117 research outputs found

    Large-scale energy spectra in surface quasi-geostrophic turbulence

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    The large-scale energy spectrum in two-dimensional turbulence governed by the surface quasi-geostrophic (SQG) equation ∂t(−Δ)1/2ψ+J(ψ,(−Δ)1/2ψ)=μΔψ+f\partial_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 Ψ1=/2\Psi_1=/2 and Ψ2=/2\Psi_2=/2 (kinetic energy), where denotes a spatial average. The energy density Ψ2\Psi_2 is bounded and its spectrum Ψ2(k)\Psi_2(k) is shallower than k−1k^{-1} in the inverse-transfer range. For bounded turbulence, Ψ2(k)\Psi_2(k) in the low-wavenumber region can be bounded by CkCk where CC is a constant independent of kk but dependent on the domain size. Results from numerical simulations confirming the theoretical predictions are presented.Comment: 11 pages, 4 figures, to appear in JF
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