Hidden conservation laws in hydrodynamics; energy and dissipation rate fluctuation spectra in strong turbulence

Victor Yakhot, Vladimir Zakharov

Research output: Contribution to journalArticle

28 Scopus citations


The Hamiltonian formulation of hydrodynamics in Clebsch variables is used for construction of a statistical theory of turbulence. The statistics of the Clebsch field is assumed to be close to Gaussian. It is shown that the energy spectrum consists of two ranges with E(k)≈k -5 3 and E(k)≈k-1. The spectrum of the dissipation rate fluctuations has three scaling regimes: Eε{lunate}(k)≈k-1; k -1 3 and k0 at the large, intermediate and small scales, respectively. The origin of the exponential distribution of velocity differences is discussed. The new scaling regime corresponds to a hidden conservation law, discovered in the Clebsch formulation of hydrodynamics. It is shown that viscous effects are responsible for production of the conserved quantity. The theoretical predictions are compared with results of numerical simulations of decaying turbulence.

Original languageEnglish (US)
Pages (from-to)379-394
Number of pages16
JournalPhysica D: Nonlinear Phenomena
Issue number4
StatePublished - Apr 30 1993


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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