2023
DOI: 10.1017/jfm.2022.1073
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Locality of triad interaction and Kolmogorov constant in inertial wave turbulence

Abstract: Using the theory of wave turbulence for rapidly rotating incompressible fluids derived by Galtier (Phys. Rev. E, vol. 68, 2003, 015301), we find the locality conditions that the solutions of the kinetic equation must satisfy. We show that the exact anisotropic Kolmogorov–Zakharov spectrum satisfies these conditions, which justifies the existence of this constant (positive) energy flux solution. Although a direct cascade is predicted in the transverse ( $\perp$ ) and parallel ( … Show more

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“…This solution takes the form , with the wavevector. As recently proved by David & Galtier (2023), this energy spectrum corresponds to a local turbulence (with an inertial range independent of the largest and smallest scale) for which we can also estimate the Kolmogorov constant. The derivation of the kinetic equation of inertial wave turbulence in the general case (without the axisymmetry assumption) is cumbersome and the use of the Hamiltonian formalism does not drastically simplify the calculation (Gelash, L'vov & Zakharov 2017).…”
Section: Introductionsupporting
confidence: 67%
“…This solution takes the form , with the wavevector. As recently proved by David & Galtier (2023), this energy spectrum corresponds to a local turbulence (with an inertial range independent of the largest and smallest scale) for which we can also estimate the Kolmogorov constant. The derivation of the kinetic equation of inertial wave turbulence in the general case (without the axisymmetry assumption) is cumbersome and the use of the Hamiltonian formalism does not drastically simplify the calculation (Gelash, L'vov & Zakharov 2017).…”
Section: Introductionsupporting
confidence: 67%