Are there two regimes in strongly rotating turbulence?

Abstract

We describe numerical experiments of freely decaying, rapidly rotating turbulence in which the Rossby number varies from Ro = O(1) down to Ro ∼ 0.02. Our central premise is that there exists two distinct dynamical regimes; one for Ro > 0.3 → 0.4, which is typical of most laboratory experiments, and another corresponding to Ro < 0.3, which covers most previous numerical studies. The case of Ro > 0.3 → 0.4 is reported in Baqui and Davidson [“A phenomenological theory of rotating turbulence,” Phys. Fluids 27, 025107 (2015)] and is characterised by: (i) a growth of the parallel integral scale according to l|| ∼ l⊥Ωt; (ii) a dissipation law which is quite different from that predicted by weak-turbulence theories, specifically ε = βu3/l|| where the pre-factor β is a constant of order unity; and (iii) an inertial-range energy spectrum for both the parallel and perpendicular wavenumbers which scales as k−5/3, a scaling that has nothing to do with Kolmogorov’s law in non-rotating turbulence. (Here, l|| is the integral length-scale parallel to the rotation vector Ω, l⊥ the integral length-scale perpendicular to Ω, u the integral scale velocity, and ε the viscous dissipation rate per unit mass.) By contrast, in the low-Ro regime, we find that l|| ∼ l⊥Ωt is replaced by l|| ∼ ut and there is no power-law scaling of the inertial range energy spectrum. While the dissipation law ε = βu3/l|| continues to hold at low Ro, at least approximately, the value of β now depends on Ro. It appears, therefore, that the dynamics of these two regimes are very different, and this may help explain why experimentalists and theoreticians sometimes present rather different interpretations of rotating turbulence.