Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque G = T/ν² L, where L is the cylinder length, scales with Reynolds number R and gap width η, G = 1.46η^3/2(1 - η)^-7/4 R ^3/2. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: G = 0.50 . These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity fluctuations are also provided. Received 7 June 2001 and Received in final form 7 December 2001     

Density-PDFs and Lagrangian statistics of highly compressible turbulence

In isothermal, highly compressible turbulent flows, density fluctuations follow a log-normal distribution. We establish a connection between these density fluctuations and the probability-density-functions (PDF) of Lagrangian tracer particles advected with the flow. Our predicted particle statistics is tested against large scale numerical simulations, which were performed with 512³ collocation points and 2 million tracer particles integrated over several dynamical times.     

Two-particle dispersion in model two-dimensional velocity fields

We consider two-particle dispersion in a velocity field, where the relative two-point velocity scales according to v ²(r) ∝r ^α and the corresponding correlation time scales as τ(r) ∝r ^β, and fix α = 2/3, as typical for turbulent flows. We show that two generic types of dispersion behavior arize: For α/2 + β < 1 the correlations in relative velocities decouple and the diffusion approximation holds. In the opposite case, α/2 + β > 1, the relative motion is strongly correlated. The case of Kolmogorov flows corresponds to a marginal, nongeneric situation. In this case, depending on the particular parameters of the flow, the dispersion behavior can be rather diffusive or rather ballistic. Received 13 March 2001     

A stochastic model of torques in von Karman swirling flow

A stochastic model is derived to predict the turbulent torque produced by a swirling flow. It is a simple Langevin process, with a colored noise. Using the unified colored noise approximation, we derive analytically the PDF of the fluctuations of injected power in two forcing regimes: constant angular velocity or constant applied torque. In the limit of small velocity fluctuations and vanishing inertia, we predict that the injected power fluctuates twice less in the case of constant torque than in the case of constant angular velocity forcing. The model is further tested against experimental data in a von Karman device filled with water. It is shown to allow for a parameter-free prediction of the PDF of power fluctuations in the case where the forcing is made at constant torque. A physical interpretation of our model is finally given, using a quasi-linear model of turbulence.Received: 29 January 2004, Published online: 18 June 2004PACS: 47.27.-i Turbulent flows, convection, and heat transfer - 47.27.Eq Turbulence simulation and modeling     

An analysis of the destabilizing curvature effects on the turbulent flow over a rotating cylinder

An analysis based on the available experimental data and second-order closures is made for a turbulent shear flow over a rotating cylinder in a quiescent fluid. The near-wall behaviour of the non-linear model for the pressure-strain correlation proposed by Speziale, Sarkar and Gatski [J. Fluid Mech. 245, 227 (1991)] is enlarged; and the methodology proposed by Lai and So [J. Fluid Mech. 221, 641 (1990)] is adopted to take into account the wall-effects. The radial profile of the curvature parameter, R_s, is examined in connection with the logarithmic law. It is shown that the log-layer is associated to the region where the mean velocity profile, V, is related to the power of the radial distance as Computations reveal that this region corresponds to the state with the most destabilizing curvature effects; which can be chararacterized by the minimum value of the parameter B _c =2R _s (1+2R _s ), and not that one of the parameter B=2R _s (1+2R _s )/(1+R _s )² firstly introduced by Bradshaw [J. Fluid Mech. 36, 171 (1969)] and extensively used to characterize the turbulence structure in curved flows. Received 9 December 1997     

Lattice Boltzmann model for three-dimensional decaying homogeneous isotropic turbulence

We implement a lattice Boltzmann method (LBM) for decaying homogeneous isotropic turbulence based on an analogous Galerkin filter and focus on the fundamental statistical isotropic property. This regularized method is constructed based on orthogonal Hermite polynomial space. For decaying homogeneous isotropic turbulence, this regularized method can simulate the isotropic property very well. Numerical studies demonstrate that the novel regularized LBM is a promising approximation of turbulent fluid flows, which paves the way for coupling various turbulent models with LBM.     

Detecting vorticity filaments using wavelet analysis: About the statistical contribution of vorticity filaments to intermittency in swirling turbulent flows

Swirling turbulent flows display intermittent pressure drops associated with intense vorticity filaments. Using the wavelet transform modulus maxima representation of pressure fluctuations, we propose a method of characterizing these pressure drop events from their time-scale properties. This method allows us to discriminate fluctuations induced by just formed (young) as well as by burst (old) filaments from background pressure fluctuations. The statistical characteristics of these filaments (core size, waiting time) are analyzed in details and compared with previously reported experimental and numerical findings. Their intermittent occurrence is found to be governed by a pure Poisson's law, the hallmark of independent events. Then we apply the wavelet transform modulus maxima (WTMM) method to the background pressure fluctuations. This study reveals that, once removed all the filaments, the “multifractal” nature of pressure fluctuations still persists. This is a clear indication that the statistical contribution of the filaments is not important enough to account for the intermittency phenomenon in turbulents flows. Received 27 July 1998 and Received in final form 23 November 1998     

Scaling in large Prandtl number turbulent thermal convection

We study the scaling properties of heat transfer Nu in turbulent thermal convection at large Prandtl number Pr using a quasi-linear theory. We show that two regimes arise, depending on the Reynolds number Re. At low Reynolds number, NuPr ^-1/2 and Re are a function of RaPr ^-3/2. At large Reynolds number NuPr ^1/3 and RePr are function only of RaPr ^2/3 (within logarithmic corrections). In practice, since Nu is always close to Ra ^1/3, this corresponds to a much weaker dependence of the heat transfer in the Prandtl number at low Reynolds number than at large Reynolds number. This difference may solve an existing controversy between measurements in SF₆ (large Re) and in alcohol/water (lower Re). We link these regimes with a possible global bifurcation in the turbulent mean flow. We further show how a scaling theory could be used to describe these two regimes through a single universal function. This function presents a bimodal character for intermediate range of Reynolds number. We explain this bimodality in term of two dissipation regimes, one in which fluctuation dominate, and one in which mean flow dominates. Altogether, our results provide a six parameters fit of the curve Nu(Ra, Pr) which may be used to describe all measurements at Pr≥0.7. Received 27 February 2002 / Received in final form 29 May 2002 Published online 31 July 2002     

Local multifractal thermodynamics of 3D turbulence

Using results of a direct numerical simulation (DNS) of 3D turbulence we show that the observed generalized scaling (i.e. scaling moments versus moments of different orders) is consistent with a lognormal-like distribution of turbulent energy dissipation fluctuations with moderate amplitudes for all space scales available in this DNS (beginning from the molecular viscosity scale up to largest ones). Local multifractal thermodynamics has been developed to interpret the data obtained using the generalized scaling, and a new interval of space scales with inverse cascade of generalized energy has been found between dissipative and inertial intervals of scales for sufficiently large values of the Reynolds number. Received 21 July 2000     

Dependence of heat transport on the strength and shear rate of prescribed circulating flows

We study numerically the dependence of heat transport on the maximum velocity and shear rate of physical circulating flows, which are prescribed to have the key characteristics of the large-scale mean flow observed in turbulent convection. When the side-boundary thermal layer is thinner than the viscous boundary layer, the Nusselt number (Nu), which measures the heat transport, scales with the normalized shear rate to an exponent 1/3. On the other hand, when the side-boundary thermal layer is thicker, the dependence of Nu on the Peclet number, which measures the maximum velocity, or the normalized shear rate when the viscous boundary layer thickness is fixed, is generally not a power law. Scaling behavior is obtained only in an asymptotic regime. The relevance of our results to the problem of heat transport in turbulent convection is also discussed. Received 28 November 2001 Published online 25 June 2002     

Rotation effect on near-wall turbulence statistics and flow structures

Turbulent flow in an axially rotating pipe, involving complicated physical mecha- nism of turbulence, is a typical problem for the study of rotating turbulent flow. The pipe rotation induces two effects on the flow. One is the stabilizing effect due to the centrifu- gal and Coriolis forces, which accounts for the relaminarization of the turbulence[1—3] and the reduction of the friction coefficient at the pipe wall. The behavior is also related to the wall streaks inclining to the azimuthal di…     

Frequency Response of Near-Wall Coherent Structures to Localized Periodic Blowing and Suction in Turbulent Boundary Layer

We experimentally investigate the frequency response of near-wall coherent structures to localized periodic blow- ing and suction through a spanwise slot in a turbulent boundary layer by changing the frequency of periodic disturbance at similar velocities of free stream. The effects of blowing and suction disturbance on energy redistri- bution, turbulent intensity U^＋ rums over y^＋ and waveforms of phase-averaged velocity during sweeping process are respectively discussed under three frequencies of periodic blowing and suction in near-wall region of turbulent boundary layer, compared with those in a standard turbulent boundary layer. The most effective disturbance frequency is figured out in this system.     

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

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 Ωt 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 two-point 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)²δu?(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.     

On the lower bound of net driving power in controlled duct flows

We examine mathematically the lower bound of the net driving power (i.e., the summation of pumping and actuation powers) of a controlled duct flow under a constant flow rate. The net power in a duct with arbitrary cross-section in the presence of the inertial term, blowing/suction from the wall, and arbitrary body forces can be decomposed into four terms: (1) dissipation due to the velocity profile of the Stokes flow (in other words, pumping power for the Stokes flow); (2) dissipation due to deviation of the mean velocity from the Stokes flow profile; (3) dissipation due to velocity fluctuations; and (4) correlation between the wall-pressure of the Stokes flow and the time-averaged blowing/suction velocity. Of these, the first three terms are shown to be non-negative, while the sign of the fourth term is indefinite. The fourth term vanishes in cases where the duct has a constant-shape cross-section, such as cylindrical pipes and plane channels. Namely, in such cases, the lower bound of net power is exactly given by the dissipation rate (pumping power) of the Stokes flow at the same flow rate.     

Velocity Fluctuations and Transport in the JET Boundary Region

A new approach for turbulent fluxes and _E×B measurements in the bulk plasma is proposed. It is based in the measurement of fluctuations in the phase velocity of fluctuations. The structure of turbulence has been investigated in the JET plasma boundary region with a fast reciprocating Langmuir probe system. Fluctuations in the radial and poloidal phase velocity have been computed from floating potential and ion saturation current measurements. The correlation between density fluctuations and fluctuations in the radial velocity of fluctuations signals show a good agreement with the turbulent transport computed from the correlation between density and poloidal electric field fluctuations. These results suggest that turbulent transport might be computed in the plasma core from measurement of density fluctuations. E×B sheared flows, both constant and varying in time, are close to the critical value to trigger the transition to improve confinement regimes below the power threshold to trigger the formation of transport barriers.     

Direct Numerical Simulation of the Rayleigh-Taylor Instability with the Spectral Element Method

A novel method is proposed to simulate Rayleigh-Taylor instabilities using a specially-developed unsteady three-dimensional high-order spectral element method code. The numerical model used consists of Navier-Stokes equations and a transport-diffusive equation. The code is first validated with the results of linear stability perturbation theory. Then several characteristics of the Rayleigh-Taylor instabilities are studied using this three-dimensional unsteady code, including instantaneous turbulent structures and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that a high-order numerical method should provide the capability of simulating small scale fluctuations of Rayleigh-Taylor instabilities of turbulent flows.     

HL-2A装置中的带状流三维特性研究和探针设计

HL-2A装置边缘等离子体测地声模带状流的三维特征采用外中平面上三组三台阶探针阵列组成具有环向、极向和径向分辨的独特结构的探针系统进行了研究.其中两组具有极向距离为65mm的三台阶5探针阵列组成极向带状流10探针组,另一组电动式带状流6探针阵列与带状流10探针组之间的环向距离为800mm. 此外,采用快速往复气动6探针组研究了磁分界面附近的温度、密度、雷诺协强及其径向分布.在HL-2A装置上同时观测到测地声模带状流(频率f=7kHz)的极向和环向对称性(m≈0,n 关键词： 三台阶式ZF探针 带状流 三维空间结构     

Direct Numerical Simulation of a Spatially Evolving Supersonic Turbulent Boundary Layer at Ma = 6

Direct numerical simulation is carried out for a spatially evolving supersonic turbulent boundary layer at freestream Mach number 6. To overcome numerical instability, the seventh-order WENO scheme is used for the convection terms of Navier-Stokes equations, and fine mesh is adopted to minimize numerical dissipation. Compressibility effects on the near-wall turbulent kinetic energy budget are studied. The cross-stream extended self-similarity and scaling exponents including the near-wall region are studied. In high Mach number flows, the coherence vortex structures are arranged to be smoother and streamwised, and the hair-pin vortices are less likely tO OCCUr.     

Derivation of a Nonlinear Reynolds Stress Model Using Renormalization Group Analysis and Two-Scale Expansion Technique

Adopting Yoshizawa＇s two-scale expansion technique, the fluctuating field is expanded around the isotropic field. The renormalization group method is applied for calculating the covariance of the fluctuating field at the lower order expansion. A nonlinear Reynolds stress model is derived and the turbulent constants inside are evaluated analytically. Compared with the two-scale direct interaction approximation analysis for turbulent shear flows proposed by Yoshizawa, the calculation is much more simple. The analytical model presented here is close to the Speziale model, which is widely applied in the numerical simulations for the complex turbulent flows.