## Abstract

The production of broadband frequency spectra from narrowband wave forcing in geophysical flows remains an open problem. Here we consider a related theoretical problem that points to the role of time-dependent vortical flow in producing this effect. Specifically, we apply multi-scale analysis to the transport equation of wave action density in a homogeneous stationary random background flow under the Wentzel-Kramers-Brillouin approximation. We find that, when some time dependence in the mean flow is retained, wave action density diffuses both along and across surfaces of constant frequency in wavenumber-frequency space; this stands in contrast to previous results showing that diffusion occurs only along constant-frequency surfaces when the mean flow is steady. A self-similar random background velocity field is used to show that the magnitude of this frequency diffusion depends non-monotonically on the time scale of variation of the velocity field. Numerical solutions of the ray-tracing equations for rotating shallow water illustrate and confirm our theoretical predictions. Notably, the mean intrinsic wave frequency increases in time, which by wave action conservation implies a concomitant increase of wave energy at the expense of the energy of the background flow.

Original language | English (US) |
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Article number | 2000837 |

Journal | Journal of Fluid Mechanics |

Volume | 905 |

DOIs | |

State | Published - 2020 |

## Keywords

- internal waves
- waves in random media
- waves in rotating fluids

## ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics