## Abstract

The large-scale energy spectrum in two-dimensional turbulence governed by the surface quasi-geostrophic (SQG) equation

partial derivative(t)(-Delta)(1/2)Psi + J(Psi, (-Delta)(1/2)Psi) = mu Delta Psi + f

is studied. The nonlinear transfer of this system conserves the two quadratic quantities Psi(1) =<[(-Delta)(1/4)Psi](2)>/2 and Psi(2) = <[(-Delta)(1/2)Psi](2)>/2 (kinetic energy), where <center dot > denotes a spatial average. The energy density Psi(2) is bounded and its spectrum Psi(2)(k) is shallower than k(-1) in the inverse-transfer range. For bounded turbulence, Psi(2)(k) in the low-wavenumber region can be bounded by Ck where C is a constant independent of k but dependent on the domain size. Results from numerical simulations confirming the theoretical predictions are presented.

Original language | English |
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Pages (from-to) | 349-359 |

Number of pages | 11 |

Journal | Journal of Fluid Mechanics |

Volume | 526 |

DOIs | |

Publication status | Published - 10 Mar 2005 |

## Keywords

- 2-DIMENSIONAL TURBULENCE
- ROSSBY WAVES
- DIFFUSION
- BEHAVIOR
- CASCADE
- FLOW