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Wave turbulence in shallow water models.

P Clark di Leoni1, P J Cobelli1, P D Mininni1

  • 1Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IFIBA, CONICET, Cuidad Universitaria, Buenos Aires 1428, Argentina.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
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Summary

This study explores wave turbulence in shallow water using numerical simulations. Results show distinct energy spectra and asymmetric surface height distributions for shallow versus deeper flows, revealing insights into nonlinear wave dynamics.

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Area of Science:

  • Fluid dynamics
  • Wave turbulence
  • Computational physics

Background:

  • Wave turbulence is a key phenomenon in fluid dynamics, governing energy transfer across scales.
  • Shallow water flows exhibit complex nonlinear wave behaviors.
  • Understanding these dynamics is crucial for various geophysical and engineering applications.

Purpose of the Study:

  • To investigate wave turbulence in shallow water flows using numerical simulations.
  • To compare the shallow water and Boussinesq models for simulating these phenomena.
  • To analyze energy spectra, dispersion relations, and surface height distributions.

Main Methods:

  • Numerical simulations employing the shallow water and Boussinesq models.
  • Utilizing periodic grids with up to 2048^2 points for high resolution.
  • Varying Froude, Reynolds, and dispersion numbers to explore different flow regimes.

Main Results:

  • Energy predominantly remains in waves over long simulation times for both models.
  • Shallow flows show nondispersive nonlinear waves with a ~k^-2 potential energy spectrum.
  • Boussinesq flows exhibit dispersive nonlinear waves with a ~k^-4/3 spectrum, consistent with weak turbulence theory.
  • Nonlinear dispersion relations in Boussinesq flows differ from linear ones, showing two branches.
  • Surface height probability density functions are asymmetric, approximated by skewed normal or Tayfun distributions.

Conclusions:

  • The choice of model (shallow water vs. Boussinesq) significantly impacts the observed wave turbulence characteristics.
  • Weak turbulence theory accurately predicts energy spectra for Boussinesq flows.
  • Nonlinear dispersion plays a critical role in deeper water wave dynamics.
  • Asymmetric surface height distributions are a common feature across different shallow water flow regimes.