V.E. Zakharov, V. S. L’vov
This chapter focuses on the statistical description of weak wave turbulence, transitioning from dynamic to statistical frameworks to analyze wave behaviors in turbulence. The objective is to determine stationary weak turbulent distributions by outlining a systematic program that encompasses identifying universal solutions of key equations, ensuring locality of interaction in k-space, and verifying the physical realizability of solutions through stability analysis. The methodology includes exploring various kinetic wave equations, including the three-wave and four-wave kinetic equations, while discussing their applicability and general properties, such as conservation laws and thermodynamic equilibrium. The results indicate the need for a stepwise (cascade) transfer of energy across different scales, requiring detailed verification of locality in interactions. Additionally, the findings suggest methods for matching universal solutions with source and sink conditions, ultimately leading to a comprehensive understanding of how weak wave turbulence can be modeled statistically. Furthermore, it highlights the significance of collision integrals and stability in developing these turbulent distributions.
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title={Statistical Description of Weak Wave Tur},
author={V.E. Zakharov and V. S. L’vov},
year={2026},
language={en}
}TY - JOUR TI - Statistical Description of Weak Wave Tur AU - V.E. Zakharov AU - V. S. L’vov PY - 2026 LA - en ER -
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