Effect of Helicity and Rotation on the Free Decay of Turbulent Flows

Teitelbaum, Tomas; Mininni, Pablo D.

doi:10.1103/physrevlett.103.014501

Cited by 44 publications

(52 citation statements)

References 29 publications

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“…Considering the nonhelical TG flow, the decay seems to follow a power law ∼(t * − t) −1 , after an initial ideal (inviscid) phase. This result is expected on the basis of the slow-down of nonlinear interactions (leading to energy transfer and its decay) because of waves, and a similar power-law decay has already been observed for stratified flows [24], for rotating flows [49], as well as for flows in the presence of a magnetic field [50]. For the ABC stratified flow, the decay of energy is substantially slower, with a power law of −1/3 as opposed to −1.…”

Section: Energy Decaysupporting

confidence: 70%

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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Section: Energy Decaysupporting

confidence: 70%

Helicity dynamics in stratified turbulence in the absence of forcing

et al. 2013

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“…This has been done in various studies over the last decades for homogeneous isotropic turbulence (HIT). Experimentally, the focus of attention was on grid-induced turbulence [8][9][10][11][12][13][14][15], whereas in numerical simulations periodic boundary conditions were used [16][17][18][19]. To what degree the decay of the turbulence depends on the initial conditions [20][21][22] and whether or not it is selfsimilar has controversially been debated [5,11,16,[23][24][25][26][27].…”

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confidence: 99%

Self-similar decay of high Reynolds number Taylor-Couette turbulence

et al. 2016

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We study the decay of high-Reynolds number Taylor-Couette turbulence, i.e. the turbulent flow between two coaxial rotating cylinders. To do so, the rotation of the inner cylinder (Rei = 2×10 6 , the outer cylinder is at rest) is stopped within 12 s, thus fully removing the energy input to the system. Using a combination of laser Doppler anemometry and particle image velocimetry measurements, six decay decades of the kinetic energy could be captured. First, in the absence of cylinder rotation, the flow-velocity during the decay does not develop any height dependence in contrast to the well-known Taylor vortex state. Second, the radial profile of the azimuthal velocity is found to be self-similar. Nonetheless, the decay of this wall-bounded inhomogeneous turbulent flow does not follow a strict power law as for decaying turbulent homogeneous isotropic flows, but it is faster, due to the strong viscous drag applied by the bounding walls. We theoretically describe the decay in a quantitative way by taking the effects of additional friction at the walls into account.Turbulence is a phenomenon far from equilibrium: Turbulent flow is driven in one or the other way by some energy input and at the same time energy is dissipated, predominantly (but not exclusively) at the smaller scales. For statistically stationary turbulence, this balance is reflected in the famous picture of the Richardson-Kolmogorov energy cascade [1,2]. While the driving on large scales clearly is non-universal, depending on the flow geometry and stirring mechanism, the energy dissipation mechanism has been hypothesized to be self-similar [3][4][5][6][7][8].How exactly is the energy taken out of the system? A good way to find out is to turn off the driving and follow the then decaying turbulence, as then all scales are probed during the decay process. This has been done in various studies over the last decades for homogeneous isotropic turbulence (HIT). Experimentally, the focus of attention was on grid-induced turbulence [8][9][10][11][12][13][14][15], whereas in numerical simulations periodic boundary conditions were used [16][17][18][19]. To what degree the decay of the turbulence depends on the initial conditions [20][21][22] and whether or not it is selfsimilar has controversially been debated [5,11,16,[23][24][25][26][27]. We note that for HIT, already from dimensional analysis one obtains power laws for the temporal evolution of the vorticity and kinetic energy in decaying turbulence, namely ω(t) ∝ t −3/2 and k(t) ∝ t −2 , respectively, in good agreement with many measurements [10,12,28]. These scaling laws are also obtained [29] when employing the 'variable range mean field theory' of Ref. [30], developed for HIT. In that way, the late-time behavior, when the flow is already viscosity dominated, can also be calculated, allowing for the calculation of the lifetime of the decaying turbulence [29].However, real turbulence is neither homogeneous nor isotropic, but it has anisotropies and is wall-bounded, with a considerable fraction of the dissipa...

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“…The critical balance with polarization alignment argument presented by Nazarenko and Scheckochihin [27] is an attempt to explain the k −2 ⊥ energy spectra observed in several numerical simulations of rotating turbulence [17,21,22,55]. However, as is evident from Figure 5 and the corresponding sketch in [27], the critical balance with polarization alignment leads to a departure from anisotropy and is a path to the recovery of isotropic scales that are prevalent above the Zeeman wavenumber [23].…”

Section: Hierarchy Of Slow Manifolds In Anisotropic Wave Turbulence Dmentioning

confidence: 94%

Anisotropic Wave Turbulence for Reduced Hydrodynamics with Rotationally Constrained Slow Inertial Waves

Sen

2017

Fluids

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Kinetic equations for rapidly rotating flows are developed in this paper using multiple scales perturbation theory. The governing equations are an asymptotically reduced set of equations that are derived from the incompressible Navier-Stokes equations. These equations are applicable for rapidly rotating flow regimes and are best suited to describe anisotropic dynamics of rotating flows. The independent variables of these equations inherently reside in a helical wave basis that is the most suitable basis for inertial waves. A coupled system of equations for the two global invariants: energy and helicity, is derived by extending a simpler symmetrical system to the more general non-symmetrical helical case. This approach of deriving the kinetic equations for helicity follows naturally by exploiting the symmetries in the system and is different from the derivations presented in an earlier weak wave turbulence approach that uses multiple correlation functions to account for the asymmetry due to helicity. Stationary solutions, including Kolmogorov solutions, for the flow invariants are obtained as a scaling law of the anisotropic wave numbers. The scaling law solutions compare affirmatively with results from recent experimental and simulation data. Thus, anisotropic wave turbulence of the reduced hydrodynamic system is a weak turbulence model for strong anisotropy with a dominant k ⊥ cascade where the waves aid the turbulent cascade along the perpendicular modes. The waves also enable an appropriate closure of the kinetic equation through averaging of their phases.

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Effect of Helicity and Rotation on the Free Decay of Turbulent Flows

Cited by 44 publications

References 29 publications

Helicity dynamics in stratified turbulence in the absence of forcing

Helicity dynamics in stratified turbulence in the absence of forcing

Self-similar decay of high Reynolds number Taylor-Couette turbulence

Anisotropic Wave Turbulence for Reduced Hydrodynamics with Rotationally Constrained Slow Inertial Waves

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