Turbulent diffusion in the geostrophic inverse cascade

K. S. Smith, G. Boccaletti, C. C. Henning, I. Marinov, C. Y. Tam, I. M. Held, G. K. Vallis

Research output: Contribution to journalArticle

Abstract

Motivated in part by the problem of large-scale lateral turbulent heat transport in the Earth's atmosphere and oceans, and in part by the problem of turbulent transport itself, we seek to better understand the transport of a passive tracer advected by various types of fully developed two-dimensional turbulence. The types of turbulence considered correspond to various relationships between the streamfunction and the advected field. Each type of turbulence considered possesses two quadratic invariants and each can develop an inverse cascade. These cascades can be modified or halted, for example, by friction, a background vorticity gradient or a mean temperature gradient. We focus on three physically realizable cases: classical two-dimensional turbulence, surface quasi-geostrophic turbulence, and shallow-water quasi-geostrophic turbulence at scales large compared to the radius of deformation. In each model we assume that tracer variance is maintained by a large-scale mean tracer gradient while turbulent energy is produced at small scales via random forcing, and dissipated by linear drag. We predict the spectral shapes, eddy scales and equilibrated energies resulting from the inverse cascades, and use the expected velocity and length scales to predict integrated tracer fluxes. When linear drag halts the cascade, the resulting diffusivities are decreasing functions of the drag coefficient, but with different dependences for each case. When β is significant, we find a clear distinction between the tracer mixing scale, which depends on β but is nearly independent of drag, and the energy-containing (or jet) scale, set by a combination of the drag coefficient and β. Our predictions are tested via high-resolution spectral simulations. We find in all cases that the passive scalar is diffused down-gradient with a diffusion coefficient that is well-predicted from estimates of mixing length and velocity scale obtained from turbulence phenomenology.

Original languageEnglish (US)
Pages (from-to)13-48
Number of pages36
JournalJournal of Fluid Mechanics
Volume469
DOIs
StatePublished - Oct 25 2002

Fingerprint

turbulent diffusion
cascades
Turbulence
turbulence
tracers
Drag
Drag coefficient
drag
drag coefficients
gradients
Earth atmosphere
Cascades (fluid mechanics)
Spectral resolution
Vorticity
Thermal gradients
shallow water
phenomenology
vorticity
diffusivity
Friction

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Physics and Astronomy(all)
  • Condensed Matter Physics

Cite this

Smith, K. S., Boccaletti, G., Henning, C. C., Marinov, I., Tam, C. Y., Held, I. M., & Vallis, G. K. (2002). Turbulent diffusion in the geostrophic inverse cascade. Journal of Fluid Mechanics, 469, 13-48. https://doi.org/10.1017/S0022112002001763

Turbulent diffusion in the geostrophic inverse cascade. / Smith, K. S.; Boccaletti, G.; Henning, C. C.; Marinov, I.; Tam, C. Y.; Held, I. M.; Vallis, G. K.

In: Journal of Fluid Mechanics, Vol. 469, 25.10.2002, p. 13-48.

Research output: Contribution to journalArticle

Smith, KS, Boccaletti, G, Henning, CC, Marinov, I, Tam, CY, Held, IM & Vallis, GK 2002, 'Turbulent diffusion in the geostrophic inverse cascade', Journal of Fluid Mechanics, vol. 469, pp. 13-48. https://doi.org/10.1017/S0022112002001763
Smith KS, Boccaletti G, Henning CC, Marinov I, Tam CY, Held IM et al. Turbulent diffusion in the geostrophic inverse cascade. Journal of Fluid Mechanics. 2002 Oct 25;469:13-48. https://doi.org/10.1017/S0022112002001763
Smith, K. S. ; Boccaletti, G. ; Henning, C. C. ; Marinov, I. ; Tam, C. Y. ; Held, I. M. ; Vallis, G. K. / Turbulent diffusion in the geostrophic inverse cascade. In: Journal of Fluid Mechanics. 2002 ; Vol. 469. pp. 13-48.
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