A generalized Rhines effect and storms on Jupiter

Abstract

[1] The Rhines effect is an interaction of Rossby waves and two-dimensional turbulence that induces alternating zonal flows, thereby deforming and eventually destroying coherent vortices that might exist. Large-scale geophysical flows are not strictly two-dimensional. To be applicable to these flows the Rhines effect is therefore generalized. A novel aspect of the generalized Rhines effect is its possible suppression. On Jupiter, it is suppressed in the polar regions and at specific lower latitudes. It is remarkable that exactly there storms (vortices) have been observed, suggesting that storms can exist only where Rossby waves cannot interact with them. Thus the Rhines effect plays not only a role in the formation of the alternating zonal winds on Jupiter, as previously suggested, but in its generalized form also dictates the latitudes at which storms can exist.

Interpretation of the propagation of surface altimetric observations in terms of planetary waves and geostrophic turbulence

“…These are essentially the left hand and equivalent right hand sides of . Our Figure 10 is similar to Theiss [2006, Figure 3] for Jupiter, except that here our dispersion relation is computed from the full vertical structure of the mean flow, rather than just the first baroclinic component (because of the dominance of the first baroclinic mode, however, the first baroclinic calculation is rather similar; not shown). Note that u t is nearly constant with latitude, varying between and 5 and 10 cm s −1 ; the strong equatorial values have been reduced, through projection onto the surface‐intensified first baroclinic mode, as explained above (if one assumed equipartition, the velocity estimate in the equatorial region would be reduced even further).…”

“…A plausible interpretation of the results presented in Section 3 is that in low latitudes, baroclinic eddies give their energy to linear Rossby waves, whereas at high latitudes, Rossby waves are less easily generated, and the SSH field remains dominated by eddies. This can be understood in terms of a matching, or not, of turbulent and wave timescales, as discussed in the barotropic context by Rhines [1975] and Vallis and Maltrud [1993], and in a (first‐mode) baroclinic context applied to the gas planets by Theiss [2004], Smith [2004], and Theiss [2006]. The central idea of the Rhines effect is that, as eddies grow in the inverse cascade, their timescale slows, and when this timescale matches the frequency of Rossby waves with the same spatial scale, turbulent energy may be converted into waves, and the cascade will slow tremendously.…”

A long-lived cyclone in Saturn’s atmosphere: Observations and models

“…Our study of CS can also be used to asses the recently proposed idea that in a two-dimensional turbulent flow extended in depth (assumed to represent the upper atmosphere of a giant planet), the ''Rhines" or ''b-effect", that acts to organize the turbulent energy into alternating zonal flows, controls the presence of vortices at a given latitude when Rossby waves are suppressed (Theiss, 2006;Penny et al, 2010). According to this effect, vortices are expected to form whenever the turbulent velocity of the flow U (measured as the root mean square, rms, of the wind speed deviations from the zonal mean) is larger than U c , a critical velocity given by This requires the term in parenthesis to be positive, where u is the flow velocity at cloud level and u deep is the flow speed at depth (below this level).…”

Suppression of the Rhines effect and the location of vortices on Saturn

“…However, observations show that vortices tend to cluster at specific latitudes, and assuming that the time scales for vortex formation are much longer than those over which Rossby wave dispersion would act to destroy the vortices, it suggests that there are certain locations where Rossby waves are suppressed. Theiss [2006] proposed that a formulation of the Rhines effect to include baroclinic modes (depth‐dependent flow) can allow for the suppression of the Rhines effect when certain criteria are met and found that the location of vortices on Jupiter correlate well with the latitudes where the Rhines effect appears to be suppressed.…”

“…By comparing the Voyager 1 and 2 zonal wind profile data from Sánchez‐Lavega et al [2000] with the recent cloud‐feature spot count from Choi et al [2009] obtained from a combination of VIMS data and an analysis of ISS data by Vasavada et al [2006], this paper expands upon the method introduced by Theiss [2006] by applying his modified Rhines scale to Saturn to determine whether latitudes predicted to be favorable for Rossby wave suppression correspond to the latitudes of observed vortices. Further expanding on the approach used by Theiss [2006], in which the deformation radius is a specified function of latitude and the deep flow is assumed to be zero, we include the possibility of a nontrivial deep layer flow and a deformation radius that can be adjusted as a free parameter.…”