The decay of turbulence in rotating flows

Teitelbaum, Tomas; Mininni, Pablo D.

doi:10.1063/1.3592325

Cited by 23 publications

(30 citation statements)

References 54 publications

(119 reference statements)

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“…We believe this may be the first evidence that the p/2 'conjecture' is checked for p = 2. Results from experiment [38] and DNS (see [6,39,40], among others) are not so simple. Seiwert et al [38] found ζ 2 = 1. with r = r ⊥ separated in the direction normal to the axis of rotation, whereas the energy spectrum is measured from fast Fourier transform of transverse velocity signals.…”

Section: Typical Flow Cases: Rotating Turbulence Qs-mhd Jet 41 Romentioning

confidence: 85%

Third-order statistics and the dynamics of strongly anisotropic turbulent flows

Cambon

Danaila

Godeferd

et al. 2013

Journal of Turbulence

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Anisotropy is induced by body forces and/or mean large-scale gradients in turbulent flows. For flows without energy production, the dynamics of second-order velocity or second-order vorticity statistics are essentially governed by triple correlations, which are at the origin of the anisotropy that penetrates towards the inertial range, deeply altering the cascade and the eventual dissipation process, with a series of consequences on the evolution of homogeneous turbulence statistics: in the case of rotating turbulence, the anisotropic spectral transfer slaves the multiscale anisotropic energy distribution; nonlinear dynamics are responsible for the linear growth in terms of t of axial integral length-scales; third-order structure functions, derived from velocity triple correlations, exhibit a significant departure from the 4/5 Kolmogorov law. We describe all these implications in detail, starting from the dynamical equations of velocity statistics in Fourier space, which yield third-order correlations at three points (triads) and allow the explicit removal of pressure fluctuations. We first extend the formalism to anisotropic rotating turbulence with 'production', in the presence of mean velocity gradients in the rotating frame. Second, we compare the spectral approach at three points to the twopoint approach directly performed in physical space, in which we consider the transport of the scalar second-order structure function (δq) 2 . This calls into play componental third-order correlations (δq) 2 δu (r) in axisymmetric turbulence. This permits to discuss inhomogeneous anisotropic effects from spatial decay, shear, or production, as in the central region of a rotating round jet. We show that the above-mentioned important statistical quantities can be estimated from experimental planar particle image velocimetry, and that explicit passage relations systematically exist between one-and two-point statistics in physical and spectral space for second-order tensors, but also sometimes for third-order tensors that are involved in the dynamics.

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Section: Typical Flow Cases: Rotating Turbulence Qs-mhd Jet 41 Romentioning

confidence: 85%

Third-order statistics and the dynamics of strongly anisotropic turbulent flows

Cambon

Danaila

Godeferd

et al. 2013

Journal of Turbulence

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“…The similar decay law found in this paper for ABC-like stratified flows may be due to the fact that, as shown here, the helicity is quasiconserved by the dynamics, due to a cyclostrophic balance, and, thus, leads to the same slow decay. We thus conclude that, for flows with either rotation or stratification, the presence of helicity considerably slows down the energy decay, and measurably so, leading to persistent structures, whereas for the unstratified nonrotating case, helicity delays the onset of the decay but does not alter its rate of decay [51].…”

Section: Energy Decaymentioning

confidence: 96%

“…The slow decay of energy has been observed previously for rotating turbulence in the presence of helicity and the different power laws one may expect have been reviewed for a variety of cases taking into account the invariance of both energy and helicity [51]. A (t * − t) −1/3 law is found on phenomenological grounds for helical rotating flows based on the fact that helicity plays a role in the dynamics: It dominates the energy transfer to small scales and alters the spatial scaling laws for the energy spectra and for higher-order structure functions as well [52,53] (see also Ref.…”

Section: Energy Decaymentioning

confidence: 98%

Helicity dynamics in stratified turbulence in the absence of forcing

et al. 2013

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A numerical study of decaying stably stratified flows is performed. Relatively high stratification (Froude number ≈ 10 −2 -10 −1 ) and moderate Reynolds (Re) numbers (Re ≈ 3-6 × 10 3 ) are considered and a particular emphasis is placed on the role of helicity (velocity-vorticity correlations), which is not an invariant of the nondissipative equations. The problem is tackled by integrating the Boussinesq equations in a periodic cubical domain using different initial conditions: a nonhelical Taylor-Green (TG) flow, a fully helical Beltrami [ArnoldBeltrami-Childress (ABC)] flow, and random flows with a tunable helicity. We show that for stratified ABC flows helicity undergoes a substantially slower decay than for unstratified ABC flows. This fact is likely associated to the combined effect of stratification and large-scale coherent structures. Indeed, when the latter are missing, as in random flows, helicity is rapidly destroyed by the onset of gravitational waves. A type of large-scale dissipative "cyclostrophic" balance can be invoked to explain this behavior. No production of helicity is observed, contrary to the case of rotating and stratified flows. When helicity survives in the system, it strongly affects the temporal energy decay and the energy distribution among Fourier modes. We discover in fact that the decay rate of energy for stratified helical flows is much slower than for stratified nonhelical flows and can be considered with a phenomenological model in a way similar to what is done for unstratified rotating flows. We also show that helicity, when strong, has a measurable effect on the Fourier spectra, in particular at scales larger than the buoyancy scale, for which it displays a rather flat scaling associated with vertical shear, as observed in the planetary boundary layer.

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“…4 for freely decaying turbulence in experiments [32,33,64] and direct numerical simulations [61,65], but also in forced rotating turbulence at various resolutions [57,59]. The quantitative statistical characterization of the elongation of structures can be done using the length scales associated with directional two-point velocity correlations…”

Section: Columnar Structures and Quasi-two-dimensionalization In Rotamentioning

confidence: 99%

Structure and Dynamics of Rotating Turbulence: A Review of Recent Experimental and Numerical Results

Godeferd

Moisy

2015

Applied Mechanics Reviews

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Rotating turbulence is a fundamental phenomenon appearing in several geophysical and industrial applications. Its study benefited from major advances in the recent years, but also raised new questions. We review recent results for rotating turbulence, from several numerical and experimental researches, and in relation with theory and models, mostly for homogeneous flows. We observe a convergence in the statistical description of rotating turbulence from the advent of modern experimental techniques and computational power that allows to investigate the structure and dynamics of rotating flows at similar parameters and with similar description levels. The improved picture about the anisotropization mechanisms, however, reveals subtle differences in the flow conditions, including its generation and boundary conditions, which lead to separate points of view about the role of linear mechanisms-the Coriolis force and inertial waves-compared with more complex nonlinear triadic interactions. This is discussed in relation with the most recent diagnostic of dynamical equations in physical and spectral space.

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The decay of turbulence in rotating flows

Cited by 23 publications

References 54 publications

Third-order statistics and the dynamics of strongly anisotropic turbulent flows

Third-order statistics and the dynamics of strongly anisotropic turbulent flows

Helicity dynamics in stratified turbulence in the absence of forcing

Structure and Dynamics of Rotating Turbulence: A Review of Recent Experimental and Numerical Results

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