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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: rferrari@mit.edu
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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.

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

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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