The role of sign indefinite invariants in shaping turbulent cascades

Abstract

We highlight a non-canonical yet natural choice of variables for an efficient derivation of a kinetic equation for the energy density in non-isotropic systems, including internal gravity waves on a vertical plane, inertial and Rossby waves. The existence of a second quadratic invariant simplifies the kinetic equation and leads to extra conservation laws for resonant interactions. We analytically determine the scaling of the radial turbulent energy spectrum. Our findings suggest the existence of an inverse energy cascade of internal gravity waves, from small to large scales, in practically relevant scenarios.

References in corpus (4)

• Hamiltonian formalism and the Garrett-Munk spectrum of internal waves in the ocean
• Rossby and Drift Wave Turbulence and Zonal Flows: the Charney-Hasegawa-Mima model and its extensions
• Dynamical Scaling and the Finite Capacity Anomaly in 3-Wave Turbulence
• Internal gravity waves in stratified flows with and without vortical modes

Cited by in corpus (3)

• On the kinetics of internal gravity waves beyond the hydrostatic regime
• Turbulent spectrum of 2D internal gravity waves
• 2D Internal Gravity Wave Turbulence