L'vov, V. S. and Nazarenko, Sergey (2006) Differential model for 2D turbulence. JETP LETTERS, 83 (12). pp. 541-545. doi:10.1134/S0021364006120046 ISSN 0021-3640.

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Abstract

We present a phenomenological model for 2D turbulence in which the energy spectrum obeys a nonlinear fourth-order differential equation. This equation respects the scaling properties of the original Navier-Stokes equations, and it has both the -5/3 inverse-cascade and the -3 direct-cascade spectra. In addition, our model has Raleigh-Jeans thermodynamic distributions as exact steady state solutions. We use the model to derive a relation between the direct-cascade and the inverse-cascade Kolmogorov constants, which is in good qualitative agreement with the laboratory and numerical experiments. We discuss a steady state solution where both the enstrophy and the energy cascades are present simultaneously, and we discuss it in the context of the Nastrom-Gage spectrum observed in atmospheric turbulence. We also consider the effect of the bottom friction on the cascade solutions and show that it leads to an additional decrease and finite-wavenumber cutoffs of the respective cascade spectra, which agrees with the existing experimental and numerical results.

Item Type:	Journal Article
Subjects:	Q Science > QC Physics
Journal or Publication Title:	JETP LETTERS
Publisher:	MAIK NAUKA/INTERPERIODICA/SPRINGER
ISSN:	0021-3640
Official Date:	25 June 2006
Dates:	Date Event 25 June 2006 UNSPECIFIED
Volume:	83
Number:	12
Number of Pages:	5
Page Range:	pp. 541-545
DOI:	10.1134/S0021364006120046
Publication Status:	Published

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