Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-29T14:13:21.375Z Has data issue: false hasContentIssue false
  • English
  • Français

Convective instability of stably stratified water in the ocean

Published online by Cambridge University Press:  12 April 2006

S. Leibovich
S. Leibovich
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853
Get access Rights & Permissions [Opens in a new window]

Abstract

A recent theoretical description of interactions between surface waves and currents in the ocean is extended to allow density stratification. The interaction leads to a convective instability even when the density stratification is statically stable. An unspecified random surface wave field is permitted provided that it is statistically stationary.

The instability can be traced to torques produced by variations of a ‘vortex force’. Non-diffusive instabilities produced by this mechanism in water of infinite depth are explored in detail for arbitrary distributions of the destabilizing force. Stability is determined by an eigenvalue problem formally identical to that determining normal modes of infinitesimal internal waves in fluid with a density profile that is not monotone and thereby has a statically unstable region. Some tentative remarks are offered about the problem when dissipation is allowed.

Application of the present theory to Langmuir circulations is discussed. Also, according to the present theory, internal wave propagation should be modified by the vortex force arising from the interaction between the surface waves and the current.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 3 , 27 September 1977 , pp. 561 - 581
Copyright
© 1977 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. & Stegun, I. A.(eds.) 1964 Handbook of Mathematical Functions. Washington: Nat. Bur. Stand.
Craik, A. D. D. 1977 The generation of Langmuir circulations by an instability mechanism. J. Fluid Mech. 81, 209–223.Google Scholar
Craik, A. D. D. & Leibovich, S. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73, 401–426.Google Scholar
Drazin, P. G. & Howard, L. N. 1966 Hydrodynamic stability of parallel flow of inviscid fluid. Adv. in Appl. Mech. 9, 1–89.Google Scholar
Foster, T. D. 1965 Stability of a homogeneous fluid cooled uniformly from above. Phys. Fluids 8, 1249–1257.Google Scholar
Foster, T. D. 1968 Effect of boundary conditions on the onset of convection. Phys. Fluids 11, 1257–1262.Google Scholar
Ince, E. L. 1956 Ordinary Differential Equations. Dover.
Leibovich, S. 1970 Weakly nonlinear waves in rotating fluids. J. Fluid Mech. 42, 803–822.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 the averaged current. J. Fluid Mech. 79, 715–743.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, 481–507.Google Scholar
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics, vol. 1. McGraw-Hill.
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Pollard, R. T. 1976 Observations and theories of Langmuir circulations and their role in nearsurface mixing. Deep-Sea Res. Sir George Deacon Anniversary Suppl.
Whitehead, J. A. & Chen, M. M. 1970 Thermal instability and convection of a thin fluid layer bounded by a stably stratified region. J. Fluid Mech. 40, 549–576.Google Scholar
Yih, C.-S. 1974 Wave motion in stratified fluids. In Nonlinear Waves (ed. S. Leibovich & A. R. Seebass), chap. 10. Cornell University Press, Ithaca, New York.