Revisiting freely decaying two-dimensional turbulence at millennial resolution

We study the evolution of vortex statistics in freely decaying two-dimensional turbulence at very large Reynolds number. The results obtained here confirm that the peak vorticity inside vortex cores is conserved and that the number of vortices as a function of time, N(t), decreases as a power law. In addition, the numerical findings are consistent with the predictions of the scaling theories proposed by Carnevale et al. [Phys. Rev. Lett. 66, 2735 (1991)] and Weiss and McWilliams [Phys. Fluids A 5, 608 (1993)]. We also obtain new evidence for a self-similar distribution of vortex radii and circulations, that suggests the possibility of a generic statistical behavior of the decaying phase of two-dimensional turbulence at high Reynolds number.

[1]  James C. McWilliams,et al.  Vortex merging in quasi-geostrophic flows , 2000, Journal of Fluid Mechanics.

[2]  J. McWilliams.  A demonstration of the suppression of turbulent cascades by coherent vortices in two‐dimensional turbulence , 1990 .

[3]  Roberto Benzi,et al.  On the Statistical Properties of Two-Dimensional Decaying Turbulence , 1987 .

[4]  Sr Saskia Maassen,et al.  Erratum: “Decaying two-dimensional turbulence in square containers with no-slip or stress-free boundaries” [Phys. Fluids 11, 611 (1999)] , 1999 .

[5]  Cardoso,et al.  Experimental study of freely decaying two-dimensional turbulence. , 1991, Physical review letters.

[6]  A. Provenzale,et al.  Velocity Probability Density Functions for Oceanic Floats , 2000 .

[7]  G. Batchelor.  Computation of the Energy Spectrum in Homogeneous Two‐Dimensional Turbulence , 1969 .

[8]  Roberto Benzi,et al.  Self-similar coherent structures in two-dimensional decaying turbulence , 1988 .

[9]  D. Dritschel.  On the persistence of non-axisymmetric vortices in inviscid two-dimensional flows , 1998, Journal of Fluid Mechanics.

[10]  A. Mariotti,et al.  Vortex stripping and the erosion of coherent structures in two‐dimensional flows , 1994 .

[11]  van Gjf Gert-Jan Heijst,et al.  Decaying two-dimensional turbulence in square containers with no-slip or stress-free boundaries , 1999 .

[12]  D. Dritschel.  Vortex properties of two-dimensional turbulence , 1993 .

[13]  P. Bartello,et al.  Self-similarity of decaying two-dimensional turbulence , 1996, Journal of Fluid Mechanics.

[14]  James C. McWilliams,et al.  Axisymmetrization and vorticity-gradient intensification of an isolated two-dimensional vortex through filamentation , 1987, Journal of Fluid Mechanics.

[15]  J. Weiss.  The dynamics of entropy transfer in two-dimensional hydrodynamics , 1991 .

[16]  D. Dritschel.  A general theory for two-dimensional vortex interactions , 1995, Journal of Fluid Mechanics.

[17]  McWilliams,et al.  Evolution of vortex statistics in two-dimensional turbulence. , 1991, Physical review letters.

[18]  J. Pedlosky.  Geophysical Fluid Dynamics , 1979 .

[19]  A. Provenzale,et al.  The velocity distribution of barotropic turbulence , 2000 .

[20]  James C. McWilliams,et al.  The vortices of two-dimensional turbulence , 1990, Journal of Fluid Mechanics.

[21]  D. Martínez,et al.  Decaying, two-dimensional, Navier-Stokes turbulence at very long times , 1991 .

[22]  James C. McWilliams,et al.  Temporal scaling behavior of decaying two‐dimensional turbulence , 1993 .

[23]  Cardoso,et al.  Equilibrium states of two-dimensional turbulence: An experimental study. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  R. Kraichnan.  Inertial Ranges in Two‐Dimensional Turbulence , 1967 .

[25]  R. Benzi,et al.  A physical model for merging in two-dimensional decaying turbulence , 1995 .

[26]  Claude Basdevant,et al.  Vorticity and passive-scalar dynamics in two-dimensional turbulence , 1987, Journal of Fluid Mechanics.

[27]  S. Patarnello,et al.  Intermittency and coherent structures in two-dimensional turbulence , 1986 .

[28]  A. Ōkubo.  Horizontal dispersion of floatable particles in the vicinity of velocity singularities such as convergences , 1970 .

[29]  Roberto Benzi,et al.  The generation of vortices in high‐resolution, two‐dimensional decaying turbulence and the influence of initial conditions on the breaking of self‐similarity , 1989 .