 Award ID(s):
 1657041
 NSFPAR ID:
 10169196
 Date Published:
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 890
 ISSN:
 00221120
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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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 timedependent vortical flow in producing this effect. Specifically, we apply multiscale 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 constantfrequency surfaces when the mean flow is steady. A selfsimilar random background velocity field is used to show that the magnitude of this frequency diffusion depends nonmonotonically on the time scale of variation of the velocity field. Numerical solutions of the raytracing 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.more » « less

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