Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-24T16:39:52.189Z Has data issue: false hasContentIssue false
  • English
  • Français

Evolution and decay of a rotating flow over random topography

Published online by Cambridge University Press:  04 December 2009

L. ZAVALA SANSÓN ,
A. GONZÁLEZ-VILLANUEVA  and
L. M. FLORES
L. ZAVALA SANSÓN*
Affiliation:
Department of Physical Oceanography, CICESE, Km 107 Carretera Tijuana-Ensenada, 22860 Ensenada, Baja California, México
A. GONZÁLEZ-VILLANUEVA
Affiliation:
Colegio de Ciencia y Tecnología, Universidad Autónoma de la Ciudad de México, Prolongación San Isidro 151, San Lorenzo Tezonco, 09790 Iztapalapa, México D.F.
L. M. FLORES
Affiliation:
Department of Physical Oceanography, CICESE, Km 107 Carretera Tijuana-Ensenada, 22860 Ensenada, Baja California, México
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The evolution and decay of a homogeneous flow over random topography in a rotating system is studied by means of numerical simulations and theoretical considerations. The analysis is based on a quasi-two-dimensional shallow-water approximation, in which the horizontal divergence is explicitly different from zero, and topographic variations are not restricted to be much smaller than the mean depth, as in quasi-geostrophic dynamics. The results are examined by comparing the evolution of a turbulent flow over different random bottom topographies characterized by a specific horizontal scale, or equivalently, a given mean slope. As in two-dimensional turbulence, the energy of the flow is transferred towards larger scales of motion; after some rotation periods, however, the process is halted as the flow pattern becomes aligned along the topographic contours with shallow water to the right. The quasi-steady state reached by the flow is characterized by a nearly linear relationship between potential vorticity and transport function in most parts of the domain, which is justified in terms of minimum-enstrophy arguments. It is found that global energy decays faster for topographies with shorter horizontal length scales due to more effective viscous dissipation. In addition, some comparisons between simulations based on the shallow-water and quasi-geostrophic formulations are carried out. The role of solid boundaries is also examined: it is shown that vorticity production at no-slip walls contributes for a slight disorganization of the flow.

JFM classification

Geophysical and Geological Flows: Geostrophic turbulence Geophysical and Geological Flows: Rotating flows Geophysical and Geological Flows: Topographic effects
Type
Papers
Information
Journal of Fluid Mechanics , Volume 642 , 10 January 2010 , pp. 159 - 180
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

Adcock, S. & Marshall, D. P. 2000 Interactions between geostrophic eddies and the mean circulation over large-scale bottom topography. J. Phys. Oceanogr. 30, 3223–3238.2.0.CO;2>CrossRefGoogle Scholar
Batchelor, G. K. 1969 Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids Suppl. II 12, 233–239.CrossRefGoogle Scholar
Bretherton, F. P. & Haidvogel, D. B. 1976 Two-dimensional turbulence above topography. J. Fluid Mech. 78, 129–154.CrossRefGoogle Scholar
Carnevale, G. F. & Frederiksen, J. S. 1987 Nonlinear stability and statistical mechanics of flow over topography. J. Fluid Mech. 175, 157–181.CrossRefGoogle Scholar
Clercx, H. J. H., van Heijst, G. J. F., Molenaar, D. & Wells, M. G. 2005 No-slip walls as vorticity sources in two-dimensional bounded turbulence. Dyn Atmos. Oceans 40, 3–21.CrossRefGoogle Scholar
Clercx, H. J. H., Maassen, S. R. & van Heijst, G. J. F. 1999 Decaying two-dimensional turbulence in square containers with no-slip or stress-free boundaries. Phys. Fluids 11, 611–626.CrossRefGoogle Scholar
Grimshaw, R., Tang, Y. & Broutman, D. 1994 The effect of vortex stretching on the evolution of barotropic eddies over a topographic slope. Geophys. Astrophys. Fluid Dyn. 76, 43–71.CrossRefGoogle Scholar
van Heijst, G. J. F. & Clercx, H. J. H. 2009 Laboratory modelling of geophysical vortices. Annu. Rev. Fluid Mech. 41, 143–164.CrossRefGoogle Scholar
Maassen, S. R., Clercx, H. J. H. & van Heijst, G. J. F. 2002 Self-organization of quasi-two-dimensional turbulence in stratified fluids in square and circular containers. Phys. Fluids 14, 2150–2169.CrossRefGoogle Scholar
Pedlosky, J. 1987 Geophysical Fluid Dynamics. Springer-Verlag.CrossRefGoogle Scholar
Salmon, R., Holloway, G. & Hendershott, M. 1976 The equilibrium statistical mechanics of simple quasi-geostrophic models. J. Fluid Mech. 75, 691–703.CrossRefGoogle Scholar
ZavalaSansón, L. Sansón, L. 2007 The long-time decay of rotating homogeneous flows over variable topography. Dyn. Atmos. Oceans 44, 29–50.CrossRefGoogle Scholar
ZavalaSansón, L. Sansón, L. & van Heijst, G. J. F. 2002 Ekman effects in a rotating flow over bottom topography. J. Fluid Mech. 471, 239–256.Google Scholar
ZavalaSansón, L. Sansón, L. & Sheinbaum, J. 2008 Elementary properties of the enstrophy and strain fields in confined two-dimensional flows. Eur. J. Mech. B/Fluids 27, 54–61.CrossRefGoogle Scholar