### Abstract

Nonlinear interactions between waves and turbulence cause systematic frequency shifts in Rossby waves. The frequency shifts in the inertial subranges of statistically steady β-plane turbulence were examined theoretically and numerically. The theoretical analysis is based on the Lagrangian closure called the Lagrangian renormalized approximation and predicts that when the β effect is small, the frequency shifts of Rossby waves are proportional to k_{x}/k^{4/3} in the inverse energy transfer range, while they are proportional to k_{x} with or without a log-correction term in the enstrophy transfer range, depending on the flow conditions, where k_{x} is the wave number in the eastward direction. Numerical simulations using 1024^{2} grid points of forced β-plane turbulence that exhibit the inertial subranges, show fairly good agreement with theoretical predictions.

Original language | English |
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Pages (from-to) | 2338-2349 |

Number of pages | 12 |

Journal | Physics of Fluids |

Volume | 13 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 2001 |

Externally published | Yes |

### ASJC Scopus subject areas

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes

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## Cite this

*Physics of Fluids*,

*13*(8), 2338-2349. https://doi.org/10.1063/1.1384468