Skip to main content Accessibility help
×
Home

Surface quasi-geostrophic dynamics

Published online by Cambridge University Press:  26 April 2006


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

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
Copyright
© 1995 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below.

References

Beland, M. 1976 Numerical study of the nonlinear Rossby wave critical level development in a barotropic flow. J. Atmos. Sci. 33, 20662078.Google Scholar
Bennett, A. F. & Kloeden, P. E. 1980 The simplified quasi-geostrophic equations: existence and uniqueness of strong solutions. Mathematika 27, 287311.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, 185203.Google Scholar
Blumen, W. 1978 Uniform potential vorticity flow. Part I. Theory of wave interactions and two-dimensional turbulence. J. Atmos. Sci. 35, 774783.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, 911.Google Scholar
Dritschel, D. G. 1988 The repeated filamentation of two-dimensional vorticity interfaces. J. Fluid Mech. 194, 511547.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, 77146.Google Scholar
Dritschel, D. G. 1989b On the stabilization of a two-dimensional vortex strip by adverse shear. J. Fluid Mech. 206, 193221.Google Scholar
Eady, E. J. 1949 Long waves and cyclone waves. Tellus 1, 3352.Google Scholar
Garner, S., Nakamura, N. & Held, I. M. 1992 Nonlinear equilibration of two-dimensional Eady waves: a new perspective. J. Atmos. Sci. 49, 19841996.Google Scholar
Hoskins, B. J. 1975 The geostrophic momentum approximation and the semi-geostrophic equations. J. Atmos. Sci. 32, 233242.Google Scholar
Hoyer, J.-M. & Sadourny, R. 1982 Closure models for fully developed baroclinic instability. J. Atmos. Sci. 39, 707721.Google Scholar
Juckes, M. 1994 Quasi-geostrophic dynamics of the tropopause. J. Atmos. Sci. 51, 27562768.Google Scholar
Kill Worth, P. D. & McIntyre, M. E. 1985 Do Rossby-wave critical layers absorb, reflect, or overreflect? J. Fluid Mech. 161, 449492.Google Scholar
Knobloch, E. & Weiss, J. B. 1987 Chaotic advection by modulated traveling waves. Phys. Rev. A 36, 15221524.Google Scholar
Mcwilliams, J. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 2143.Google Scholar
Miller, J. 1990 Statistical mechanics of Euler equations in two dimensions. Phys. Rev. Lett. 65, 21372140.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, 285320.Google Scholar
Pierrehumbert, R. T. 1994 Tracer microstructure in the large-eddy dominated regime. Chaos, Solitons, and Fractals 4, 10911110.Google Scholar
Pierrehumbert, R. T., Held, I. M. & Swanson, K. 1994 Spectra of local and nonlocal two dimensional turbulence. Chaos, Solitons, and Fractals 4, 11111116.(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, 225263.Google Scholar
Rhines, P. B. 1975 Waves and turbulence on a beta-plane. J. Fluid Mech. 69, 417443.Google Scholar
Rhines, P. B. & Young, W. R. 1982 Homogenization of potential vorticity in planetary gyres. J. Fluid Mech. 122, 347367.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, 21202138.Google Scholar
Rivest, C. & Farrell, B. 1992 Upper tropospheric synoptic-scale waves, 1. Maintenance as Eady normal modes. J. Atmos. Sci. 49, 21082119.Google Scholar
Rose, H. A. & Sulem, P. L. 1978 Fully developed turbulence and statistical mechanics. J. Phys. Paris 47, 441484.Google Scholar
Schar, C. & Davies, H. C. 1990 An instability of mature cold front. J. Atmos. Sci. 47, 929950.Google Scholar
Smith, R. B. 1984 A theory of lee cyclogenesis. J. Atmos. Sci. 41, 11591168.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, 553586.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, 13461362.Google Scholar
Waugh, D. & Dritschel, D. G. 1991 The stability of filamentary vorticity in two-dimensional geophysical vortex-dynamics models. J. Fluid Mech. 231, 575598.Google Scholar
Weiss, J. B. & Knobloch, E. 1988 Mass transport and mixing by modulated travelling waves. Phys. Rev. A 40, 25792589.Google Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 405 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 1st December 2020. This data will be updated every 24 hours.

Hostname: page-component-6d4bddd689-2x8bj Total loading time: 0.594 Render date: 2020-12-01T12:38:57.686Z Query parameters: { "hasAccess": "0", "openAccess": "0", "isLogged": "0", "lang": "en" } Feature Flags last update: Tue Dec 01 2020 11:43:06 GMT+0000 (Coordinated Universal Time) Feature Flags: { "metrics": true, "metricsAbstractViews": false, "peerReview": true, "crossMark": true, "comments": true, "relatedCommentaries": true, "subject": true, "clr": false, "languageSwitch": true }

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Surface quasi-geostrophic dynamics
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Surface quasi-geostrophic dynamics
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Surface quasi-geostrophic dynamics
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *