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Statistics of an Unstable Barotropic Jet from a Cumulant Expansion

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  • 1 Brown University, Providence, Rhode Island
  • 2 California Institute of Technology, Pasadena, California
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Abstract

Low-order equal-time statistics of a barotropic flow on a rotating sphere are investigated. The flow is driven by linear relaxation toward an unstable zonal jet. For relatively short relaxation times, the flow is dominated by critical-layer waves. For sufficiently long relaxation times, the flow is turbulent. Statistics obtained from a second-order cumulant expansion are compared to those accumulated in direct numerical simulations, revealing the strengths and limitations of the expansion for different relaxation times.

Corresponding author address: J. B. Marston, Department of Physics, Brown University, Providence, RI 02912-1843. Email: brad_marston@brown.edu

Abstract

Low-order equal-time statistics of a barotropic flow on a rotating sphere are investigated. The flow is driven by linear relaxation toward an unstable zonal jet. For relatively short relaxation times, the flow is dominated by critical-layer waves. For sufficiently long relaxation times, the flow is turbulent. Statistics obtained from a second-order cumulant expansion are compared to those accumulated in direct numerical simulations, revealing the strengths and limitations of the expansion for different relaxation times.

Corresponding author address: J. B. Marston, Department of Physics, Brown University, Providence, RI 02912-1843. Email: brad_marston@brown.edu

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