On the decrease of intermittency in decaying rotating turbulence

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...

Experiments on rapidly rotating turbulent flows

“…Basically, we find C Ϸ 0.64, 0.70, and 0.64 for ⍀ = 1, 5, and 10 rad/s, respectively. The slope C appears to depend weakly on the rotation rate ⍀ for I = 4 A, which might be attributed to the limited range of Re , and the measured values are close to the one observed by Seiwert et al, 24 …”

“…Numerical simulations have shown that the faster growth of certain integral length scales is also related to the inhibited energy cascade. [21][22][23] Among the most recent experimental studies are those by Baroud et al, 13,14 Morize and co-workers, 15,24 and by Davidson an co-workers. 16, 17 Baroud and co-workers studied the flow in a rotating annulus with forcing created by pumping water into ͑out of͒ the annulus through an inner ͑outer͒ ring of holes on the bottom of the annulus.…”

Sign cancellation and scaling in the vertical component of velocity and vorticity in rotating turbulence

“…While there are many tools to characterize intermittency in isotropic and homogeneous flows, its study in anisotropic flows is less developed. Numerical simulations and experiments indicate that rotating turbulence is less intermittent than isotropic and homogeneous turbulence [9,12,[14][15][16]. However, for rotating flows, it has been argued that the observed scaling laws may actually be spurious and the result of applying methods devised for isotropic turbulence to anisotropic flows [17].…”

“…(16). As an example, for run T3, and using the value of h obtained from numerical simulations of nonhelical rotating turbulence (h ≈ 1/2; see [12,13] Leaving aside the fractal dimension, several things are worth pointing out from the values of the cancellation exponent obtained.…”

“…Note that this value is consistent with Eq. (16), assuming that h ≈ 1/3 (as expected for isotropic and homogeneous turbulence), and that the dimension of the structures in the flow is D = 1 (i.e., vortex filaments).…”