Variable energy flux in turbulence

Mahendra K. Verma

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


In three-dimensional hydrodynamic turbulence forced at large length scales, a constant energy flux Πu flows from large scales to intermediate scales, and then to small scales. It is well known that for multiscale energy injection and dissipation, the energy flux Πu varies with scales. In this review we describe this principle and show how this general framework is useful for describing a variety of turbulent phenomena. Compared to Kolmogorov's spectrum, the energy spectrum steepens in turbulence involving quasi-static magnetofluid, Ekman friction, stable stratification, magnetohydrodynamics, and solution with dilute polymer. However, in turbulent thermal convection, in unstably stratified turbulence such as Rayleigh–Taylor turbulence, and in shear turbulence, the energy spectrum has an opposite behaviour due to an increase of energy flux with wavenumber. In addition, we briefly describe the role of variable energy flux in quantum turbulence, in binary-fluid turbulence including time-dependent Landau–Ginzburg and Cahn–Hillianrd equations, and in Euler turbulence. We also discuss energy transfers in anisotropic turbulence.
Original languageEnglish (US)
Pages (from-to)013002
Issue number1
StatePublished - Dec 9 2021
Externally publishedYes

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Modeling and Simulation
  • Mathematical Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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