We present direct numerical simulations of statistically homogeneous, freely decaying, rotating turbulence in which the Rossby number, Ro = u⊥/2Ωℓ⊥, is of order unity. This is the regime normally encountered in laboratory experiments. The initial condition consists of fully developed turbulence in which Ro is sufficiently high for rotational effects to be weak. However, as the kinetic energy falls, so also does Ro, and quite quickly, we enter a regime in which the Coriolis force is relatively strong and anisotropy grows rapidly, with ℓ⊥ ≪ ℓ∥. This regime occurs when Ro ∼ 0.4 and is characterised by an almost constant perpendicular integral scale, ℓ⊥ ∼ constant, a rapid linear growth in the integral scale parallel to the rotation axis, ℓ∥ ∼ ℓ⊥Ωt, and a slow decline in the value of Ro. We observe that the rate of dissipation of energy scales as ε ∼ u3/ℓ∥ and that both the perpendicular and parallel energy spectra exhibit a k−5/3 inertial range; Ek⊥∼ε2/3k⊥−5/3 and Ek∥∼ε2/3k∥−5/3. We show that these power-law spectra have nothing to do with Kolmogorov’s theory, since the equivalent non-rotating turbulence, which has the same initial condition and Reynolds number, does not exhibit a k−5/3 inertial range, the Reynolds number being too low. Nor are the spectra a manifestation of traditional critical balance theory, as this requires ε ∼ u3/ℓ⊥. We develop a phenomenological theory of the inertial range that assumes that the observed linear growth in anisotropy, ℓ∥/ℓ⊥ ∼ Ωt, also occurs on a scale-by-scale basis most of the way down to the Zeman scale, the linear growth in ℓ∥ being a consequence of inertial wave propagation. Below the Zeman scale, however, inertial waves cannot propagate, and so there is necessarily a transition in spectral behaviour around this scale. The observed spectra are consistent with the predictions of our phenomenological theory.

Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractThis paper presents some of the principal findings of an experimental investigation of forced statistically steady turbulence in a rapidly rotating background.The experiment is conducted in a large cylindrical mixing tank and bulk rotation is produced by two large co-rotating impellers installed near the top and the bottom of the tank. The mean flow motion generated in such a configu- the fluctuating vorticity. It is found that skewness is not a monotonic function of Ro; in this particular experimental arrangement, symmetry is broken to a maximum extent at Ro∼ 1.5 based on velocity length scale. Turbulence quantities are also computed along with the turbulent energy dissipation, which is estimated using velocity structure functions and lends support to previous findings that purport that dissipation is suppressed in such flows.

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.