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The turbulent cascade of inertia-gravity waves in rotating shallow water

Published online by Cambridge University Press:  25 November 2024

Jim Thomas Open the ORCID record for Jim Thomas [Opens in a new window] ,
Rajendra S. Rajpoot Open the ORCID record for Rajendra S. Rajpoot [Opens in a new window]  and
Prateek Gupta Open the ORCID record for Prateek Gupta [Opens in a new window]
Jim Thomas*
Affiliation:
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India Centre for Applicable Mathematics, Tata Institute of Fundamental Research, Bangalore 560065, India
Rajendra S. Rajpoot
Affiliation:
Centre for Applicable Mathematics, Tata Institute of Fundamental Research, Bangalore 560065, India
Prateek Gupta
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology Delhi, New Delhi 110016, India
*
†Email address for correspondence: jimthomas.edu@gmail.com
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Abstract

In this work we study features of inertia-gravity wave turbulence in the rotating shallow water equations. On examining the dynamics of waves with varying rotation rates, we find that the turbulent cascade of waves is strongest at low rotation rates, forming a $k^{-2}$ energy spectrum, and a rich distribution of shocks in physical space. At high rotation rates, the forward cascade of waves weakens along with a steeper energy spectra and vanishing of shocks in physical space. The wave cascade is seen to be scale-local, resulting in a noticeable time interval for energy to get transferred from domain scale to dissipative scale. Furthermore, we find that the vortical flow has a non-negligible effect on the wave cascade, especially at high rotation rates. The vortical flow assists in the forward cascade of waves and shock formation at high rotation rates, while the waves by themselves in the absence of the vortical flow lack a forward cascade and shock formation at such high rotation rates. On investigating the physical space structures in the vortical flow and their connections to the wave cascade, we find that strain-dominant regions, that are located around the boundaries of coherent vortices, are the physical space regions that contribute majorly to the forward cascade of waves. Our results in general highlight intriguing features of dispersive inertia-gravity wave turbulence that are qualitatively similar to those seen in three-dimensional homogeneous isotropic turbulence and are beyond the predictions of asymptotic resonant wave interaction theory.

JFM classification

Turbulent Flows: Wave-turbulence interactions Geophysical and Geological Flows: Waves in rotating fluids Geophysical and Geological Flows: Shallow water flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1000 , 10 December 2024 , A30
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Copyright
© Jim Thomas, 2024. Published by Cambridge University Press

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