Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-19T04:12:55.340Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of rotation and shear on doubly diffusive instability

Published online by Cambridge University Press:  20 April 2006

Sylvia Worthem ,
E. Mollo-Christensen  and
F. Ostapoff
Sylvia Worthem
Affiliation:
Sea–Air Interaction Laboratory, NOAA, Miami, Florida
E. Mollo-Christensen
Affiliation:
Massachusetts Institute of Technology, Cambridge, Massachusetts
F. Ostapoff
Affiliation:
Sea-Air Interaction Laboratory, NOAA, Miami, Florida
Get access Rights & Permissions [Opens in a new window]

Abstract

A linear stability analysis of a doubly diffusive system, with rotation and shear, shows that overstable oscillations can occur in stratifications typical of the equatorial ocean, that internal waves encountering an equatorial current can exchange energy with the current, and that the wave-induced fluxes of salt and heat can lead to layer formation in the salinity, temperature and velocity fields.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 133 , August 1983 , pp. 297 - 319
Copyright
© 1983 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.) 1965 Handbook of Mathematical Functions. Dover.
Baines, P. G. & Gill, A. E. 1963 On thermohaline convection with linear gradients J. Fluid Mech. 37, 289–306.Google Scholar
Calman, J. 1977 Experiments on high Richardson number instability of a rotating stratified shear flow Dyn. Atmos. Oceans 1, 277–297.Google Scholar
Cramer, H. 1946 Mathematical Methods of Statistics. Princeton University Press.
Crawford, W. R. 1982 Pacific equatorial turbulence J. Phys. Oceanogr. 12, 1137–1149.Google Scholar
Dowden, J. M. 1972 An equatorial boundary layer J. Fluid Mech. 56, 193–200.Google Scholar
Duing, W., Ostapoff, F. & Merle, J. (eds.) 1980 Physical Oceanography of the Tropical Atlantic during GATE. University of Miami.
Elliott, J. A. & Oakey, N. S. 1980 Average microstructure levels and vertical diffusion for Phase III, GATE. Deep-Sea Res. 26, (Suppl I), 273–294.Google Scholar
Fedorov, K. N. 1978 The Thermohaline Finestructure of the Ocean. Pergamon.
Gans, R. F. 1975 On the stability of a shear flow in a rotating gas J. Fluid Mech. 68, 403–412.Google Scholar
Gregg, M. C., Cox, C. S. & Hacker, P. W. 1973 Vertical microstructure measurements in the central North Pacific J. Phys. Oceanogr. 3, 458–469.Google Scholar
Gurvich, A. S. & Yaglom, A. M. 1967 Breakdown of eddies and probability distributions for small-scale turbulence Phys. Fluids Suppl. 10, 959–965.Google Scholar
Holyer, J. 1981 On the collective instability of salt fingers J. Fluid Mech. 110, 195–207.Google Scholar
Hsu, Y. S. 1974 Double diffusive instabilities with and without a weak vertical shear. Ph.D. thesis, Harvard University.
Huppert, H. E. & Turner, J. S. 1981 Double-diffusive convection J. Fluid Mech. 106, 299–329.Google Scholar
Kolmogorov, A. N. 1962 A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number J. Fluid Mech. 13, 82–85.Google Scholar
Kozlov, V. F. 1967 On the theory of a baroclinic layer at the equator Oceanology 7, 448–455.Google Scholar
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows J. Fluid Mech. 98, 243–251.Google Scholar
Linden, P. F. 1974 Salt fingers in a steady shear flow Geophys. Fluid Dyn. 6, 1–27.Google Scholar
Mcintyre, M. E. 1970a Diffusive destabilization of the baroclinic circular vortex Geophys. Fluid Dyn. 1, 19–57.Google Scholar
Mcintyre, M. E. 1970b Role of diffusive overturning in nonlinear axisymmetric convection in a differentially heated rotating annulus Geophys. Fluid Dyn. 1, 59–89.Google Scholar
Maslowe, S. A. 1974 Instability of rigidly rotating flows to non-axisymmetric disturbances J. Fluid Mech. 64, 307–317.Google Scholar
Munk, W. H. 1966 Abyssal recipes Deep-Sea Res. 13, 707–730.Google Scholar
Obukhov, A. M. 1962 Some specific features of atmospheric turbulence J. Fluid Mech. 13, 77–81.Google Scholar
Pearlstein, A. J. 1981 Effect of rotation on the stability of a doubly diffusive fluid layer J. Fluid Mech. 103, 389–412.Google Scholar
Perkins, H. T. & VAN LEER, J. C. 1977 Simultaneous current-temperature profiles in the Equatorial Countercurrent J. Phys. Oceanogr. 7, 264–271.Google Scholar
Proctor, M. R. E. 1981 Steady subcritical thermohaline convection J. Fluid Mech. 105, 507–521.Google Scholar
Proni, J. R., Ostapoff, F. & Sellers, R. L. 1978 Acoustic observations of high-frequency, near-surface internal wave groups in the deep ocean during GATE Deep-Sea Res. 25, 299–307.Google Scholar
Rayleigh, Lord 1878 On the instability of jets Proc. Lond. Math. Soc. 10, 4–13.Google Scholar
Schmitt, R. W. & Lambert, R. B. 1979 The effects of rotation on salt fingers J. Fluid Mech. 90, 449–463.Google Scholar
Siegmann, W. L. 1974 Evolution of unstable shear layers in a rotating fluid J. Fluid Mech. 64, 289–305.Google Scholar
Stern, M. E. 1960 The ‘salt-fountain’ and thermohaline convection. Tellus 12, 172–175.Google Scholar
Stern, M. E. 1969 Collective instability of salt fingers J. Fluid Mech. 35, 209–218.Google Scholar
Stern, M. E. 1975 Ocean Circulation Physics. Academic.
Stommel, H. 1962 Examples of mixing and self-stimulated convection on the S-T diagram. Okeanologiya 2, 205–209.Google Scholar
Synge, J. L. 1938 Hydrodynamic Stability. Semi-centennial Publ. Am. Math. Soc., vol. 2 (addresses), pp. 227–269.
Turner, J. S. & Stommel, H. 1964 A new case of convection in the presence of combined vertical salinity and temperature gradients Proc. Natl. Acad. Sci. 52, 49–53.Google Scholar
Veronis, G. 1965 On finite-amplitude instability in thermohaline convection J. Mar. Res. 23, 1–17.Google Scholar
Woods, J. D. 1968 Wave-induced shear instability in the summer thermocline J. Fluid Mech. 32, 791–800.Google Scholar