Quantifying resonant and near-resonant interactions in rotating turbulence

Abstract

Nonlinear triadic interactions are at the heart of our understanding of turbulence. In flows where waves are present modes must not only be in a triad to interact, but their frequencies must also satisfy an extra condition: the interactions that dominate the energy transfer are expected to be resonant. We derive equations that allow direct measurement of the actual degree of resonance of each triad in a turbulent flow. We then apply the method to the case of rotating turbulence, where eddies coexist with inertial waves. We show that for a range of wave numbers, resonant and near-resonant triads are dominant, the latter allowing a transfer of net energy towards two-dimensional modes that would be inaccessible otherwise. The results are in good agreement with approximations often done in theories of rotating turbulence, and with the mechanism of parametric instability proposed to explain the development of anisotropy in such flows. We also observe that, at least for the moderate Rossby numbers studied here, marginally near-resonant and non-resonant triads play a non-negligible role in the coupling of modes.

References in corpus (5)

• Nonlocal resonances in weak turbulence of gravity-capillary waves
• Exact two-dimensionalization of rapidly rotating large-Reynolds-number flows
• Scaling and energy transfer in rotating turbulence
• Rotating Taylor-Green Flow
• Investigation of resonances in gravity-capillary wave turbulence

Cited by in corpus (10)

• Condensates in rotating turbulent flows
• Inverse cascades and resonant triads in rotating and stratified turbulence
• Near-resonant instability of geostrophic modes: beyond Greenspan's theorem
• Direct Evidence of a Dual Cascade in Gravitational Wave Turbulence
• On the inverse energy transfer in rotating turbulence
• Statistics of incompressible hydrodynamic turbulence: an alternative approach
• Complete Hamiltonian formalism for inertial waves in rotating fluids
• Direct measurement of energy transfer in strongly driven rotating turbulence
• Geophysical flows over topography, a playground for laboratory experiments
• The stability of propagating plane inertial waves in rotating fluids