Skip to main content Accessibility help
×
Home

Entropy budget and coherent structures associated with a spectral closure model of turbulence

  • Rick Salmon (a1)

Abstract

We ‘derive’ the eddy-damped quasi-normal Markovian model (EDQNM) by a method that replaces the exact equation for the Fourier phases with a solvable stochastic model, and we analyse the entropy budget of the EDQNM. We show that a quantity that appears in the probability distribution of the phases may be interpreted as the rate at which entropy is transferred from the Fourier phases to the Fourier amplitudes. In this interpretation, the decrease in phase entropy is associated with the formation of structures in the flow, and the increase of amplitude entropy is associated with the spreading of the energy spectrum in wavenumber space. We use Monte Carlo methods to sample the probability distribution of the phases predicted by our theory. This distribution contains a single adjustable parameter that corresponds to the triad correlation time in the EDQNM. Flow structures form as the triad correlation time becomes very large, but the structures take the form of vorticity quadrupoles that do not resemble the monopoles and dipoles that are actually observed.

Copyright

Corresponding author

Email address for correspondence: rsalmon@ucsd.edu

References

Hide All
Ayala, D., Doering, C. R. & Simon, T. M. 2018 Maximum palinstrophy amplification in the two-dimensional Navier–Stokes equations. J. Fluid Mech. 837, 839857.
Batchelor, G. K. 1969 Computation of the energy spectrum in homogeneous two-dimensional turbulence. Phys. Fluids 12, II-233II-239.
Benzi, R., Patarnello, S. & Santangelo, P. 1988 Self-similar coherent structures in two-dimensional decaying turbulence. J. Phys. A: Math. Gen. 21, 12211237.
Boffetta, G. & Ecke, R. E. 2012 Two-dimensional turbulence. Ann. Rev. Fluid Mech. 44, 427451.
Burgess, B. H., Dritschel, D. G. & Scott, R. K. 2017 Vortex scaling ranges in two-dimensional turbulence. Phys. Fluids 29, 11104.
Carnevale, G. F., Frisch, U. & Salmon, R. 1981 H theorems in statistical fluid dynamics. J. Phys. A: Math. Gen. 14, 17011718.
Carnevale, G. F. 1982 Statistical features of the evolution of two-dimensional turbulence. J. Fluid Mech. 122, 143153.
Eyink, G. L. & Sreenivasan, K. R. 2006 Onsager and the theory of hydrodynamic turbulence. Rev. Mod. Phys. 78, 87135.
Frisch, U., Lesieur, M. & Brissaud, A. 1974 A Markovian random coupling model for turbulence. J. Fluid Mech. 65, 145152.
Kalos, M. H. & Whitlock, P. A. 2008 Monte Carlo Methods, 2nd edn. Wiley.
Kaneda, Y. 2007 Lagrangian renormalized approximation of turbulence. Fluid Dyn. Res. 39, 526551.
Kraichnan, R. H. 1967 Inertial ranges in two-dimensional turbulence. Phys. Fluids 10, 14171423.
Kraichnan, R. H. 1971 An almost-Markovian Galilean-invariant turbulence model. J. Fluid Mech. 47, 513524.
Leith, C. E. 1968 Diffusion approximation for two-dimensional turbulence. Phys. Fluids 11, 671673.
Lesieur, M. 1987 Turbulence in Fluids. Kluwer.
McWilliams, J. C. 1984 The emergence of isolated coherent vortices in turbulent flow. J. Fluid Mech. 146, 2143.
Orszag, S. A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41, 363386.
Salmon, R. 1998 Lectures on Geophysical Fluid Dynamics. Oxford.
Weiss, J. 1991 The dynamics of enstrophy transfer in two-dimensional hydrodynamics. Physica D 48, 273294.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Entropy budget and coherent structures associated with a spectral closure model of turbulence

  • Rick Salmon (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.