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In Sect. 2.1, we apply the universal Hamiltonian formalism to the dynamical description of waves in continuous media. Then, we move from the dynamic description of a wave system to the statistical one. This is done in terms of the mean occupation numbers of waves in the \(\boldsymbol k\) -space. In Sect. 2.2, we derive the wave kinetic equations, which are the main mathematical objects of this book. In Sect. 2.3, we study the general properties of different kinetic equations and derive stationary equilibrium solutions. Section 2.3.3 deals with the general conditions that are necessary for stationary turbulent spectra to exist.

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Dynamics and Statistics of Waves

  • 章节

  • 发表日期：

    2025年

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  • Vladimirs Zakharov,
  • Victor Lvov,
  • Gregory Falkovich

摘要

In Sect. 2.1, we apply the universal Hamiltonian formalism to the dynamical description of waves in continuous media. Then, we move from the dynamic description of a wave system to the statistical one. This is done in terms of the mean occupation numbers of waves in the \(\boldsymbol k\) -space. In Sect. 2.2, we derive the wave kinetic equations, which are the main mathematical objects of this book. In Sect. 2.3, we study the general properties of different kinetic equations and derive stationary equilibrium solutions. Section 2.3.3 deals with the general conditions that are necessary for stationary turbulent spectra to exist.