A Hamiltonian formulation for long internal waves

Yuri Lvov, Esteban G. Tabak

Research output: Contribution to journalArticlepeer-review


A novel canonical Hamiltonian formalism is developed for long internal waves in a rotating environment. This includes the effects of background vorticity and shear on the waves. By restricting consideration to flows in hydrostatic balance, superimposed on a horizontally uniform background of vertical shear and vorticity, a particularly simple Hamiltonian structure arises, which can be thought of as describing a nonlinearly coupled infinite collection of shallow water systems. The kinetic equation describing the time evolution of the spectral energy of internal waves is subsequently derived. In the high-frequency limit, the Coriolis effects may be neglected, and a family of stationary Kolmogorov solutions can be found, which includes the Garrett-Munk spectrum of oceanic internal waves.

Original languageEnglish (US)
Pages (from-to)106-122
Number of pages17
JournalPhysica D: Nonlinear Phenomena
Issue number1-2
StatePublished - Aug 1 2004


  • Coriolis effect
  • Hamiltonian formulation
  • Internal wave interactions
  • Internal waves
  • Kolmogorov solution
  • Spectral energy density of internal waves
  • Wave kinetic equation
  • Wave turbulence

ASJC Scopus subject areas

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


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