A model for eastward and westward jets in laboratory experiments and planetary atmospheres

Physics of Fluids

Volumn 10, Issue 6, 1998, Pages 1474-1489

  Marcus, P S ^a   Lee, C ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b University of Seoul   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001755217     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869668     Document Type: Article

References (40)

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2. J. Sommeria, S. D. Meyers, and H. L. Swinney, "Laboratory model of a planetary eastward jet," Nature (London) 337, 58 (1989).
3. T. H. Solomon, W. J. Holloway, and H. L. Swinney, "Shear flow instabilities and Rossby waves in barotropic flow in a rotating annulus," Phys. Fluids A 5, 1971 (1993).
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6. P. S. Marcus, "Jupiter's Great Red Spot and other vortices," Annu. Rev. Astron. Astrophys. 431, 523 (1993).
7. In the atmospheric literature eastward jets, which flow from west to east, are "westerlies."
8. P. S. Marcus and C. Lee, "Jupiter's Great Red Spot and zonal winds as a self-consistent, one-layer, quasigeostrophic flow," Chaos 4, 269 (1994).
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14. Numerical calculations are spectral with Fourier modes in the azimuthal and Chebyshev modes in the radial direction. The method has no splitting errors due to the fractional steps. Details are in Refs. 18 and 20.
15. lock, the Reynolds number of the vortex chains (defined as the circulation of a vortex divided by v) is ∼500, the Rossby number (based on their vorticities divided by f) is ∼0.1 and the Ekman spin-down time τ≃T where T is the characteristic turn-around time of a vortex.
16. P. S. Marcus, "Numerical simulations of Jupiter's Great Red Spot," Nature (London) 331, 693 (1988).
17. agr̂xfẑ which is equivalent to F in equation (3). One could include the Coriolis acceleration due to U, Uxfẑ, in equation (2), but it is equal to ∇(fψ), so it can be incorporated into the definition of Π/ρ (when ρ is constant) and is not included.
18. C. Lee, "Basic instability and transition to chaos in a rapidly rotating annulus on a β-plane," Ph. D. dissertation, University of California at Berkeley, 1993.
19. P. S. Marcus, "Spatial self-organization of vortices in chaotic shearing flows," Nucl. Phys. B, Proc. Suppl. 2, 127 (1988).
20. P. S. Marcus, "Vortex dynamics in a shearing zonal flow," J. Fluid Mech. 215, 393 (1990).
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24. -2kLb) otherwise.
25. The dispersion relation for a flow as in fig. 8b has been previously published. L. D. Talley, "Radiating barotropic instability," J. Phys. Oceanogr. 13, 972 (1983).
26. 2] where n is an integer and D is the width of the region of constant ū. Since there is no forcing in the regions of constant ū, there would be no reason for these modes to be excited. Indeed, our numerical calculations show no evidence of these channel Rossby waves, so we do not consider them.
27. out which is impossible.
28. E. Weeks and T. Solomon (private communication, 1995).
29. out than a Rossby wavelength, typically 5% of a wave length or less than 2 cm.
30. C. Lee and P. S. Marcus, "Eastward and westward jets in a rotating annulus model of a barotropic atmosphere," in the Proceedings of the CERCA Workshop in Semi-analytic Methods in Turbulence, edited by K. Coughlin (Montreal, Canada, 1997).
31. 6 The best results were with the initial q of the east-west velocity approximately equal to a step-function. Use of the traditional sinusoidal east-west velocity was particularly bad. When the initial q was approximately a step function, the chains of cyclonic and anti-cyclonic vortices were intertwined and centered at the westward jets, similar to the observed jovian vortex streets. An initially sinusoidal east-west velocity produced vortex chains widely spaced in latitude with each chain located near a local zero of the east-west velocity. Inclusion of a finite Rossby deformation radius in the QG equations or use of the shallow-water equations made these results even more pronounced.
32. 8 In this case ū is a series of connected cosh functions rather than parabolas.
33. S. Kim, "Dynamics of the Great Red Spot and Jovian Zonal Flows," Ph. D. thesis, University of California at Berkeley, 1996).
34. P. S. Marcus and C. Lee, "Two-dimensional turbulence and the formation of β-jets with forcing and dissipation" (in preparation).
35. R. L. Panetta, "Zonal jets in wide baroclincally unstable regions-Persistence and scale selection," J. Atmos. Sci. 50, 2073 (1993).
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37. G. Williams, "Jovian and comparative atmospheric modeling," Adv. Geophys. 28A, 381 (1985).
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39. J. Y.-K. Cho and L. M. Polvani, "The emergence of jets and vortices in freely evolving, shallow-water turbulence on a sphere," Phys. Fluids 8, 1531 (1996).
40. slit.