Hostname: page-component-745bb68f8f-kw2vx Total loading time: 0 Render date: 2025-01-09T22:06:32.336Z Has data issue: false hasContentIssue false
  • English
  • Français

On the equilibration of a symmetrically unstable front via a secondary shear instability

Published online by Cambridge University Press:  10 March 2009

JOHN R. TAYLOR  and
RAFFAELE FERRARI
JOHN R. TAYLOR
Affiliation:
Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA
RAFFAELE FERRARI*
Affiliation:
Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, USA
*
†Corresponding author address: Department of Earth, Atmospheric and Planetary Sciences, 54-1420, 77 Massachusetts Ave. Cambridge, MA, 02139, USA. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The equilibration of a symmetrically unstable density front is examined using linear stability theory and nonlinear numerical simulations. The initial state, chosen to approximate conditions in the surface ocean, consists of a weakly stratified mixed layer above a strongly stratified thermocline. Each layer has a uniform horizontal density gradient and a velocity field in thermal wind balance. The potential vorticity (PV) in the mixed layer is negative, indicating conditions favourable for symmetric instability. Once the instability reaches finite amplitude, a secondary Kelvin–Helmholtz (K-H) instability forms. Linear theory accurately predicts the time and the wavenumber at which the secondary instability occurs. Following the secondary instability, small-scale turbulence injects positive PV into the mixed layer from the thermocline and from the upper boundary, resulting in a rapid equilibration of the flow as the PV is brought back to zero. While the physical parameters used in this study correspond to typical conditions near a surface ocean front, many of the conclusions apply to symmetric instabilities in the atmosphere.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 622 , 10 March 2009 , pp. 103 - 113
Copyright
Copyright © Cambridge University Press 2009

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

REFERENCES

Allen, J. S. & Newberger, P. A. 1998 On symmetric instabilities in oceanic bottom boundary layers. J. Phys. Oceanogr. 28 (6), 1131–1151.2.0.CO;2>CrossRefGoogle Scholar
Dunkerton, T. J. 1981 On the inertial stability of the equatorial middle atmosphere. J. Atmos. Sci. 38, 2354–2364.2.0.CO;2>CrossRefGoogle Scholar
Emanuel, K. A. 1988 Observational evidence of slantwise convective adjustment. Mon. Weather Rev. 116, 1805–1816.2.0.CO;2>CrossRefGoogle Scholar
Griffiths, S. D. 2003 a The nonlinear evolution of zonally symmetric equatorial inertial instability. J. Fluid Mech. 474, 245–273.CrossRefGoogle Scholar
Griffiths, S. D. 2003 b Nonlinear vertical scale selection in equatorial inertial instability. J. Atmos. Sci. 60, 977–990.2.0.CO;2>CrossRefGoogle Scholar
Haine, T. W. N. & Marshall, J. 1998 Gravitational, symmetric, and baroclinic instability of the ocean mixed layer. J. Phys. Oceanogr. 28, 634–658.2.0.CO;2>CrossRefGoogle Scholar
Holton, J. R. 1992 An Introduction to Dynamic Meteorology, 3rd ed.Academic Press.Google Scholar
Hua, B. L., Moore, D. W. & Le Gentil, S. equilibration of equatorial flows. J. Fluid Mech. 331, 345–371.CrossRefGoogle Scholar
O'Dwyer, J. & Williams, R. G. 1997 The climatological distribution of potential vorticity over the abyssal ocean. J. Phys. Oceanogr. 27, 2488–2506.2.0.CO;2>CrossRefGoogle Scholar
Rayleigh, L. 1917 On the dynamics of revolving fluids. Proc. R. Soc. Lond. A 93, 148–154.Google Scholar
Stone, P. H. 1966 On non-geostrophic baroclinic stability. J. Atmos. Sci. 23, 390–400.2.0.CO;2>CrossRefGoogle Scholar
Stone, P. H. 1970 On non-geostrophic baroclinic stability. Part II. J. Atmos. Sci. 27, 721–726.2.0.CO;2>CrossRefGoogle Scholar
Taylor, J. R. 2008 Numerical simulations of the stratified oceanic bottom boundary layer. PhD thesis, University of California.Google Scholar
Thomas, L. N. & Lee, C. M. 2005 Intensification of ocean fronts by down-front winds. J. Phys. Oceanogr. 35, 1086–1102.CrossRefGoogle Scholar
Thorpe, A. J. & Rotunno, R. 1989 Nonlinear aspects of symmetric instability. J. Atmos. Sci. 46 (9), 1285–1299.2.0.CO;2>CrossRefGoogle Scholar