Energy Spectrum of Quasi-Geostrophic Turbulence

Abstract

We consider the energy spectrum of a quasi-geostrophic model of forced, rotating turbulent flow. We provide a rigorous a priori bound E(k) <= Ck^{-2} valid for wave numbers that are smaller than a wave number associated to the forcing injection scale. This upper bound separates this spectrum from the Kolmogorov-Kraichnan k^{-{5/3}} energy spectrum that is expected in a two-dimensional Navier-Stokes inverse cascade. Our bound provides theoretical support for the k^{-2} spectrum observed in recent experiments.

References in corpus (1)

• Nonsingular Surface-Quasi-Geostrophic Flow

Cited by in corpus (19)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Long time dynamics of forced critical SQG
• Active and passive fields face to face
• Nonlinear transfer and spectral distribution of energy in $\alpha$ turbulence
• Absence of anomalous dissipation of energy in forced two dimensional fluid equations
• A direct approach to nonuniqueness and failure of compactness for the SQG equation
• Experimental Study of Energy Transfer by Inertial Waves During the Build up of Turbulence in a Rotating System
• Global regularity of the three-dimensional fractional micropolar equations
• Effects of anisotropy in geostrophic turbulence
• Direct and inverse cascades in the geodynamo
• Metastability for the dissipative quasi-geostrophic equation and the non-local enhancement
• Holder Continuous Solutions of Active Scalar Equations
• Non-uniqueness in law of three-dimensional magnetohydrodynamics system forced by random noise
• On analyticity up to the boundary for critical quasi-geostrophic equations
• Self-similar solutions to the hypoviscous Burgers and SQG equations at criticality
• Diminishing inverse transfer and non-cascading dynamics in surface quasi-geostrophic turbulence
• Surface Quasi-Geostrophic Equation driven by Space-Time White Noise
• Large-Time Behaviour of Solutions to the Surface Quasi-Geostrophic Equations
• Regularity and blow up for active scalars