Exact third-order structure functions for two-dimensional turbulence

Jin Han Xie, Oliver Bühler

Research output: Contribution to journalArticlepeer-review


We derive and investigate exact expressions for third-order structure functions in stationary isotropic two-dimensional turbulence, assuming a statistical balance between random forcing and dissipation both at small and large scales. Our results extend previously derived asymptotic expressions in the enstrophy and energy inertial ranges by providing uniformly valid expressions that apply across the entire non-dissipative range, which, importantly, includes the forcing scales. In the special case of white noise in time forcing this leads to explicit predictions for the third-order structure functions, which are successfully tested against previously published high-resolution numerical simulations. We also consider spectral energy transfer rates and suggest and test a simple robust diagnostic formula that is useful when forcing is applied at more than one scale.

Original languageEnglish (US)
Pages (from-to)672-686
Number of pages15
JournalJournal of Fluid Mechanics
StatePublished - Sep 25 2018


  • homogeneous turbulence
  • isotropic turbulence
  • turbulence theory

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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