Reduction in the dimensionality of turbulence due to a strong rotation

Hossain, Murshed

doi:10.1063/1.868278

Cited by 51 publications

(44 citation statements)

References 11 publications

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“…2 one notices that, at a fixed value of V ns , increasing the rotation rate makes the vortices polarized, changing the dynamics from three-dimensional to two-dimensional. This reduction of the dimensionality of turbulence has been observed in classical fluid mechanics 31 .…”

Section: Discussionmentioning

confidence: 84%

Instability of vortex array and transitions to turbulence in rotating helium II

et al. 2004

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We consider superfluid helium inside a container which rotates at constant angular velocity and investigate numerically the stability of the array of quantized vortices in the presence of an imposed axial counterflow. This problem was studied experimentally by Swanson et al., who reported evidence of instabilities at increasing axial flow but were not able to explain their nature. We find that Kelvin waves on individual vortices become unstable and grow in amplitude, until the amplitude of the waves becomes large enough that vortex reconnections take place and the vortex array is destabilized. The eventual nonlinear saturation of the instability consists of a turbulent tangle of quantized vortices which is strongly polarized. The computed results compare well with the experiments. Finally we suggest a theoretical explanation for the second instability which was observed at higher values of the axial flow.

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Section: Discussionmentioning

confidence: 84%

Instability of vortex array and transitions to turbulence in rotating helium II

et al. 2004

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“…Therefore, the present theorems effectively say nothing about the validity of the resonant wave theory at high Re, for realistic values of the Rossby number. Since previous numerical simulations of rotating turbulence by Bardina, Ferziger & Rogallo (1985), Bartello, Mètais & Lesieur (1994), Mansour, Cambon & Speziale (1992), Hossain (1994), Smith & Waleffe (1999) have also not verified the predictions of (2.7), its status for turbulent flow has remained unclear.…”

Section: Resonant Wave Theorymentioning

confidence: 99%

“…At each time step, the velocity in Fourier spaceû(k, t) is decomposed into the two helical modes and these two modes are evolved according to Eq.(2.6). The nonlinear term is calculated using the usual pseudospectral method and then projected onto the two helical modes (Smith & Waleffe (1999) Yeung & Zhou (1998) were interested in the dynamics in the range k > k f , while we and others (Smith & Waleffe (1999), Hossain (1994)) focus on the dynamics in the inverse energy cascade range k < k f . We consider a transient flow state, in which rotation is begun after a statistically steady state is reached without rotation.…”

Section: Numerical Simulations and Analysismentioning

confidence: 99%

“…Bartello, Mètais & Lesieur (1994) observed two-dimensional vortices emerging from the three-dimensional flow. Hossain (1994) showed that the turbulent flow reduced to an approximate two-dimensional state and the energy cascaded to longer length scales in a 128 3 forced simulation. These results are roughly in accord with the wave resonance theory.…”

Section: Introductionmentioning

confidence: 99%

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Resonant interactions in rotating homogeneous three-dimensional turbulence

et al. 2005

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Direct numerical simulations of three-dimensional (3D) homogeneous turbulence under rapid rigid rotation are conducted to examine the predictions of resonant wave theory for both small Rossby number and large Reynolds number. The theory predicts that "slow modes" of the velocity, with zero wavenumber parallel to the rotation axis (k z = 0), will decouple from the remaining "fast modes" and solve an autonomous system of twodimensional (2D) Navier-Stokes equations for the horizontal velocity components, normal to the rotation axis, and a 2D passive scalar equation for the vertical velocity component, parallel to the rotation axis. The Navier-Stokes equation for three-dimensional rotating turbulence is solved in a 128 3 mesh after being diagonalized via "helical decomposition" into normal modes of the Coriolis term. A force supplies constant energy input at intermediate scales. To verify the theory, we set up parallel simulations for the 2D Navier-Stokes equation and 2D passive scalar equation to compare them with the slowmode dynamics of the 3D rotating turbulence. The simulation results reveal that there is a clear inverse energy cascade to the large scales, as predicted by 2D Navier-Stokes equations for resonant interactions of slow modes. As the rotation rate increases, the vertically-averaged horizontal velocity field from 3D Navier-Stokes converges to the velocity field from 2D Navier-Stokes, as measured by the energy in their difference field. Likewise, the vertically-averaged vertical velocity from 3D Navier-Stokes converges to a solution of the 2D passive scalar equation. The slow-mode energy spectrum approaches k, where k h is the horizontal wavenumber, and energy flux becomes closer to constant, as in 2D, the greater the rotation rate. Furthermore, the energy flux directly into small wave numbers in the k z = 0 plane from non-resonant interactions decreases, while fast-mode energy concentrates closer to that plane. The simulations are consistent with an increasingly dominant role of resonant triads for more rapid rotation.

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“…[25][26][27][28][29] Other effects of rotation are two dimensionalization, easily inferred from increased integral length scales along the axis of rotation, and a major reduction of the high wave number part of the radial energy spectrum. It should be emphasized here that most issues discussed so far by numerical studies mainly concern rotating statistically homogeneous turbulence.…”

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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Reduction in the dimensionality of turbulence due to a strong rotation

Cited by 51 publications

References 11 publications

Instability of vortex array and transitions to turbulence in rotating helium II

Instability of vortex array and transitions to turbulence in rotating helium II

Resonant interactions in rotating homogeneous three-dimensional turbulence

Experiments on rapidly rotating turbulent flows

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