Two-dimensional isotropic inertia-gravity wave turbulence

Jin Han Xie, Oliver Bühler

Research output: Contribution to journalArticlepeer-review


We present an idealized study of rotating stratified wave turbulence in a two-dimensional vertical slice model of the Boussinesq equations, focusing on the peculiar case of equal Coriolis and buoyancy frequencies. In this case the fully nonlinear fluid dynamics can be shown to be isotropic in the vertical plane, which allows the classical methods of isotropic turbulence to be applied. Contrary to ordinary two-dimensional turbulence, here a robust downscale flux of total energy is observed in numerical simulations that span the full parameter regime between Ozmidov and forcing scales. Notably, this robust downscale flux of the total energy does not hold separately for its various kinetic and potential components, which can exhibit both upscale and downscale fluxes, depending on the parameter regime. Using a suitable extension of the classical Kármán-Howarth-Monin equation, exact expressions that link third-order structure functions and the spectral energy flux are derived and tested against numerical results. These expressions make obvious that even though the total energy is robustly transferred downscale, the third-order structure functions are sign indefinite, which illustrates that the sign and the form of measured third-order structure functions are both crucially important in determining the direction of the spectral energy transfer.

Original languageEnglish (US)
Pages (from-to)752-783
Number of pages32
JournalJournal of Fluid Mechanics
StatePublished - Aug 10 2019


  • isotropic turbulence
  • rotating turbulence
  • stratified turbulence

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'Two-dimensional isotropic inertia-gravity wave turbulence'. Together they form a unique fingerprint.

Cite this