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Intermittency in two-dimensional turbulence with drag.

Yue-Kin Tsang1, Edward Ott, Thomas M Antonsen

  • 1Department of Physics, University of Maryland, College Park, Maryland 20742 USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2005
PubMed
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Linear drag in two-dimensional turbulence causes faster energy decay and intermittent vorticity. This study compares numerical simulations with theory for spectral energy decay and vorticity scaling, revealing insights into turbulence dynamics.

Area of Science:

  • Fluid Dynamics
  • Turbulence Theory
  • Computational Physics

Background:

  • Two-dimensional turbulence exhibits an enstrophy cascade, transferring energy to smaller scales.
  • Linear drag introduces dissipation, altering the energy and vorticity dynamics.
  • Intermittency in turbulent flows signifies deviations from homogeneous and isotropic statistical properties.

Purpose of the Study:

  • To investigate the effects of linear drag on the enstrophy cascade in forced two-dimensional turbulence.
  • To compare numerical simulation results with theoretical predictions for energy spectra and vorticity structure functions.
  • To analyze the multifractal nature of enstrophy dissipation and its relation to turbulence intermittency.

Main Methods:

  • Numerical simulations on a 4096 x 4096 grid to model forced two-dimensional turbulence with linear drag.

Related Experiment Videos

  • Calculation of energy wave-number spectra and vorticity structure functions (zeta(2q)).
  • Theoretical analysis of the multifractal structure (Rényi dimension spectrum D(q)) and probability distribution of vorticity differences.

    • Main Results:

    • Linear drag leads to a faster power-law decay of the energy wave-number spectrum compared to undragged turbulence.
    • Anomalous scaling of vorticity structure functions indicates intermittency in the vorticity field.
    • A relationship between the Rényi dimension spectrum D(q) and vorticity scaling exponents zeta(2q) was derived and validated.
    • Theoretical and numerical results for the probability distribution of vorticity differences were found to be in agreement.

    Conclusions:

    • Linear drag significantly modifies the energy cascade and enhances intermittency in two-dimensional turbulence.
    • The derived relationship between multifractal dimensions and scaling exponents supports a refined similarity hypothesis for this system.
    • The study provides a comprehensive comparison of numerical and theoretical findings, advancing the understanding of dissipative turbulence.