Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-29T13:44:18.139Z Has data issue: false hasContentIssue false
  • English
  • Français

On spatially growing baroclinic waves in the ocean

Published online by Cambridge University Press:  11 April 2006

Nelson G. Hogg
Nelson G. Hogg
Affiliation:
Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown that spatially growing waves with complex wavenumber and real frequency can exist in a baroclinic flow and that these waves are substantially different from the more commonly studied temporally growing ones. They are bounded by a low wavenumber cut-off which separates them from the temporally growing waves. Their amplitude and phase change most rapidly near their steering level and are almost depth independent away from it. Most of the energy conversion from mean flow to the waves occurs at this level. It is suggested that these motions may be forced by steady disturbances such as bottom relief.

The theory is compared with recent observations of strong small-scale motions in a region of rough topography of MODE and in the vicinity of the Gulf Stream. The vertical structure can be well matched with the theory but the complex wavenumber appears to be a factor of 2–3 greater than that predicted.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 78 , Issue 2 , 23 November 1976 , pp. 217 - 235
Copyright
© 1976 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

Bretherton, F. P. 1966 Critical layer instability in baroclinic flows Quart. J. Roy. Met. Soc. 92, 325–334.Google Scholar
Bryden, H. & Millard, R. 1973 Spatially-averaged MODE-I CTD stations. MODE Hot Line News, 43.
Charney, J. G. 1947 The dynamics of long waves in a baroclinic westerly current J. Met. 4, 135–163.Google Scholar
Charney, J. G. & Stern, M. E. 1962 On the stability of internal baroclinic jets in a rotating atmosphere J. Atmos. Sci. 19, 159–172.Google Scholar
Eady, E. T. 1949 Long waves and cyclone waves Tellus, 1, 33–52.Google Scholar
Gaster, M. 1962 A note on a relation between temporally increasing and spatially increasing disturbances in hydrodynamic stability J. Fluid Mech. 14, 222–224.Google Scholar
Gaster, M. 1965a The role of spatially growing waves in the theory of hydrodynamic stability Prog. Aero. Sci. 6, 251–270.Google Scholar
Gaster, M. 1965b On the generation of spatially growing waves in a boundary layer J. Fluid Mech. 22, 433–441.Google Scholar
Gill, A. E., Green, J. S. A. & Simmons, A. J. 1974 Energy partition in the large-scale ocean circulation and the production of mid-ocean eddies Deep-Sea Res. 21, 499–528.Google Scholar
Green, J. S. A. 1960 A problem in baroclinic stability Quart. J. Roy. Met. Soc. 26, 157–185.Google Scholar
Leaman, K. D. & Sanford, T. B. 1975 Vertical energy propagation of inertial waves: a vector spectral analysis of velocity profiles. J. Geophys. Res. 80, 1975–1980.
Lighthill, M. J. 1967 On waves generated in dispersive systems by travelling forcing effects, with applications to the dynamics of rotating fluids J. Fluid Mech. 27, 725–752.Google Scholar
Lin, C. C. 1955 The Theory of Hydrodynamic Stability. Cambridge University Press.
Luyten, J. R. 1976 Scales of motion in the deep Gulf Stream and across the Continental Rise. To be published.
Mcintyre, M. E. 1972 Baroclinic instability of an idealized model of the polar night jet Quart. J. Roy. Met. Soc. 98, 165–174.Google Scholar
Mcwilliams, J. C. & Flierl, G. R. 1976 Optimal quasigeostrophic wave analysis of MODE array data Deep-Sea Res. 23, 285–300.Google Scholar
Richman, J., Hogg, N. G. & Wunsch, C. 1976 Analysis of MODE-I moored temperature observations. In preparation.
Sanford, T. B. 1976 Observations of the vertical structure of internal waves J. Geophys. Res. 80, 3861–3871.Google Scholar
Saunders, P. & Luyten, J. 1976 Velocity profiles in and near the Gulf Stream. In preparation.
Watson, J. 1962 On spatially-growing finite disturbances in plane Poiseuille flow J. Fluid Mech. 14, 211–221.Google Scholar