Skip to main content Accessibility help

Passive scalar transport in β-plane turbulence

  • Peter Bartello (a1) (a2) and Greg Holloway (a1)


Evaluation of spectral closure theory and direct numerical simulation are used to examine the eddy transport of a passive scalar in barotropic β-plane flow. When a large-scale gradient of scalar concentration is imposed, the implied scale separation between fixed background gradient and eddies supports the concept of ‘eddy diffusion’. The results can be cast in terms of an eddy diffusion tensor K, whose behaviour as a function of mean vorticity gradient β is examined. Earlier theoretical work by Holloway & Kristmannsson (1984) is extended to include cases where strong vorticity–scalar correlations are observed, and corrected in order to restore random Galilean invariance.

The anisotropy of eddy energy and the direct influence of Rossby wave propagation contribute to the overall anisotropy of K, The resulting suppression of meridional diffusivity Kyy, and enhancement of zonal diffusivity Kxx, with increased β is examined. The variation in simulation Kyy is closely reproduced in the closure equations. However, the increased Kxx is the result of zonal jets whose persistence is not accounted for in the statistical theory.



Hide All
Babiano, A., Basdevant, C., Legras, B. & Sadourny, R., 1987 Vorticity and passive scalar dynamics in two-dimensional turbulence. J. Fluid Mech. 183, 379397.
Basdevant, C., Legras, B., Sadourny, R. & Béland, M. 1981 A study of barotropic model flows: intermittency, waves and predictability. J. Atmos. Sci. 38, 23052326.
Basdevant, C. & Sadourny, R., 1983 Modélisation des échelles virtuelles dans la simulation numérique des ecoulements turbulents bidimensionels. J. Méc. Théor. Appl., Numéro SpEaécial, pp. 243269.
Carnevale, G. & Martin, P., 1982 Field theoretical techniques in statistical fluid dynamics: with application to nonlinear wave dynamics. Geophys. Astrophys. Fluid Dyn. 20, 131164.
Fornberg, B.: 1977 A numerical study of 2-D turbulence. J. Comput. Phys. 25, 131.
Frisch, U., Lesieur, M. & Brissaud, A., 1974 A Markovian random coupling model for turbulence. J. Fluid Mech. 65, 145152.
Herring, J. & McWilliams, J., 1985 Comparison of direct numerical simulation of two-dimensional turbulence with two-point closure: the effects of intermittency. J. Fluid Mech. 153, 229242.
Herring, J., Orszag, S., Kraichnan, R. & Fox, D., 1974 Decay of two-dimensional homogeneous turbulence. J. Fluid Mech. 66, 417444.
Herring, J., Schertzer, D., Lesieur, M., Newman, G., Chollet, J. P. & Larchevěque, M. 1982 A comparative assessment of spectral closures as applied to passive scalar diffusion. J. Fluid Mech. 124, 411437.
Holloway, G.: 1984 Contrary roles of planetary wave propagation in atmospheric predictability. In Predictability of Fluid Motions (ed. G. Holloway & B. J. West). American Institute of Physics.
Holloway, G.: 1986 Estimation of oceanic eddy transports from satellite altimetry. Nature 323, 243244.
Holloway, G.: 1987 Systematic forcing of large-scale geophysical flows by eddy-topography interaction. J. Fluid Mech. 184, 463476.
Holloway, G. & Hendehshott, M. C., 1977 Stochastic closure for nonlinear Rossby waves. J. Fluid Mech. 82, 747765.
Holloway, G. & Kristmannsson, S. S., 1984 Stirring and transport of tracer fields by geostrophic turbulence. J. Fluid Mech. 141, 2750 (referred to herein as HK).
Keffer, T. & Holloway, G., 1988 Estimating Southern Ocean eddy flux of heat and salt from satellite altimetry. Nature 332, 91147.
Kraichnan, R.: 1971 An almost-Markovian Galilean-invariant turbulence model. J. Fluid Mech. 47, 512524.
Larchevěque, M. & Lesieur, M. 1981 The application of eddy-damped Markovian closures to the problem of dispersion of particle pairs. J. Méc. 20, 113134.
Legras, B.: 1980 Turbulent phase shift of Rossby waves. Geophys. Astrophys. Fluid Dyn. 15, 253281.
Lesieur, M.: 1987 Turbulence in Fluids. Martin Nijhoff.
Lesieub, M. & Herring, J., 1985 Diffusion of a passive scalar in two-dimensional turbulence. J. Fluid Mech. 161, 7795.
Lesieur, M., Sommeria, J. & Holloway, G., 1981 Zones inertielles du spectre d'un contaminant passif en turbulence bidimensionelle. CR. Acad. Sci. Paris 292 (II), 271274.
Leslie, D. C.: 1973 Developments in the Theory of Turbulence. Clarendon.
McWllliams, J. C.: 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 2143.
Newman, G. & Herring, J., 1979 A test field model study of a passive scalar in isotropic turbulence. J. Fluid Mech. 94, 163194.
Orszag, S.: 1971 Numerical simulation of incompressible flows within simple boundaries. I Galerkin (spectral) representations. Stud. Appl. Maths 50, 293327.
Orszag, S.: 1977 Statistical theory of turbulence. In Fluid Dynamics, 1973, Les Houches Summer School of Theoretical Physics (ed. R. Balian & J.-L. Peube), Gordon and Breach.
Panetta, R. L. & Held, I., 1988 Baroclinic eddy fluxes in a one-dimensional model of quasi-geostrophic turbulence. J. Atmos. Sci. 45, 33543365.
Pouquet, A., Lesieub, M., Andre, J. C. & Basdevant, C., 1975 Evolution of high Reynolds number two-dimensional turbulence. J. Fluid Mech. 72, 305319.
Ramsden, D., Whitfield, D. & Holloway, G., 1985 Spectral transform simulations of turbulent flows, with geophysical applications. Can. Tech. Rep. Hydrogr. Ocean Sci. No. 57.
Robert, A.: 1966 The integration of a low order spectral form of the primitive meteorological equations. J. Met. Soc. Japan (2) 44, 237245.
Shepherd, T.: 1987 Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere. J. Fluid Mech. 184, 289302.
MathJax is a JavaScript display engine for mathematics. For more information see

Related content

Powered by UNSILO

Passive scalar transport in β-plane turbulence

  • Peter Bartello (a1) (a2) and Greg Holloway (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.