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Surface quasi-geostrophic dynamics

Published online by Cambridge University Press:  26 April 2006

Isaac M. Held ,
Raymond T. Pierrehumbert ,
Stephen T. Garner  and
Kyle L. Swanson
Isaac M. Held
Affiliation:
Geophysical Fluid Dynamics Laboratory/NOAA, Princeton University, Princeton, NJ 08542, USA
Raymond T. Pierrehumbert
Affiliation:
Department of Geophysical Sciences, University of Chicago, Chicago, IL 60637, USA
Stephen T. Garner
Affiliation:
Geophysical Fluid Dynamics Laboratory/NOAA, Princeton University, Princeton, NJ 08542, USA
Kyle L. Swanson
Affiliation:
Department of Geophysical Sciences, University of Chicago, Chicago, IL 60637, USA
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Abstract

The dynamics of quasi-geostrophic flow with uniform potential vorticity reduces to the evolution of buoyancy, or potential temperature, on horizontal boundaries. There is a formal resemblance to two-dimensional flow, with surface temperature playing the role of vorticity, but a different relationship between the flow and the advected scalar creates several distinctive features. A series of examples are described which highlight some of these features: the evolution of an elliptical vortex; the start-up vortex shed by flow over a mountain; the instability of temperature filaments; the ‘edge wave’ critical layer; and mixing in an overturning edge wave. Characteristics of the direct cascade of the tracer variance to small scales in homogeneous turbulence, as well as the inverse energy cascade, are also described. In addition to its geophysical relevance, the ubiquitous generation of secondary instabilities and the possibility of finite-time collapse make this system a potentially important, numerically tractable, testbed for turbulence theories.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 282 , 10 January 1995 , pp. 1 - 20
Copyright
© 1995 Cambridge University Press

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References

Beland, M. 1976 Numerical study of the nonlinear Rossby wave critical level development in a barotropic flow. J. Atmos. Sci. 33, 2066–2078.Google Scholar
Bennett, A. F. & Kloeden, P. E. 1980 The simplified quasi-geostrophic equations: existence and uniqueness of strong solutions. Mathematika 27, 287–311.Google Scholar
Bennett, A. F. & Kloeden, P. E. 1982 The periodic quasi-geostrophic equations: existence and uniqueness of strong solutions. Proc. R. Soc. Edin. 91A, 185–203.Google Scholar
Blumen, W. 1978 Uniform potential vorticity flow. Part I. Theory of wave interactions and two-dimensional turbulence. J. Atmos. Sci. 35, 774–783.Google Scholar
Borue, V. 1994 Spectral exponents of enstrophy cascade in stationary two-dimensional homogeneous turbulence. Phys. Rev. Lett. 72, 1475.Google Scholar
Constantin, P., Majda, A. J. & Tabak, E. G. 1994 Singular front formation in a model for quasigeostrophic flow. Phys. Fluids 6, 9–11.Google Scholar
Dritschel, D. G. 1988 The repeated filamentation of two-dimensional vorticity interfaces. J. Fluid Mech. 194, 511–547.Google Scholar
Dritschel, D. G. 1989a Contour dynamics and contour surgery: numerical algorithms for extended, high-resolution, modeling of vortex dynamics in two-dimensional, inviscid incompressible flows. Comput. Phys. Rep. 10, 77–146.Google Scholar
Dritschel, D. G. 1989b On the stabilization of a two-dimensional vortex strip by adverse shear. J. Fluid Mech. 206, 193–221.Google Scholar
Eady, E. J. 1949 Long waves and cyclone waves. Tellus 1, 33–52.Google Scholar
Garner, S., Nakamura, N. & Held, I. M. 1992 Nonlinear equilibration of two-dimensional Eady waves: a new perspective. J. Atmos. Sci. 49, 1984–1996.Google Scholar
Hoskins, B. J. 1975 The geostrophic momentum approximation and the semi-geostrophic equations. J. Atmos. Sci. 32, 233–242.Google Scholar
Hoyer, J.-M. & Sadourny, R. 1982 Closure models for fully developed baroclinic instability. J. Atmos. Sci. 39, 707–721.Google Scholar
Juckes, M. 1994 Quasi-geostrophic dynamics of the tropopause. J. Atmos. Sci. 51, 2756–2768.Google Scholar
Kill Worth, P. D. & McIntyre, M. E. 1985 Do Rossby-wave critical layers absorb, reflect, or overreflect? J. Fluid Mech. 161, 449–492.Google Scholar
Knobloch, E. & Weiss, J. B. 1987 Chaotic advection by modulated traveling waves. Phys. Rev. A 36, 1522–1524.Google Scholar
Mcwilliams, J. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 21–43.Google Scholar
Miller, J. 1990 Statistical mechanics of Euler equations in two dimensions. Phys. Rev. Lett. 65, 2137–2140.Google Scholar
Pedlosky, J. 1979 Geophysical Fluid Dynamics. Springer.
Pierrehumbert, R. T. 1991 Chaotic mixing of tracers and vorticity by modulated traveling Rossby waves. Geophys. Astrophys. Fluid Dyn. 59, 285–320.Google Scholar
Pierrehumbert, R. T. 1994 Tracer microstructure in the large-eddy dominated regime. Chaos, Solitons, and Fractals 4, 1091–1110.Google Scholar
Pierrehumbert, R. T., Held, I. M. & Swanson, K. 1994 Spectra of local and nonlocal two dimensional turbulence. Chaos, Solitons, and Fractals 4, 1111–1116.(referred to herein as PHS).Google Scholar
Pozrikidis, P. & Higdon, J. J. L. 1985 Nonlinear Kelvin-Helmholtz instability of a finite vortex layer. J. Fluid Mech. 157, 225–263.Google Scholar
Rhines, P. B. 1975 Waves and turbulence on a beta-plane. J. Fluid Mech. 69, 417–443.Google Scholar
Rhines, P. B. & Young, W. R. 1982 Homogenization of potential vorticity in planetary gyres. J. Fluid Mech. 122, 347–367.Google Scholar
Rivest, C., Davies, C. & Farrell, B. 1992 Upper tropospheric synoptic-scale waves. 2. Maintenance and excitation of quasi-modes. J. Atmos. Sci. 49, 2120–2138.Google Scholar
Rivest, C. & Farrell, B. 1992 Upper tropospheric synoptic-scale waves, 1. Maintenance as Eady normal modes. J. Atmos. Sci. 49, 2108–2119.Google Scholar
Rose, H. A. & Sulem, P. L. 1978 Fully developed turbulence and statistical mechanics. J. Phys. Paris 47, 441–484.Google Scholar
Schar, C. & Davies, H. C. 1990 An instability of mature cold front. J. Atmos. Sci. 47, 929–950.Google Scholar
Smith, R. B. 1984 A theory of lee cyclogenesis. J. Atmos. Sci. 41, 1159–1168.Google Scholar
Thompson, L. & Flierl, G. R. 1993 Barotropic flow over finite isolated topography: steady solutions on the beta plane and the initial value problem. J. Fluid Mech. 250, 553–586.Google Scholar
Vallis, G. K. & Maltrud, M. E. 1993 Generation of mean flows and jets on a beta plane and over topography. J. Phys. Oceanogr. 23, 1346–1362.Google Scholar
Waugh, D. & Dritschel, D. G. 1991 The stability of filamentary vorticity in two-dimensional geophysical vortex-dynamics models. J. Fluid Mech. 231, 575–598.Google Scholar
Weiss, J. B. & Knobloch, E. 1988 Mass transport and mixing by modulated travelling waves. Phys. Rev. A 40, 2579–2589.Google Scholar