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Spectrum of shallow water gravity waves generated by confined two-dimensional turbulence

Claudio Falcón*

Edgar Knobloch†

  • Departamento de Física, Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile, Casilla 487-3, Santiago, Chile, and Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

  • Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA

  • *cfalcon@ing.uchile.cl
  • †knobloch@berkeley.edu
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Phys. Rev. Fluids 3, 094802 – Published 4 September, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.094802

Abstract

We apply Lighthill's theory of aeroacoustic sound generation to shallow water gravity waves generated by spatially confined two-dimensional turbulence. We show that the frequency spectrum of surface waves at large distances from the source of turbulence is, under suitable conditions, proportional to the spatiotemporal spectrum of the energy momentum tensor associated with the turbulent fields acting as the wave source and hence that it follows a power-law behavior. We compute the exponent for shallow water waves generated by isotropic two-dimensional turbulence and show that the integrated power radiated scales as ω−3 when the turbulent fluctuations arise from an inverse energy cascade and as ω−7 when they arise from the enstrophy cascade.

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Phys. Rev. Fluids 3, 094802– Published 4 September, 2018
  • Received 31 August 2017
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