. 1972 A note on the growth of small scale Langmuir circulations. J. Geophys. Res. 77, 16831688.Google Scholar
Moen, J. 1978 A theoretical model for Langmuir circulations. Ph.D. thesis, University of Southampton.
Myer, G. E. 1971 Structure and mechanism of Langmuir circulations on a small inland lake. Ph.D. dissertation, State University of New York at Albany.
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.