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On the formation of geophysical and planetary zonal flows by near-resonant wave interactions

Published online by Cambridge University Press:  28 March 2007

YOUNGSUK LEE  and
LESLIE M. SMITH
YOUNGSUK LEE
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
LESLIE M. SMITH
Affiliation:
Departments of Mathematics and Engineering Physics, University of Wisconsin, Madison, WI 53706, USA
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Abstract

Numerical simulations on a β-plane are used to further understand the formation of zonal flows from small-scale fluctuations. The dynamics of ‘reduced models’ are computed by restricting the nonlinear term to include a subset of triad interactions in Fourier space. Reduced models of near-resonant triads are considered, as well as the complement set of non-resonant triads. At moderately small values of the Rhines number, near-resonant triad interactions are shown to be responsible for the generation of large-scale zonal flows from small-scale random forcing. Without large-scale drag, both the full system and the reduced model of near resonances produce asymmetry between eastward and westward jets, in favour of stronger westward jets. When large-scale drag is included, the long-time asymmetry is reversed in the full system, with eastward jets that are thinner and stronger than westward jets. Then the reduced model of near resonances exhibits a weaker asymmetry, but there are nevertheless more eastward jets stronger than a threshold value.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 576 , 10 April 2007 , pp. 405 - 424
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Afanasyev, Y. & Wells, J. 2005 Quasi-two-dimensional turbulence on the polar beta-plane: laboratory experiments. Geophys. Astrophys. Fluid Dyn. 99, 1–17.CrossRefGoogle Scholar
Balk, A. 1991 A new invariant for Rossby wave systems. Phys. Lett. A 155, 20–24.CrossRefGoogle Scholar
Balk, A. 2005 Angular distribution of {R}ossby wave energy. Phys. Lett. A 345, 154–160.CrossRefGoogle Scholar
Balk, A., Nazarenko, S. & Zakharov, V. 1991 New invariant for drift turbulence. Phys. Lett. A 152, 276–280.CrossRefGoogle Scholar
Baroud, C., Plapp, B., Swinney, H. & She, Z. 2003 Scaling in three-dimensional and quasi two-dimensional rotating turbulent flows. Phys. Fluids 15, 2091–2104.CrossRefGoogle Scholar
Boyd, J. 2001 Chebyshev and Fourier Spectral Methods, 2nd edn. Dover.Google Scholar
Canuto, C., Hussaini, M., Quarteroni, A. & Zang, T. 1988 Spectral Methods in Fluid Dynamics. Springer.CrossRefGoogle Scholar
Chekhlov, A., Orszag, S., Galperin, B., Sukoriansky, S. & Staroselsky, I. 1996 The effect of small-scale forcing on large-scale structures in two-dimensional flows. Physica D 98, 321–334.Google Scholar
Connaughton, C., Nazarenko, S. & Pushkarev, A. 2001 Discreteness and quasiresonances in weak turbulence of capillary waves. Phys. Rev. E 63, 046306.Google ScholarPubMed
Danilov, S. & Gryanik, V. 2004 Barotropic beta-plane turbulence in a regime with strong zonal jets revisited. J. Atmos. Sci. 61, 2283–2295.2.0.CO;2>CrossRefGoogle Scholar
Danilov, S. & Gurarie, D. 2004 Scaling, spectra and zonal jets in beta-plane turbulence. Phys. Fluids 16, 2592–2603.CrossRefGoogle Scholar
Galperin, B., Sukoriansky, S. & Huang, H. 2001 Universal n −5 spectrum of zonal flows on giant planets. Phys. Fluids 13, 1545–1548.CrossRefGoogle Scholar
Gierasch, P., Ingersoll, A., BanField, D. et al. 2000 Observation of moist convection in Jupiter's atmosphere. Nature 403, 628–630.Google Scholar
Holloway, G. & Hendershott, M. 1977 Statistical closure for nonlinear {R}ossby waves. J. Fluid Mech. 82, 747–765.CrossRefGoogle Scholar
Hopfinger, E., Browand, K. & Gagne, Y. 1982 Turbulence and waves in a rotating tank. J. Fluid Mech. 125, 505–534.CrossRefGoogle Scholar
Huang, H. & Robinson, W. 1998 Two-dimensional turbulence and persistent zonal jets ins a global barotropic model. J. Atmos. Sci. 55, 611–632.2.0.CO;2>CrossRefGoogle Scholar
Huang, H., Galperin, B. & Sukoriansky, S. 2001 Anisotropic spectra in two-dimensional turbulence on the surface of a rotating sphere. Phys. Fluids 13, 225–240.CrossRefGoogle Scholar
Ingersoll, A., Gierasch, P., Banfield, D et al. . 2000 Moist convection as an energy source for the large-scale motions in Jupiter's atmosphere. Nature 403, 630–632.Google Scholar
Kuo, H. 1949 Dynamic instability of two-dimensional nondivergent flow in a barotropic atmosphere. J. Met. 6, 105–122.2.0.CO;2>CrossRefGoogle Scholar
Lollini, L. & Godeferd, F. 1999 Direct numerical simulations of turbulence with confinement and rotation. J. Fluid Mech. 393, 257–307.Google Scholar
Longhetto, A., Montabone, L., Provenzale, A., Didelle, H., Giraud, C., Bertoni, D. & Forza, R. 2002 Coherent vortices in rotating flows: a laboratory view. Il Nuovo Cimento 25, 233–249.Google Scholar
Longuet-Higgins, M. & Gill, A. 1967 Resonant interactions between planetary waves. Proc. R. Soc. Lond. A 299, 120–140.Google Scholar
Manfroi, A. & Young, W. 2002 Stability of β-plane Kolmogorov flow. Physica D 162, 208–232.Google Scholar
Marcus, P., Kundu, T. & Lee, C. 2000 Vortex dynamics and zonal flows. Phys. Plasmas 7, 1630–1640.CrossRefGoogle Scholar
Newell, A. 1969 Rossby wave packet interactions. J. Fluid Mech. 35, 255–271.CrossRefGoogle Scholar
Nozawa, R. & Yoden, S. 1997 Formation of zonal band structure in forced two-dimensional turbulence on a rotating sphere. Phys. Fluids 9, 2081–2093.CrossRefGoogle Scholar
Okuno, A. & Masuda, A. 2003 Effect of horizontal divergence on the geostrophic turbulence on a beta-plane: suppression of the {R}hines effect. Phys. Fluids 15, 56–65.CrossRefGoogle Scholar
Pedlosky, J. 1986 Geophysical Fluid Dynamics. Springer.Google Scholar
Pushkarev, A. & Zakharov, V. 2000 Turbulence of capillary waves – theory and numerical simulation. Physica D 135, 98–116.Google Scholar
Reznik, G. & Soomere, T. 1983 On generalized spectra of weakly nonlinear {R}ossby waves. Oceanology 23, 692–694.Google Scholar
Rhines, P. 1975 Waves and turbulence on a beta-plane. J. Fluid Mech. 69, 417–443.CrossRefGoogle Scholar
Rhines, P. 1979 Geostrophic turbulence. Annu. Rev. Fluid Mech. 11, 401–441.CrossRefGoogle Scholar
Salmon, R. 1998 Lectures on Geophysical Fluid Dynamics. Oxford University Press.CrossRefGoogle Scholar
Smith, K. S. 2004 A local model for planetary atmospheres forced by small-scale convection. J. Atmos. Sci. 61, 1420–1433.2.0.CO;2>CrossRefGoogle Scholar
Smith, L. 2001 Numerical study of two-dimensional stratified turbulence. Advances in Wave Intercation and Turbulence (ed. Milewski, P. A., Smith, L. M., Waleffe, F. & Tabak, E. G.). Am. Math. Soc. Providence, RI.Google Scholar
Smith, L. & Lee, Y. 2005 On near resonances and symmetry breaking in forced rotating flows at moderate {R}ossby number. J. Fluid Mech. 535, 111–142.CrossRefGoogle Scholar
Smith, L. & Waleffe, F. 1999 Transfer of energy to two-dimensional large scales in forced, rotating three-dimensional turbulence. Phys. Fluids 11, 1608–1622.CrossRefGoogle Scholar
Smith, L. & Waleffe, F. 2002 Generation of slow, large scales in forced rotating, stratified turbulence. J. Fluid Mech. 451, 145–168.CrossRefGoogle Scholar
Smith, L. & Yakhot, V. 1994 Finite-size effects in forced two-dimensional turbulence. J. Fluid Mech. 274, 115–138.CrossRefGoogle Scholar
Sommeria, J., Meyers, S. & Swinney, H. 1988 Laboratory simulation of Jupiter's great red spot. Lett. Nature 331, 689–693.CrossRefGoogle Scholar
Sukoriansky, S., Galperin, B. & Dikovskaya, N. 2002 Universal spectrum of two-dimensional turbulence on a rotating sphere and some basic features of atmospheric circulation on giant planets. Phys. Rev. Lett. 89, 124501.CrossRefGoogle ScholarPubMed
Vallis, G. & Maltrud, M. 1993 Generation of mean flows and jets on a beta plane and over topography. J. Phys. Oceanogr. 23, 1346–1362.2.0.CO;2>CrossRefGoogle Scholar
Williams, G. 1978 Planetary circulations: 1. Barotropic representation of {J}ovian and terrestrial turbulence. J. Atmos. Sci. 35, 1399–1426.2.0.CO;2>CrossRefGoogle Scholar