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PreprintarXiv licencearXiv

Kolmogorov scale in turbulence of surface gravity waves

  • Zhou Zhang
  • Yulin Pan
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Abstract

In this paper, we study the analogue of the Kolmogorov scale in surface gravity wave turbulence, characterized by the cutoff wavenumber kc at which the power-law inertial range transitions into the dissipation range. We perform numerical simulations of the primitive dynamical equations with a broad-scale dissipation of magnitude γ0 k2 in spectral space to establish the relation between kc and γ0. Our results show a scaling kc∼γ0β, where β depends on the slope α of the power-law spectrum. We find that β(α) agrees more closely with the prediction obtained by balancing the nonlinear and dissipation terms in the dynamical equations than with that based on the kinetic equation. This observation reveals that non-resonant triad interactions play a more significant role than resonant quartet interactions in the formation of kc.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026kolmogorov,
  title = {{Kolmogorov scale in turbulence of surface gravity waves}},
  author = {Zhou Zhang and Yulin Pan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25600},
  eprint = {2609.25600},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25600},
}
RIS
TY  - UNPB
TI  - Kolmogorov scale in turbulence of surface gravity waves
AU  - Zhou Zhang
AU  - Yulin Pan
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.25600
UR  - https://arxiv.org/abs/2609.25600
AB  - In this paper, we study the analogue of the Kolmogorov scale in surface gravity wave turbulence, characterized by the cutoff wavenumber k_c at which the power-law inertial range transitions into the dissipation range. We perform numerical simulations of the primitive dynamical equations with a broad-scale dissipation of magnitude γ_0 k^2 in spectral space to establish the relation between k_c and γ_0. Our results show a scaling k_c∼γ_0^β, where β depends on the slope α of the power-law spectrum. We find that β(α) agrees more closely with the prediction obtained by balancing the nonlinear and dissipation terms in the dynamical equations than with that based on the kinetic equation. This observation reveals that non-resonant triad interactions play a more significant role than resonant quartet interactions in the formation of k_c.
ER  -