Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-08T22:06:57.407Z Has data issue: false hasContentIssue false
  • English
  • Français

Homogeneous intrusions in a rotating stratified fluid

Published online by Cambridge University Press:  20 April 2006

A. E. Gill
A. E. Gill
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
Get access Rights & Permissions [Opens in a new window]

Abstract

A study is made of intrusions of fixed volumes of fluid of constant density into a uniformly stratified and uniformly rotating environment. In particular, the eventual steady-state configuration is sought for the ideal fluid case. Exact two-dimensional solutions can be found using a co-ordinate transformation which converts the equations satisfied outside the intrusion into the Cauchy-Riemann equations. The same technique does not, however, yield linear equations in the axisymmetric case.

Effects of friction are also considered for cases where the quasi-geostrophic approximation can be made. Vertical advection by the viscosity-induced motion is shown to have the same effect on the temperature field as a greatly enhanced lateral diffusion, and therefore tends to spread the intrusion out laterally.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 103 , February 1981 , pp. 275 - 295
Copyright
© 1981 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

Armi, L. 1978 Some evidence for boundary mixing in the deep ocean. J. Geophys. Res. 83, 1971–1979.Google Scholar
Armi, L. & D'Asaro, E. 1980 Flow structures of the benthic ocean. J. Geophys. Res. 85, 469–484.Google Scholar
Baker, D. J. 1971 Density gradients in a rotating stratified fluid: experimental evidence for a new instability. Science 172, 1029–1031.Google Scholar
Blumen, W. 1972 Geostrophic adjustment. Rev. Geophys. Space Phys. 10, 485–528.Google Scholar
Charney, J. G. 1973 Planetary fluid mechanics. In Dynamical Meteorology (ed. P. Morel). Reidel.
Eliassen, A. & Kleinschmidt, E. 1957 Dynamic Meteorology. Handbuch der Physik, vol. 58, pp. 1–154. Springer.
Gill, A. E., Smith, J. M. Cleaver, P., Hide, R. & Jonas, P. 1979 The vortex created by mass transfer between layers of a rotating fluid. Geophys. Astrophys. Fluid Dyn. 12, 195–220.Google Scholar
Gregg, M. C. 1976 Fine structure and microstructure observations during the passage of a mild storm. J. Phys. Oceanog. 6, 528–555.Google Scholar
Griffiths, R. W. & Linden, P. F. 1981 The stability of vortices in a rotating stratified fluid. J. Fluid Mech. (to appear).Google Scholar
Horne, E. P. W. 1978 Interleaving at the subsurface front in the slope water off Nova Scotia. J. Geophys. Res. 83, 3659–3671.Google Scholar
Hoskins, B. J. 1975 The geostrophic approximation and the semi-geostrophic equations. J. Atmos. Sci. 32, 233–242.Google Scholar
Hoskins, B. J. & Bretherton, F. P. 1972 Atmospheric frontogenesis models: mathematical formulation and solution. J. Atmos. Sci. 29, 11–37.Google Scholar
Hoskins, B. J. & Draghici, I. 1977 The forcing of a geostrophic motion according to the semi geostrophic equations and in an isentropic coordinate model. J. Atmos Sci. 34, 1859–1867.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
McCartney, M. S., Worthington, L. V. & Raymer, M. E. 1980 Anomalous water mass distributions at 55 W in the North Atlantic in 1977. J. Mar. Res. 38, 147–171.Google Scholar
McIntyre, M. E. 1970 Diffusive destabilization of a baroclinic circular vortex. Geophys. Fluid Dyn. 1, 19–57.Google Scholar
Milne-Thomson, L. M. 1967 Theoretical Hydrodynamics, 5th ed. MacMillan.
Rossby, C. G. 1938 On the mutual adjustment of pressure and velocity distributions in certain simple current systems. J. Mar. Res. 1, 15–28, 239–263.Google Scholar
Yudin, M. I. 1955 Invariant quantities in large-scale atmospheric processes. Tr. Glav. Geofiz. Observ. No. 55, 3–12.Google Scholar