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Cited by 155Fluid Dynamics and Turbulent FlowsOceanographic and Atmospheric ProcessesMeteorological Phenomena and Simulations

On the Arrest of Inverse Energy Cascade and the Rhines Scale

Sukoriansky, Semion, Dikovskaya, Nadejda, Galperin, Boris·2007·Journal of the Atmospheric Sciences
DOI 10.1175/jas4013.1
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Abstract

Abstract The notion of the cascade arrest in a β-plane turbulence in the context of continuously forced flows is revised in this paper using both theoretical analysis and numerical simulations. It is demonstrated that the upscale energy propagation cannot be stopped by a β effect and can only be absorbed by friction. A fundamental dimensional parameter in flows with a β effect, the Rhines scale, LR, has traditionally been associated with the cascade arrest or with the scale that separates turbulence and Rossby wave–dominated spectral ranges. It is shown that rather than being a measure of the inverse cascade arrest, LR is a characteristic of different processes in different flow regimes. In unsteady flows, LR can be identified with the moving energy front propagating toward the decreasing wavenumbers. When large-scale energy sink is present, β-plane turbulence may attain several steady-state regimes. Two of these regimes are highlighted: friction-dominated and zonostrophic. In the former, LR does not have any particular significance, while in the latter, the Rhines scale nearly coincides with the characteristic length associated with the large-scale friction. Spectral analysis in the frequency domain demonstrates that Rossby waves coexist with turbulence on scales smaller than LR thus indicating that the Rhines scale cannot be viewed as a crossover between turbulence and Rossby wave ranges.

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  • The zonostrophy index Rβ has been introduced to distinguish friction-dominated regimes (small Rβ) and zonostrophic regimes (Rβ > 2.5).

    “In the context of eddy-driven jets in forced-dissipative experiments, the zonostrophy index R β has been introduced to distinguish friction-dominated regimes (small R β , Earth's ocean and atmosphere) and zonostrophic regimes, i.e. regimes of strong jets ( R β > 2 . 5, Jupiter and Saturn) (Galperin et al. 2006; Sukoriansky et al. 2007; Galperin et al. 2019, table 13.1).”

    From Zonal jets at the laboratory scale: hysteresis and Rossby waves resonance (2021) · cites this paper as Sukoriansky et al. 2007

  • The strength of the jets and the quality of their delineation can be classified depending on the zonostrophy index R_β.

    “Galperin et al. (2006); Sukoriansky et al. (2007) demonstrated that the strength of the jets and the quality of their delineation can be classified depending on the zonostrophy index R β defined as the ratio”

    From Zonal jets at the laboratory scale: hysteresis and Rossby waves resonance (2021) · cites this paper as Sukoriansky et al. (2007)

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Related

Authors
Sukoriansky, S., Dikovskaya, N., & Galperin, B.
Affiliations
  • Ben-Gurion University of the Negev (IL)
  • University of South Florida St. Petersburg (US)
ORCID
Venue
Journal of the Atmospheric Sciences
Publisher
American Meteorological Society
Published
2007-09-01
Volume
64
Issue
9
Pages
3312-3327
ISSN
  • 0022-4928 (ISSN-L)
  • 1520-0469
DOI
10.1175/jas4013.1
OpenAlex
W2073636625
Cited by
155
References
70
Citations by year
2026: 5 · 2025: 5 · 2024: 10 · 2023: 10 · 2022: 18 · 2021: 9 · 2020: 7 · 2019: 6 · 2018: 10 · 2017: 8 · 2016: 2 · 2015: 8 · 2014: 10 · 2013: 11 · 2012: 7
FWCI
9.98
Type
journal article
Language
en
Open access
closed
Locations
  • Journal of the Atmospheric Sciences (publishedVersion)
  • Digital Commons - University of South Florida (University of South Florida) (submittedVersion)
Topics
  • Physical Sciences › Engineering › Computational Mechanics › Fluid Dynamics and Turbulent Flows
  • Physical Sciences › Earth and Planetary Sciences › Oceanography › Oceanographic and Atmospheric Processes
  • Physical Sciences › Earth and Planetary Sciences › Atmospheric Science › Meteorological Phenomena and Simulations
Keywords
inverse energy cascade, Rhines scale, Rossby waves, spectral analysis

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