Scaling in three-dimensional and quasi-two-dimensional rotating turbulent flows

Baroud, Charles N.; Plapp, Brendan B.; Swinney, Harry L.; She, Zhen‐Su

doi:10.1063/1.1577120

Cited by 95 publications

(114 citation statements)

References 25 publications

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“…The hot-wire measurements of Baroud et al 1 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.…”

Section: 8mentioning

confidence: 99%

On the decrease of intermittency in decaying rotating turbulence

2008

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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...

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Section: 8mentioning

confidence: 99%

On the decrease of intermittency in decaying rotating turbulence

2008

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“…Early Lagrangian measurements in grid-generated decaying rotating turbulence were performed using Particle Tracking by Dalziel (1992). Recently, Baroud et al (2003) investigated turbulent water jets in a rotating annulus at Re λ = 360, and found the turbulent flow to be highly intermittent, independently of the Rossby number. Morize, Moisy, and Rabaud recently performed several experiments of decaying rotating turbulence in large and small facilities (Morize et al, 2005, Morize and Moisy, 2006, Moisy et al, 2010, and described in details some aspects of the coupling between the inertial wave pattern and the decaying turbulent field using high-resolution PIV.…”

Section: Chapter 4 Large-scale Eulerian Flow Features In Rotating Turmentioning

confidence: 99%

Table-top rotating turbulence: an experimental insight through particle tracking

Castello

Clercx

Trieling

et al. 2009

Springer Proceedings in Physics

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Experiments on rapidly rotating turbulent flows

et al. 2009

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A novel laboratory experiment for investigating statistically steady rotating turbulence is presented. Turbulence is produced nonintrusively by means of electromagnetic forcing. Depending on the rotation rate the Taylor-based Reynolds number is found to be in the range of 90Շ Re Շ 240. Relevant properties of the turbulence, both with and without rotation, have been quantified with stereoscopic particle image velocimetry ͑SPIV͒. This method enables instantaneous measurement of all three velocity components in horizontal planes at a distance H from the bottom. The root-mean-square turbulent velocity decreases inversely proportional to H in the nonrotating experiments and is approximately constant when background rotation is applied. The integral length scale shows a weak H-dependence in the nonrotating experiments which is presumably due to the spatial extent of the forcing. Based on the behavior of the principal invariants of the Reynolds stress anisotropy tensor, the rotating turbulence has been characterized as a three-dimensional two-component flow. Furthermore, these SPIV measurements provide supporting evidence for ͑i͒ reduction of the dissipation rate, ͑ii͒ suppression of the vertical velocity as compared to the horizontal velocity, and ͑iii͒ increased spatial and temporal correlation of the horizontal velocity components, with the temporal correlation growing ever stronger as the rotation rate is increased. A less commonly known feature of rotating turbulence, quantified here for the first time in a laboratory setting, is the reverse dependence on the rotation rate of the spatial horizontal velocity correlation functions. Another interesting result concerns the linear ͑anomalous͒ scaling of the longitudinal spatial structure function exponents in the presence of rotation, consistent with a study by Baroud et al. ͓Phys. Rev. Lett. 88, 114501 ͑2002͔͒.

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Scaling in three-dimensional and quasi-two-dimensional rotating turbulent flows

Cited by 95 publications

References 25 publications

On the decrease of intermittency in decaying rotating turbulence

On the decrease of intermittency in decaying rotating turbulence

Table-top rotating turbulence: an experimental insight through particle tracking

Experiments on rapidly rotating turbulent flows

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