Upscale transfer of waves in one-dimensional rotating shallow water

Thomas, Jim; Ding, Liuqian

doi:10.1017/jfm.2023.114

Cited by 4 publications

(1 citation statement)

References 81 publications

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“…The paper by Thomas & Ding (2023) thoroughly contributes to this intense scientific activity. It investigates, for the first time by direct numerical integration of the constitutive equations, the upscale transfer of waves in a rotating shallow water (RSW) system.…”

Section: Overviewmentioning

confidence: 95%

Wave turbulence in geophysical flows

Bars

2023

J. Fluid Mech.

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Despite elegant theoretical descriptions and numerous potential applications in nature, the various features of wave turbulence and its associated transfers across scales are still debated. One reason is the difficulty, both experimentally and numerically, of studying a chaotic nonlinear wavy system with sufficient precision, over a sufficient duration, and with sufficient separation between the injection scale, the system scale and the dissipation scale, to dwell in detail on the description of a statistically converged state. The numerical study of Thomas & Ding (J. Fluid Mech., 2023, this issue) sheds new light on one key aspect of this global problem: the upscale transfer of waves in rotating shallow water equations, which is of relevance to atmosphere and ocean dynamics. Their results first confirm the theoretical predictions, with a robust inverse wave cascade, a predominant role of quartic resonances and a slope value of the wave spectrum in agreement with the expected range. But their deeper analysis of the results also highlights some weakness in the theoretical foundations, exhibiting strong intermittency and departure from ideal Gaussian statistics. This work thus calls for improved modelling, acknowledging that important large-scale climatic features could actually result from the piling up of small-scale waves, unresolved by typical Earth system models. Beyond rotating shallow water systems, this study more generically resonates with open questions in the field of wave turbulence and its geophysical applications, including recent research in deep rotating and stably stratified systems.

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Section: Overviewmentioning

confidence: 95%

Wave turbulence in geophysical flows

Bars

2023

J. Fluid Mech.

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Bilinear Form, Bilinear Bäcklund Transformations, Breather and Periodic-Wave Solutions for a (2+1)-Dimensional Shallow Water Equation with the Time-Dependent Coefficients

Feng,

Tian,

Yang

et al. 2023

Qual. Theory Dyn. Syst.

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

Thomas,

Rajpoot,

Gupta

2024

J. Fluid Mech.

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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.

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Upscale transfer of waves in one-dimensional rotating shallow water

Cited by 4 publications

References 81 publications

Wave turbulence in geophysical flows

Wave turbulence in geophysical flows

Bilinear Form, Bilinear Bäcklund Transformations, Breather and Periodic-Wave Solutions for a (2+1)-Dimensional Shallow Water Equation with the Time-Dependent Coefficients

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

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