## Abstract

he inverse transfer in the forced-dissipative surface quasi-geostrophic equation is studied, when the natural dissipation operator mu(-Delta)(1/2) lis employed. The nonlinear transfer of this system conserves the two quadratic quantities psi(1) = (vertical bar(-Delta)(1/4) psi vertical bar(2)>/2 and psi(2) = (vertical bar(-Delta)(1/2) psi vertical bar(2))/2 (kinetic energy), where psi is the stream function and <.> denotes a spatial average. In the limit of infinite domain, the kinetic energy density psi(2) remains bounded, for the natural dissipation operator. For the power-law inverse-transfer region, the inverse flux of T-1 diminishes as it proceeds toward sufficiently low wavenumbers, whenever the kinetic energy psi(2) remains bounded. This implies that no persistent (non-dissipative) inverse cascade of psi(1) to ever-lower wavenumbers is sustainable, as long as the dissipation parameter mu it is held fixed. This result does not rule out the possibility that for sufficiently small mu, a finite inverse flux would reach a certain low wavenumber. Numerical results supporting the theoretical predictions are presented. (c) 2005 Elsevier B.V. All rights reserved.

Original language | English |
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Pages (from-to) | 76-84 |

Number of pages | 9 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 213 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2006 |

## Keywords

- surface quasi-geostrophic turbulence
- inverse transfer
- diminishing inverse flux
- 2-DIMENSIONAL TURBULENCE
- SPECTRAL DISTRIBUTION
- ENERGY
- FLOW
- DIFFUSION
- BEHAVIOR
- LIMIT
- MODEL
- 2D