The decay of initially three-dimensional homogeneous turbulence in a rotating frame is experimentally investigated. Turbulence is generated by rapidly towing a grid in a rotating water tank, and the velocity field in a plane perpendicular to the rotation axis is measured by means of particle image velocimetry. During the decay, strong cyclonic coherent vortices emerge, as the result of enhanced stretching of the cyclonic vorticity by the background rotation, and the selective instability of the anticyclonic vorticity by the Coriolis force. This asymmetry towards cyclonic vorticity grows on a time scale ⍀ −1 ͑⍀ is the rotation rate͒, until the friction from the Ekman layers becomes dominant. The energy spectrum perpendicular to the rotation axis becomes steeper as the instantaneous Rossby number Ro = Ј /2⍀ decreases below the value 2 ± 0.5 ͑Ј is the root-mean square of the vertical vorticity͒. The spectral exponent increases in time from its classical Kolmogorov value 5 / 3 up to values larger than 2. Below the threshold Ro Ͻ 2, the velocity derivative skewness decreases as ͉S͉ ϰ Ro , reflecting the inhibition of the energy transfers by the background rotation, with a net inverse energy cascade that develops at large scales.

The effect of a background rotation on the decay of homogeneous turbulence produced by a grid is experimentally investigated. Experiments have been performed in a channel mounted in the large-scale 'Coriolis' rotating platform, and measurements have been carried out in the planes normal and parallel to the rotation axis using particle image velocimetry. After a short period of about 0.4 tank rotation where the energy decays as t −6/5 , as in classical isotropic turbulence, the energy follows a shallower decay law compatible with t −3/5 , as dimensionally expected for energy transfers governed by the linear timescale Ω −1 . The crossover occurs at a Rossby number Ro ≃ 0.25, without noticeable dependence with the grid Rossby number. After this transition, anisotropy develops in the form of vertical layers where the initial vertical velocity remains trapped. These layers of nearly constant vertical velocity become thinner as they are advected and stretched by the large-scale horizontal flow, producing significant horizontal gradient of vertical velocity which eventually become unstable. After the Ro ≃ 0.25 transition, the vertical vorticity field first develops a cyclone-anticyclone asymmetry, reproducing the growth law of the vorticity skewness, S ω (t) ≃ (Ωt) 0.7 , reported by Morize, Moisy & Rabaud [Phys. Fluids 17 (9), 095105 (2005)]. At larger time, however, the vorticity skewness decreases and eventually returns to zero. The present results indicate that the shear instability of the vertical layers contribute significantly to the re-symmetrisation of the vertical vorticity at large time, by re-injecting vorticity fluctuations of random sign at small scales. These results emphasize the importance of the initial conditions in the decay of rotating turbulence.

The energy decay of grid-generated turbulence in a rotating tank is experimentally investigated by means of particle image velocimetry. For times smaller than the Ekman time scale, a range of approximate self-similar decay is found, in the form u2(t)∝t−n, with the exponent n decreasing from 2 to values close to 1 as the rotation rate is increased. Even at very weak rotation rates, rotation is shown to have a strong indirect influence on the decay law, by making the integral length scale to quickly saturate to the experiment size through the propagation of inertial waves. The experimental decay exponents are found in good agreement with the predicted values from a phenomenological model based on the exponent of the energy spectrum, in which both the effects of the rotation and the confinement are taken into account.

We study both experimentally and numerically the steady zonal flow generated by longitudinal librations of a spherical rotating container. This study follows the recent weakly nonlinear analysis of Busse (2010), developed in the limit of small libration frequency -rotation rate ratio, and large libration frequency -spin-up time product. Using PIV measurements as well as results from axisymmetric numerical simulations, we confirm quantitatively the main features of Busse's analytical solution: the zonal flow takes the form of a retrograde solid body rotation in the fluid interior, which does not depend on the libration frequency nor on the Ekman number, and which varies as the square of the amplitude of excitation. We also report the presence of an unpredicted prograde flow at the equator near the outer wall.

We describe a new phenomenon of zonal wind generation by tidal forcing. Following a recent theoretical and numerical analysis [A. Tilgner, Phys. Rev. Lett. 99, 194501 (2007)], we present the first experimental evidence that the nonlinear self-interaction of a tidally forced inertial mode can drive an intense axisymmetric flow in a rotating deformed sphere. Systematic measurements of zonal flows are carried out by an embarked system of particle image velocimetry, allowing the determination of general scaling laws. These results are fully relevant for zonal winds generation in planets and stars, and illustrate a generic mechanism of geostrophic flow generation by periodic forcing.

Abstract

The scaling of the longitudinal velocity structure functions, Sq(r) = |δu(r)| q ∼ r ζq , is analyzed up to order q = 8 in a decaying rotating turbulence experiment from a large Particle Image Velocimetry (PIV) dataset. The exponent of the second-order structure function, ζ2, increases throughout the self-similar decay regime, up to the Ekman time scale. The normalized higher-order exponents, ζq/ζ2, are close to those of the intermittent non-rotating case at small times, but show a marked departure at larger times, on a time scale Ω −1 (Ω is the rotation rate), although a strictly non-intermittent linear law ζq/ζ2 = q/2 is not reached.Whether intermittency of isotropic three-dimensional (3D) turbulence is decreased or even suppressed in the presence of system rotation has recently received a marked interest.1,2 Here, intermittency refers to the anomalous scaling of the structure functions (SF) of order q, S q (r) = |δu(r)| q ∼ r ζq , where δu(x, r) = [u(x + r) − u(x)] · r/r is the longitudinal velocity increment, r an inertial separation normal to the rotation vector Ω and · denotes spatial and ensemble average. A linear variation of the exponents ζ q with the order q is the signature of self-similar (non-intermittent) velocity fluctuations, a situation which is found in the inverse cascade of two-dimensional (2D) turbulence.3 On the other hand, anomalous exponents, ζ q /ζ 2 = q/2, are the landmark of 3D isotropic turbulence. 4,5,6 Based on the qualitative ground that rotating turbulence experiences a partial two-dimensionalization, one may naively expect a reduction or a suppresion of intermittency by comparison with the 3D non-rotating case. More precisely, describing rapidly rotating turbulence in the limit of zero Rossby numbers as a sum of weakly interacting random inertial waves, the vanishing of non-linear effects should lead to a special case of non-intermittent wave turbulence. 7,8Two papers have recently addressed the issue of the scaling of the SF in rotating turbulence with a stationary forcing. The hot-wire measurements of Baroud et al. in a turbulent flow generated by radial jets in a rotating tank showed a transition from an intermittent to a nonintermittent behavior, characterized by a E(k) ∼ k −2 energy spectrum (i.e. ζ 2 = 1) and linear higher-order exponents ζ q = q/2. In a Direct Numerical Simulation (DNS) of rotating turbulence with a large-scale isotropic forcing, Müller and Thiele 2 have observed reduced intermittency, also characterized with ζ 2 1, but higher-order exponents ζ q intermediate between q/2 and the values usually found in classical (intermittent) 3D turbulence. Those observations are in qualitative agreement with the increase of ζ q reported by Simand 9 from hot-wire measurements in the vicinity of a strong vortex, although no clear separation between a constant background rotation and an otherwise homogeneous turbulence advected by the rotation can be defined in this geometry. To date, no theoretical description of the scaling of the anisotropic higher order SF in rotating tu...

Abstract