Decay Of Turbulence Research Articles

Turbulence decay towards the linearly stable regime of Taylor–Couette flow

AbstractTaylor–Couette (TC) flow is used to probe the hydrodynamical (HD) stability of astrophysical accretion disks. Experimental data on the subcritical stability of TC flow are in conflict about the existence of turbulence (cf. Ji et al. (Nature, vol. 444, 2006, pp. 343–346) and Paoletti et al. (Astron. Astroph., vol. 547, 2012, A64)), with discrepancies attributed to end-plate effects. In this paper we numerically simulate TC flow with axially periodic boundary conditions to explore the existence of subcritical transitions to turbulence when no end plates are present. We start the simulations with a fully turbulent state in the unstable regime and enter the linearly stable regime by suddenly starting a (stabilizing) outer cylinder rotation. The shear Reynolds number of the turbulent initial state is up to $Re_s \lesssim 10^5$ and the radius ratio is $\eta =0.714$. The stabilization causes the system to behave as a damped oscillator and, correspondingly, the turbulence decays. The evolution of the torque and turbulent kinetic energy is analysed and the periodicity and damping of the oscillations are quantified and explained as a function of shear Reynolds number. Though the initially turbulent flow state decays, surprisingly, the system is found to absorb energy during this decay.

Radiofrequency plasma stabilization of a low-Reynolds-number channel flow

AbstractThe effects of plasma heating and thermal non-equilibrium on the statistical properties of a low-Reynolds-number ($Re_{\tau } = 49$) turbulent channel flow were experimentally quantified using particle image velocimetry, two-line planar laser-induced fluorescence, coherent anti-Stokes Raman spectroscopy and emission spectroscopy. Tests were conducted at two radiofrequency plasma settings. The nitrogen, in air, was vibrationally excited to $T_{vib} \sim 1240\ \mathrm{K}$ and 1550 K for 150 W and 300 W plasma settings, respectively, while the vibrational temperature of the oxygen and the rotational/translational temperatures of all species remained near room temperature. The peak axial turbulence intensities in the shear layers were reduced by 15 and 30 % in moving across the plasma for the 150 and 300 W cases, respectively. The plasma did not alter the transverse intensities. The Reynolds shear stresses were reduced by 30 and 50 % for the 150 and 300 W cases. The corresponding Reynolds shear stress correlation coefficient was also reduced, which indicates that the large-scale structures were diminished. Finally, the plasma enhanced the turbulence decay in the zero-shear regions, where the power law decay $t^{-1/n}$ exponential factor $n$ decreased from 1.0 to 0.8.

Empirical Correlations for Slightly Heated Decaying Passive-Grid Turbulence

For homogeneous isotropic turbulence approximated by grid turbulence, velocity and temperature fluctuations decay under the effects of viscosity and thermal diffusivity of the fluid. In the self-similar region of grid flow, there is no mean shear and no turbulence production, and the decay rate is well represented by a power law; this is supported by the present measurements in three different grid flows and by previously published data for passive-grid turbulence obtained over different ranges of streamwise distance and/or Reynolds number. The grid flow is slightly heated so that temperature acts as a passive scalar. From dimensional analysis and empirical power-law correlations, relations for basic flow parameters, such as the Kolmogorov, Taylor, and Corrsin microscales, and the Reynolds and Péclet numbers, are established as functions of the normalized streamwise distance downstream of the grid. With these relations, it is possible to determine the flow parameters for a specific passive-grid geometry or, more generally, a specific set of initial conditions.

Wave turbulence in quantum fluids

Wave turbulence (WT) occurs in systems of strongly interacting nonlinear waves and can lead to energy flows across length and frequency scales much like those that are well known in vortex turbulence. Typically, the energy passes although a nondissipative inertial range until it reaches a small enough scale that viscosity becomes important and terminates the cascade by dissipating the energy as heat. Wave turbulence in quantum fluids is of particular interest, partly because revealing experiments can be performed on a laboratory scale, and partly because WT among the Kelvin waves on quantized vortices is believed to play a crucial role in the final stages of the decay of (vortex) quantum turbulence. In this short review, we provide a perspective on recent work on WT in quantum fluids, setting it in context and discussing the outlook for the next few years. We outline the theory, review briefly the experiments carried out to date using liquid H2 and liquid (4)He, and discuss some nonequilibrium excitonic superfluids in which WT has been predicted but not yet observed experimentally. By way of conclusion, we consider the medium- and longer-term outlook for the field.

Dynamics of quantum turbulence of different spectra

Turbulence in a superfluid in the zero-temperature limit consists of a dynamic tangle of quantized vortex filaments. Different types of turbulence are possible depending on the level of correlations in the orientation of vortex lines. We provide an overview of turbulence in superfluid (4)He with a particular focus on recent experiments probing the decay of turbulence in the zero-temperature regime below 0.5 K. We describe extensive measurements of the vortex line density during the free decay of different types of turbulence: ultraquantum and quasiclassical turbulence in both stationary and rotating containers. The observed decays and the effective dissipation as a function of temperature are compared with theoretical models and numerical simulations.

The effects of variable viscosity on the decay of homogeneous isotropic turbulence

In this paper, we investigate the decay of incompressible homogeneous isotropic turbulence in a variable viscosity fluid. The viscosity coefficient is assumed to depend linearly on a scalar, representing either a temperature or a concentration, and obeying a simple advection-diffusion equation. At high Reynolds numbers, Direct Numerical Simulations (DNS) allow us to confirm the validity of Taylor's postulate that the dissipation is independent from the viscosity and its fluctuations. At low Reynolds numbers, we report the presence of extra energy at small scales due to these variable viscosity effects. This implies that the turbulent kinetic energy decreases less rapidly as a function of time in variable viscosity fluids. In order to explain this phenomenon and quantify its importance on the turbulent flow, we propose a statistical approach based on an eddy-damped quasi-normal Markovian (EDQNM) spectral closure which takes into account the nonlinearity introduced by variable viscosity. It is shown that this latter additional term is of constant sign in the energy spectrum equation and reduces the dissipation of the flow as observed. Also, by assuming the dominance of distant interactions between wave numbers, we can propose a simple formula expressing that variable viscosity effects lead to an effective reduction of the mean viscosity proportional to the variance of viscosity fluctuations.

Computational technologies for simulation of complex near-wall turbulent flows using unstructured meshes

The work is devoted to the peculiarities of the implementation of hybrid Reynolds’ Averaged Navier-Stokes equations-Large Eddy Simulation (RANS-LES) approaches of the Detached Eddy Simulation (DES) family for simulation of complex near-wall turbulent flows using unstructured meshes. The problems of determining required geometric characteristics in the mesh nodes and adaptation of hybrid approaches to the used accurate numerical approximation scheme in space are considered. The classic benchmark problem of the decay of homogeneous isotropic turbulence and the results of the computation of a complex turbulent flow near the wall with the presence of flow separation and reattachment are considered to verify the implemented technique and to demonstrate its efficiency.

Decay of turbulence generated by a square-fractal-element grid

AbstractA novel square-fractal-element grid was designed in order to increase the downstream measurement range of fractal grid experiments relative to the largest element of the grid. The grid consists of a series of square fractal elements mounted to a background mesh with spacing$L_0 = 100\, {\rm mm}$. Measurements were performed in the region$3.5 \le x/L_0 \le 48.5$, which represents a significant extension to the$x/L_0 < 20$of previously reported square fractal grid measurements. For the region$x/L_0 \gtrsim 24$it was found that a power-law decay region following$\langle {q}^2 \rangle \sim (x - x_0)^m$exists with decay exponents of$m = -1.39$and$-1.37$at$\mathit{Re}_{L_0} = 57\, 000$and$65\, 000$, respectively. This agrees with decay values previously measured for regular grids ($-1 \gtrsim m \gtrsim -1.4$). The turbulence in the near-grid region,$x/L_0 < 20$, is shown to be inhomogeneous and anisotropic, in apparent contrast with previous fractal grid measurements. Nonetheless, power-law fits to the decay of turbulent kinetic energy in this region result in$m = -2.79$, similar to$m \approx -2.5$recently reported by Valente & Vassilicos (J. Fluid Mech., vol. 687, 2011, pp. 300–340) for space-filling square fractals. It was also found that$C_\epsilon $is approximately constant for$x/L_0 \ge 25$, while it grows rapidly for$x/L_0 < 20$. These results reconcile previous fractal-generated turbulence measurements with classical grid turbulence measurements.

RECONNECTION AND ELECTRON TEMPERATURE ANISOTROPY IN SUB-PROTON SCALE PLASMA TURBULENCE

Turbulent behavior at sub-proton scales in magnetized plasmas is important for a full understanding of the energetics of astrophysical flows such as the solar wind. We study the formation of electron temperature anisotropy due to reconnection in the turbulent decay of sub-proton scale fluctuations using two dimensional, particle-in-cell (PIC) plasma simulations with realistic electron-proton mass ratio and a guide field out of the simulation plane. A fluctuation power spectrum with approximately power law form is created down to scales of order the electron gyroradius. In the dynamic magnetic field topology, which gradually relaxes in complexity, we identify the signatures of collisionless reconnection at sites of X-point field geometry. The reconnection sites are generally associated with regions of strong parallel electron temperature anisotropy. The evolving topology of magnetic field lines connected to a reconnection site allows spatial mixing of electrons accelerated at multiple, spatially separated reconnection regions. This leads to the formation of multi-peaked velocity distribution functions with a strong parallel temperature anisotropy. In a three-dimensional system, supporting the appropriate wave vectors, the multi-peaked distribution functions would be expected to be unstable to kinetic instabilities, contributing to dissipation. The proposed mechanism of anisotropy formation is also relevant to space and astrophysical systems where the evolution of the plasma is constrained by linear temperature anisotropy instability thresholds. The presence of reconnection sites leads to electron energy gain, nonlocal velocity space mixing and the formation of strong temperature anisotropy; this is evidence of an important role for reconnection in the dissipation of turbulent fluctuations.

Numerical investigation on the partial return to isotropy of freely decaying homogeneous axisymmetric turbulence

The return to isotropy of freely decaying homogeneous axisymmetric turbulence is numerically studied using the Eddy-Damped Quasi-Normal Markovian closure. The model, whose classical formulation has been extended to moderately anisotropic flows by Cambon, Jeandel, and Mathieu [“Spectral modelling of homogeneous non-isotropic turbulence,” J. Fluid Mech. 104, 247–262 (1981)], allows for an accurate description of the turbulence decay for very long times. More specifically, the observed results encompass both the high and low Reynolds number asymptotic regimes. Such an analysis escapes both wind tunnel experiments and direct numerical simulations possibilities at the present time. Anisotropy generation mechanisms considered in the present paper do not affect the nature of nonlinear interactions and the related energy cascade mechanisms. Their influence on the decay regime is quantified by the investigation of the features of the initial three dimensional kinetic energy spectrum. The initial anisotropy level is always chosen in agreement with experimental grid turbulence observations. The present results show that the relaxation towards an isotropic state is observed in the inertial range of the energy spectrum E(k, t) during the initial high Reynolds regime, while the large scales conserve the imposed anisotropy level if the permanence of large eddies hypothesis is verified. A direct consequence is that the ratio between axial and transverse kinetic energies γ increases when the low Reynolds asymptotic regime is reached. Saturation effects, i.e., effects related to the boundedness of the physical domain under consideration, are also investigated. Isotropic saturation (same cut off scale in every direction) leads to the relaxation towards a fully isotropic state in all cases, whereas anisotropic saturation (unbounded domain in the axial direction) leads to an amplification of the initial anisotropy.

Evaluation of scale resolving turbulence generation methods for Large Eddy Simulation of turbulent flows

Large Eddy Simulation (LES) has become an attractive simulation method even for technical processes and it usually provides space and time resolved fluctuations of a significant portion of the spectrum. However, in contrast to a RANS simulation an accurate LES requires the definition of suitable initial and boundary conditions, which includes turbulent structures with physically sound spatial and temporal correlations. Such turbulent structures are usually generated artificially at the boundary. Three different algorithms for generating turbulent fluctuations are evaluated in the present work. The investigated methods are Filtered noise [1], Diffused noise [2] and an Inverse Fourier approach [3,4]. These techniques were developed for generating inflow data for LES and have already been used in published research [5–15], e.g. for investigating turbulent combustion processes. In the present work the turbulent statistics i.e. energy spectra and velocity correlations as well as derived quantities such as turbulent kinetic energy and subgrid scale viscosity are investigated in more detail in a comparative fashion for the generated turbulent velocity fields. As a simple test case, the decay of turbulence in a cubical box, is considered here to provide information on the initially generated turbulence as well as its temporal evolution. The results are analyzed in detail and are compared to experimental data. Turbulence fluctuations generated by Filtered noise and Diffused noise lead to similar results. The resulting energy spectra and velocity correlations agree generally well with experimental data despite some discrepancies at very early times after initialization. The Inverse Fourier approach yielded good agreement at all times, but at increased computational cost. In addition, the implementation of Filtered noise and Diffused noise might be easier for most cases of practical interest. In particular, the Diffused noise approach can be used for the generation of inhomogeneous turbulence on arbitrary grids.

Weighted Non-linear Compact Schemes for the Direct Numerical Simulation of Compressible, Turbulent Flows

A new class of compact-reconstruction weighted essentially non-oscillatory (CRWENO) schemes were introduced (Ghosh and Baeder in SIAM J Sci Comput 34(3): A1678---A1706, 2012) with high spectral resolution and essentially non-oscillatory behavior across discontinuities. The CRWENO schemes use solution-dependent weights to combine lower-order compact interpolation schemes and yield a high-order compact scheme for smooth solutions and a non-oscillatory compact scheme near discontinuities. The new schemes result in lower absolute errors, and improved resolution of discontinuities and smaller length scales, compared to the weighted essentially non-oscillatory (WENO) scheme of the same order of convergence. Several improvements to the smoothness-dependent weights, proposed in the literature in the context of the WENO schemes, address the drawbacks of the original formulation. This paper explores these improvements in the context of the CRWENO schemes and compares the different formulations of the non-linear weights for flow problems with small length scales as well as discontinuities. Simplified one- and two-dimensional inviscid flow problems are solved to demonstrate the numerical properties of the CRWENO schemes and its different formulations. Canonical turbulent flow problems--the decay of isotropic turbulence and the shock-turbulence interaction--are solved to assess the performance of the schemes for the direct numerical simulation of compressible, turbulent flows.

An adaptive numerical method for solving EDQNM equations for the analysis of long-time decay of isotropic turbulence

A new numerical formulation for the Eddy-Damped Quasi-Normal Markovian (EDQNM) model is proposed in the present paper. This formulation is based on an adaptive procedure that progressively modifies the spectral mesh at the large scales, forcing a resolution requirement set by the user.The resulting adaptive numerical method for the EDQNM model has been systematically tested by comparison with the classical model, covering a wide range of initial conditions. In particular, the sensitivity of the results to the initial Reynolds number Reλ and to the slope of the energy spectrum at the large scales σ (E(k→0)∝kσ) has been investigated. For all the initial conditions prescribed, the adaptive numerical method recovers exactly the same solution of the classical version. This result has been observed in the analysis of the main statistical quantities of interest, such as the turbulent kinetic energy K and the energy dissipation rate ε. The same conclusions have been drawn by the direct comparison of the energy spectra E.An extension of the adaptive numerical method for the analysis of sheared/rotating turbulence is as well proposed and successfully assessed.The numerical algorithm proves to be progressively more efficient when long-time simulations are performed. In particular, a reduction up to one order of magnitude in the computational resources required is observed. Due to its efficiency and precision, the adaptive formulation of the EDQNM model promises to be an optimal tool to be blended with the methods of the Uncertainty Quantification (UQ) theory, in order to provide new insights about isotropic turbulence decay.

Application of Millionschikov's hypothesis to homogeneous and isotropic turbulence possessing helicity

In this manuscript we construct a deductive theory for the stationary homogeneous turbulence, which is invariant under translations and rotations but lacks reflexional symmetry, considering the appropriate forms for the second- and third-order correlation functions. Appropriate invariant forms are considered for some second and third order correlation tensors, formed from the fluctuating components of velocity, acceleration, components of external force and pressures. In the light of the formulation of Millionschikov’s hypothesis we would point out further the treatment of first author [4] on the final period decay of isotropic turbulence using the points-merging technique employed here. We include also some enlightments of the process of future work that could be undertaken in this field of research.

S0510104 フラクタル格子のマルチスケール的要素による後流乱流の空間発展と減衰特性([S051-01]噴流,後流およびはく離流れ現象の探求と先端的応用(1),流体工学部門)

S0510104 フラクタル格子のマルチスケール的要素による後流乱流の空間発展と減衰特性([S051-01]噴流,後流およびはく離流れ現象の探求と先端的応用(1),流体工学部門)

Near-wake characteristics of a model horizontal axis tidal stream turbine

The results of a detailed experimental investigation of the near-wake (up to seven turbine diameters downstream) of a model horizontal axis tidal turbine (HATT) device in a large-scale recirculating water channel facility are reported. An Acoustic Doppler Velocimeter is used to provide detailed three-dimensional mean and turbulent flow field information at five different depths across the full width of the channel downstream of the turbine, giving the most complete three-dimensional velocities and Reynolds normal and shear stress data set yet available. In addition the Reynolds-stress anisotropy tensor is used to illustrate the degree of anisotropy of the Reynolds stress within the turbine's wake. These results reveal the strongly anisotropic nature of the near-wake turbulence suggesting isotropic turbulence models should not be used to model near-wake dynamics. Finally the power-law decay rates of the maximum normalised turbulent kinetic energy differ significantly from those found downstream of grids, meshes or perforated disks, suggesting that previous modelling approaches, which neglected swirl effects and modelled the turbine by absorption discs, may significantly over predict the turbulent kinetic energy decay rate of HATT wakes.

Direct numerical simulation of turbulent liquid metal flow entering a magnetic field

This paper presents direct numerical simulations (DNS) of fully developed turbulent liquid-metal flow in a circular duct entering a magnetic field. The case of a magnetohydrodynamic flow leaving a strong magnetic field has been extensively studied experimentally and numerically owing to its similarity to typical flow configurations appearing in liquid metal blankets of nuclear fusion reactors. Although also relevant to the design of fusion reactor blankets, the flow entering the fringing field of a magnet remains unexplored because its high intricacy precludes any simplification of the governing equations. Indeed, the complexity of the magnetohydrodynamic–turbulence interaction can only be analysed by direct numerical simulations or experiments. With that purpose, this paper addresses the case of a fully developed turbulent flow (Reτ≈520) entering low, intermediate and strong magnetic fields under electrically insulating and poorly conducting walls by means of three-dimensional direct numerical simulations. Purely hydrodynamic computations (without the effect of the magnetic field) reveal an excellent agreement against previous experimental and numerical results. Current MHD results provide a very detailed information of the turbulence decay and reveal new three-dimensional features related to liquid-metal flow entering strong increasing magnetic fields, such as flow instabilities due to the effect of the Lorentz forces within the fringing region at high Ha numbers.

Decay of the vortex tangle at zero temperature and quasiclassical turbulence

We review and analyze a series of works, both experimental and numerical and theoretical, dealing with the decay of quantum turbulence at zero temperature. Free decay of the vortex tangle is a key argument in favor of the idea that a chaotic set of quantum vortices can mimic classical turbulence, or at least reproduce many of the basic features. The corresponding topic is referred as the quasiclassical turbulence. Appreciating significance of the challenging problem of classical turbulence it can be expressed that the idea to study it in terms of quantized line is indeed very important and may be regarded as a breakthrough. For this reason, the whole theory, together with the supporting experimental results and numerical simulations should be carefully scrutinized. One of the main arguments, supporting the idea of quasiclassical turbulence is the fact that vortex tangle decays at zero temperature, when the mutual friction is absent. Since all other possible mechanisms of dissipation of the vortex energy, discussed in literature, are related to the small scales, it is natural to suggest that the Kolmogorov cascade takes place with the flow of the energy in space of scales, just like as in the classical turbulence. In the present work we discuss an alternative mechanism of decay of the vortex tangle, which is not associated with dissipation at small scales. This mechanism is a diffusive-like spreading of the vortex tangle due to evaporation of small vortex loops. We discuss a number of experiments and numerical simulations, considering them from the point of view of alternative mechanism.

Simulation and modeling of turbulence subjected to a period of uniform plane strain

Direct numerical simulation is used to evaluate the effect of plane strain on isotropic homogeneous turbulence. The subsequent return to isotropy after the removal of the strain is also investigated. Large, moderate, and small strain rates are computed at moderate turbulence Reynolds numbers. The initial turbulence is generated via mechanical mixing so that the large scale turbulence develops relatively naturally. Turbulence length scales, Reynolds numbers, decay rates, and anisotropy are computed over the range of the simulations, with the goal of quantifying how anisotropic decay behaves. The simulations indicate that large scale anisotropy may not decay to zero at very large times. In agreement with experimental data, the presence of a recovery region is discerned before the return process is observed. Trajectory crossing is observed on the anisotropy invariant map indicating that anisotropy itself is not sufficient to determine its time evolution. Model constants for classic return-to-isotropy models are determined from the data and shown to vary with time. The oriented-eddy collision model [M. B. Martell and J. B. Perot, “The oriented-eddy collision turbulence model,” Flow, Turbul. Combust. 89(3), 335 (2012)], which includes turbulent structure information, is shown to predict the salient structure of the straining and return process.

Flow and Mixing Pattern of Transverse Turbulent Jet in Venturi-Jet Mixer

In this paper, computational simulations of three dimensional flow mixing process of turbulent jet with crossflow in a venturi-jet mixer using a standard Computational Fluid Dynamics solver is presented. In addition to the prediction of velocity and pressure fields, the turbulent intensity, concentration decay and mixture parameter using tracer (suction fluid) spatial distributions in the downstream distances from the jet injection point are obtained numerically to deduce certain design information related to the orientation and position of the jet in the mixer. The jet injection angle (θ o ) is varied from 45° to 135° and Reynolds number (Re) is set in the range of 32,000–51,000. A jet centreline trajectory is traced based on maximum concentration values of tracer along the flow field for the theoretical cases and compared with previously published trajectory correlation of the author. A reasonable agreement was indicated between both traces. Also a comparison of numerical results and measured data for flow mixing process in the venturi-jet mixer is made to check the results of numerical simulations.