Decay Of Turbulence Research Articles

New findings in vorticity dynamics of turbulent buoyant plumes

The vorticity dynamics of turbulent, buoyant, and pure plumes released into the quiescent ambience has been investigated using large-eddy simulations with plume Reynolds number in the range of 6 × 107 to 108. The plume is generated by a circular heat source and sustained by buoyancy forcings generated by heating. As the starting plume rises vertically, it expands radially, entraining ambient fluid into the plume and two distinct stages of evolution are evident. During stage one (initial stage), in the near-source region the plume is accelerating characterized by developing turbulence. During the next stage (mixing stage), the plume is significantly altered by turbulence resulting in significant entrainment and expansion in the radial direction. As turbulent intensities decay during the mixing stage, the enstrophy decays in an exponential manner with height with an exponent of −7/4. The turbulent kinetic energy budget analysis reveals—baroclinic torque, stretching, and compression—as the three dominant mechanisms for the plume growth. The probability distribution function (PDF) of vorticity shows that vorticity is mainly aligned along the transverse direction near the source and slowly reaches to a quasi-isotropy state downstream. Turbulence spectra demonstrate the presence of a buoyancy-regime with a −3 spectral slope. The PDF of vorticity further shows extreme dominance of the strain rate rather than rotation within the plume. Consistent with studies in the literature, the vorticity fluctuations align with the intermediate eigen-vector of strain-rate tensor.

Reconnection-Controlled Decay of Magnetohydrodynamic Turbulence and the Role of Invariants

We present a new theoretical picture of magnetically dominated, decaying turbulence in the absence of a mean magnetic field. We demonstrate that such turbulence is governed by the reconnection of magnetic structures, and not by ideal dynamics, as has previously been assumed. We obtain predictions for the magnetic-energy decay laws by proposing that turbulence decays on reconnection timescales, while respecting the conservation of certain integral invariants representing topological constraints satisfied by the reconnecting magnetic field. As is well known, the magnetic helicity is such an invariant for initially helical field configurations, but does not constrain non-helical decay, where the volume-averaged magnetic-helicity density vanishes. For such a decay, we propose a new integral invariant, analogous to the Loitsyansky and Saffman invariants of hydrodynamic turbulence, that expresses the conservation of the random (scaling as $\mathrm{volume}^{1/2}$) magnetic helicity contained in any sufficiently large volume. Our treatment leads to novel predictions for the magnetic-energy decay laws: in particular, while we expect the canonical $t^{-2/3}$ power law for helical turbulence when reconnection is fast (i.e., plasmoid-dominated or stochastic), we find a shallower $t^{-4/7}$ decay in the slow `Sweet-Parker' reconnection regime, in better agreement with existing numerical simulations. For non-helical fields, for which there currently exists no definitive theory, we predict power laws of $t^{-10/9}$ and $t^{-20/17}$ in the fast- and slow-reconnection regimes, respectively. We formulate a general principle of decay of turbulent systems subject to conservation of Saffman-like invariants, and propose how it may be applied to MHD turbulence with a strong mean magnetic field and to isotropic MHD turbulence with initial equipartition between the magnetic and kinetic energies.

Large-scale characteristics of a stably stratified turbulent shear layer

Implicit large eddy simulation is performed to investigate large-scale characteristics of a temporally evolving, stably stratified turbulent shear layer arising from the Kelvin–Helmholtz instability. The shear layer at late time has two energy-containing length scales: the scale of the shear layer thickness, which characterizes large-scale motions (LSM) of the shear layer; and the larger streamwise scale of elongated large-scale structures (ELSS), which increases with time. The ELSS forms in the middle of the shear layer when the Richardson number is sufficiently large. The contribution of the ELSS to velocity and density variances becomes relatively important with time although the LSM dominate the momentum and density transport. The ELSS have a highly anisotropic Reynolds stress, to a degree similar to the near-wall region of turbulent boundary layers, while the Reynolds stress of the LSM is as anisotropic as in the outer region. Peaks in the spectral energy density associated with the ELSS emerge because of the slow decay of turbulence at very large scales. A forward interscale energy transfer from large to small scales occurs even at a small buoyancy Reynolds number. However, an inverse transfer also occurs for the energy of spanwise velocity. Negative production of streamwise velocity and density spectra, i.e. counter-gradient transport of momentum and density, is found at small scales. These behaviours are consistent with channel flows, indicating similar flow dynamics in the stratified shear layer and wall-bounded shear flows. The structure function exhibits a logarithmic law at large scales, implying a $k^{-1}$ scaling of energy spectra.

Turbulent radiative diffusion and turbulent Newtonian cooling

Radiation transport plays an important role in stellar atmospheres, but the effects of turbulence are being obscured by other effects such as stratification. Using radiative hydrodynamic simulations of forced turbulence, we determine the decay rates of sinusoidal large-scale temperature perturbations of different wavenumbers in the optically thick and thin regimes. Increasing the wavenumber increases the rate of decay in both regimes, but this effect is much weaker than for the usual turbulent diffusion of passive scalars, where the increase is quadratic for small wavenumbers. The turbulent decay is well described by an enhanced Newtonian cooling process in the optically thin limit, which is found to show a weak increase proportional to the square root of the wavenumber. In the optically thick limit, the increase in turbulent decay is somewhat steeper for wavenumbers below the energy-carrying wavenumber of the turbulence, but levels off toward larger wavenumbers. In the presence of turbulence, the typical cooling time is comparable to the turbulent turnover time. We observe that the temperature takes a long time to reach equilibrium in both the optically thin and thick cases, but in the former, the temperature retains smaller scale structures for longer.

Triple Hill’s Vortex Synthetic Eddy Method

The generation of initial or inflow synthetic turbulent velocity or scalar fields reproducing statistical characteristics of realistic turbulence is still a challenge. The synthetic eddy method, previously introduced in the context of inflow conditions for large eddy simulations, is based on the assumption that turbulence can be regarded as a superposition of coherent structures. In this paper, a new type of synthetic eddy method is proposed, where the fundamental eddy is constructed by superposing three Hill's vortices, with their axes orthogonal to each other. A distribution of Hill's vortices is used to synthesize an anisotropic turbulent velocity field that satisfies the incompressibility condition and match a given Reynolds stress tensor. The amplitudes of the three vortices that form the fundamental eddy are calculated from known Reynolds stress profiles through a transformation from the physical reference frame to the principal-axis reference frame. In this way, divergence-free anisotropic turbulent velocity fields are obtained that can reproduce a given Reynolds stress tensor. The model was tested on both isotropic and anisotropic turbulent velocity fields, in the framework of grid turbulence decay and turbulent channel flow, respectively. The transition from artificial to realistic turbulence in the proximity to the inflow boundary was found to be small in all test cases that were considered.

On the numerical accuracy in finite‐volume methods to accurately capture turbulence in compressible flows

AbstractThe goal of the present article is to understand the impact of numerical schemes for the reconstruction of data at cell faces in finite‐volume methods, and to assess their interaction with the quadrature rule used to compute the average over the cell volume. Here, third‐, fifth‐ and seventh‐order WENO‐Z schemes are investigated. On a problem with a smooth solution, the theoretical order of convergence rate for each method is retrieved, and changing the order of the reconstruction at cell faces does not impact the results, whereas for a shock‐driven problem all the methods collapse to first‐order. Study of the decay of compressible homogeneous isotropic turbulence reveals that using a high‐order quadrature rule to compute the average over a finite‐volume cell does not improve the spectral accuracy and that all methods present a second‐order convergence rate. However the choice of the numerical method to reconstruct data at cell faces is found to be critical to correctly capture turbulent spectra. In the context of simulations with finite‐volume methods of practical flows encountered in engineering applications, it becomes apparent that an efficient strategy is to perform the average integration with a low‐order quadrature rule on a fine mesh resolution, whereas high‐order schemes should be used to reconstruct data at cell faces.

Response of turbulent pipe flow to targeted wall shapes at a range of Reynolds numbers

The response and recovery of turbulent pipe flow to three-dimensional perturbed wall changes were examined numerically in a wide range of Reynolds numbers between Re=5×103 and 1.58×105. The perturbations were based on distinct azimuthal Fourier modes corresponding to m = 3, 15, and 3 + 15. The long-lasting response of the flow was examined by characterizing both the mean and turbulent field in the wake of pipe inserts for each Re. The variation of the recovery with increasing Reynolds number revealed an asymptotic behavior for Re≥7.5×104, which scaled with Re4 for both mean velocity and turbulence kinetic energy. Two peaks were observed for the mean velocity along the wake centerline, where the location of peaks followed a power-law trend in the form of Lp/D∝Re4/3, where D is the pipe diameter. A fast decay of turbulence past the wall change further suggested that maximum Reynolds shear stress in the downstream wake decays as (x/D)−1/3 for all Re. The flow also exhibited long-lasting responses that obstructed its relaxation at 20D downstream of the perturbation, even for low Re of 5×103. Overall, the recovery exhibited a second-order response.

Low-Noise Synthetic Turbulence Tailored to Lateral Periodic Boundary Conditions

The present work is dedicated to turbulence synthesis tailored to lateral periodic boundary conditions for direct noise computations through compressible large eddy simulations. Synthetic turbulence can be essential for aeroacoustic applications when computing airfoil turbulent inflow noise or for accurately capturing the behavior of boundary layers. This behavior determines both trailing edge noise and complex flow structures such as laminar separation bubbles. For airfoil simulation purposes, spanwise periodic boundary conditions are usually considered. If synthetic perturbations are injected without observing the periodicity rule, strong spurious pressure waves are emitted and pollute the entire computational domain. In this work, the random Fourier modes method for turbulence generation is adapted in order to respect the spanwise periodicity constraint right at the computational domain inlet. This approach does not affect the turbulence properties such as the spectral shape and the turbulent kinetic energy decay. Since the emphasis is put on the generation and convection of the turbulence, only the turbulence convection region between the inlet and the airfoil is considered in this paper, without the airfoil. Two geometrical configurations are tested: the first one is a simple box with a constant mesh size, and the second one concentrates the fine cells on the area in front of the airfoil. In the second configuration, the computational cost is reduced by up to 25%, but more spurious noise is present because of interpolation areas between different grids using the Chimera method. Finally, the results’ reproducibility is assessed using different turbulence realizations.

Turbulence generation and decay in the Taylor–Couette system due to an abrupt stoppage

Abstract

Simultaneous laser-induced fluorescence and capacitance probe measurement of downwards annular gas-liquid flows

This study focuses on the characterisation of downwards annular gas-liquid (air-water) flows, by employing a combination of advanced laser-based and capacitance-based measurement methods. A variant of laser-induced fluorescence (LIF), referred to as structured-planar laser-induced fluorescence (S-PLIF), eliminates biases commonly encountered during film-thickness measurements of gas-liquid flows, due to refraction and reflection of the light at the interface. A bespoke capacitance probe is also assembled to enable temporally resolved film-thickness measurements with high temporal resolution along the circumferential perimeter of the pipe. We compare the film mean thickness, roughness, and probability density functions obtained with each method. We find that both methods are able to measure time-averaged film thickness to within <20% deviations from each other and from results obtained from the available literature. The resulting probe data suggest a biased (suppressed) standard deviation of the film thickness, which can be attributed to its working principle, i.e., measuring the film thickness averaged along the circumferential perimeter of the pipe. The autocorrelation functions of the time-traces provide an insight into the characteristic time-scales of the interfacial phenomena in these flows, which span a range from ∼10 ms for highly gas-sheared flows and increase to about 30 ms for the smoother falling films. The power spectral densities reveal modal frequencies that start from 2.5 Hz for falling films, and increase with the gas Reynolds number by almost an order of magnitude. The turbulent wave activity (slope in the power spectrum) reduces with a decrease in gas shear, and shows similarities to the decay of homogeneous and isotropic turbulence. The sizes of the bubbles entrained in the liquid film are measured from the S-PLIF images, and exhibit log-normal distribution that become flatter with a decrease in the gas Reynolds number. The normalised location of the bubbles (quantified as the relative entrainment depth, i.e., distance of the bubble from the wall over the local film thickness) follows a Gaussian distribution, with the peaks located between 0.5 and 0.6, indicating that the majority of the bubbles accumulate in the middle of the thin film.

Extended Lattice Boltzmann Model.

Conventional lattice Boltzmann models for the simulation of fluid dynamics are restricted by an error in the stress tensor that is negligible only for small flow velocity and at a singular value of the temperature. To that end, we propose a unified formulation that restores Galilean invariance and the isotropy of the stress tensor by introducing an extended equilibrium. This modification extends lattice Boltzmann models to simulations with higher values of the flow velocity and can be used at temperatures that are higher than the lattice reference temperature, which enhances computational efficiency by decreasing the number of required time steps. Furthermore, the extended model also remains valid for stretched lattices, which are useful when flow gradients are predominant in one direction. The model is validated by simulations of two- and three-dimensional benchmark problems, including the double shear layer flow, the decay of homogeneous isotropic turbulence, the laminar boundary layer over a flat plate and the turbulent channel flow.

Arbitrary-angle rotation of the polarization of a dipolar Bose-Einstein condensate

We have employed the theory of harmonically trapped dipolar Bose-Einstein condensates to examine the influence of a uniform magnetic field that rotates at an arbitrary angle to its own orientation. This is achieved by semi-analytically solving the dipolar superfluid hydrodynamics of this system within the Thomas-Fermi approximation and by allowing the body frame of the condensate's density profile to be tilted with respect to the symmetry axes of the nonrotating harmonic trap. This additional degree of freedom manifests itself in the presence of previously unknown stationary solution branches for any given dipole tilt angle. We also find that the tilt angle of the stationary state's body frame with respect to the rotation axis is a nontrivial function of the trapping geometry, rotation frequency, and dipole tilt angle. For rotation frequencies of at least an order of magnitude higher than the in-plane trapping frequency, the stationary state density profile is almost perfectly equivalent to the profile expected in a time-averaged dipolar potential that effectively vanishes when the dipoles are tilted along the ``magic angle'' 54.7 deg. However, by linearizing the fully time-dependent superfluid hydrodynamics about these stationary states, we find that they are dynamically unstable against the formation of collective modes, which we expect would result in turbulent decay.

Decay of streaks and rolls in plane Couette–Poiseuille flow

We report the results of an experimental investigation into the decay of turbulence in plane Couette–Poiseuille flow using ‘quench’ experiments where the flow laminarises after a sudden reduction in Reynolds number $Re$ . Specifically, we study the velocity field in the streamwise–spanwise plane. We show that the spanwise velocity containing rolls decays faster than the streamwise velocity, which displays elongated regions of higher or lower velocity called streaks. At final Reynolds numbers above $425$ , the decay of streaks displays two stages: first a slow decay when rolls are present and secondly a more rapid decay of streaks alone. The difference in behaviour results from the regeneration of streaks by rolls, called the lift-up effect. We define the turbulent fraction as the portion of the flow containing turbulence and this is estimated by thresholding the spanwise velocity component. It decreases linearly with time in the whole range of final $Re$ . The corresponding decay slope increases linearly with final $Re$ . The extrapolated value at which this decay slope vanishes is $Re_{a_z}\approx 656\pm 10$ , close to $Re_g\approx 670$ at which turbulence is self-sustained. The decay of the energy computed from the spanwise velocity component is found to be exponential. The corresponding decay rate increases linearly with $Re$ , with an extrapolated vanishing value at $Re_{A_z}\approx 688\pm 10$ . This value is also close to the value at which the turbulence is self-sustained, showing that valuable information on the transition can be obtained over a wide range of $Re$ .

Impact of numerical hydrodynamics in turbulent mixing transition simulations

Underresolved simulations are unavoidable in high Reynolds (Re) and Mach (Ma) number turbulent flow applications at scale. Implicit large-Eddy simulation (ILES) often becomes the effective strategy to capture the dominating effects of convectively driven flow instabilities. We evaluate the impact of three distinct numerical strategies in simulations of transition and turbulence decay with ILES: the Harten–Lax–van Leer (HLL) Riemann solver applying Strang splitting and a Lagrange-plus-Remap formalism to solve the directional sweep—denoted split; the Harten–Lax–Van Leer-Contact (HLLC) Riemann solver using a directionally unsplit strategy and parabolic reconstruction—denoted unsplit; and the HLLC Riemann solver using unsplit and a low-Ma correction (LMC)—denoted unsplit*. Three case studies are considered: (1) a shock tube problem prototyping shock-driven turbulent mixing, (2) the Taylor–Green Vortex (TGV) prototyping transition to turbulence, and, (3) an homogeneous isotropic turbulence (HIT) case, focusing on the impact of discretization on transition and decay from fixed well-characterized initial conditions. Significantly more accurate predictions are provided by the unsplit schemes, in particular, when augmented with the LMC. For given resolution, only the unsplit schemes predict the turbulent mixing transition after reshock observed in the shock tube experiments. Relevant comparisons of ILES based on Euler and Navier–Stokes equations addressing potential occurrence of low-Re regimes in the applications are presented. Unsplit* schemes are instrumental in allowing to capture the spatial development of the TGV flow and its validation at prescribed Re with significantly less resolution. HIT analysis confirms higher simulated turbulence Re and increased small-scale content associated with the unsplit discretizations.

NANOGrav signal from magnetohydrodynamic turbulence at the QCD phase transition in the early Universe

The NANOGrav collaboration has recently reported evidence for the existence of a stochastic gravitational wave background in the 1-100 nHz frequency range. We argue that such background could have been produced by magneto-hydrodynamic (MHD) turbulence at the QCD scale. From the NANOGrav measurement one can infer the magnetic field parameters: comoving field strength close to microGauss and a correlation length close to 10\% of the Hubble radius at the QCD phase transition epoch. We point out that the turbulent decay of a non-helical magnetic field with such parameters leads to a magnetic field at the recombination epoch, which would be sufficiently strong to provide a solution to the Hubble tension problem, as recently proposed. We also show that the MHD turbulence interpretation of the NANOGrav signal can be tested via measurements of the relic magnetic field in the voids of the large scale structure, with gamma-ray telescopes like CTA.

Do extreme events trigger turbulence decay? – a numerical study of turbulence decay time in pipe flows

Abstract

Numerical Modeling of Freestream Turbulence Decay Using Different Commercial Computational Fluid Dynamics Codes

Abstract This work models the spatial decay of freestream turbulence using three different commercial computational fluid dynamics (CFD) codes: Fluent, star-ccm+, and cfx. The two-equation shear stress transport k–ω (SST-k–ω) steady Reynolds-averaged-Navier–Stokes (RANS) model was used, within each of these three different commercial codes, and the modeling variations were analyzed. Comparison of the results from the SST-k–ω model with experiments and large eddy simulation (LES) (carried out using star-ccm+) were also made, which reveal that all the commercial CFD codes demonstrate either a higher or slower rate of spatial turbulent kinetic energy (TKE) decay. Attempts were then made to unify the resultant modeling approach between these three CFD tools, by careful manipulation of the inlet boundary conditions and subsequent fine-tuning of the SST-k–ω model constant (β∞∗). The results obtained not only displayed uniformity among the three CFD codes but also demonstrated a much better agreement to the experiments and the LES results. Thereafter, the optimized model coefficient (β∞∗) was integrated with the three-equation k–kl–ω transition model to examine its applicability in modeling a turbulent boundary layer flow over a flat plate with low incoming turbulence. The results showed good agreement with the theoretical boundary layer correlations, with correct prediction of the transition location. The findings from this study can be used as a suitable modeling method to accurately model the effects of freestream turbulence on bluff-body and boundary layer flows.

Decay of two-dimensional quantum turbulence in binary Bose-Einstein condensates

We study two-dimensional quantum turbulence in miscible binary Bose-Einstein condensates in either a harmonic trap or a steep-wall trap through the numerical simulations of the Gross-Pitaevskii equations. The turbulence is generated through a Gaussian stirring potential. When the condensates have unequal intracomponent coupling strengths or asymmetric trap frequencies, the turbulent condensates undergo a dramatic decay dynamics to an interlaced array of vortex-antidark structures, a quasiequilibrium state, of like-signed vortices with an extended size of the vortex core. The time of formation of this state is shortened when the parameter asymmetry of the intracomponent couplings or the trap frequencies is enhanced. The corresponding spectrum of the incompressible kinetic energy exhibits two noteworthy features: (i) a ${k}^{\ensuremath{-}3}$ power law around the range of the wave number determined by the spin healing length (the size of the extended vortex core) and (ii) a flat region around the range of the wave number determined by the density healing length. The latter is associated with the small scale phase fluctuation relegated outside the Thomas-Fermi radius and is more prominent as the strength of intercomponent interaction approaches the strength of intracomponent interaction. We also study the impact of the intercomponent interaction to the cluster formation of like-signed vortices in an elliptical steep-wall trap, finding that the intercomponent coupling gives rise to the decay of the clustered configuration.

Drift waves enstrophy, zonal flow, and nonlinear evolution of the modulational instability

The interaction of the drift wave (DW) turbulence and zonal flow (ZF) is investigated with the modified Hasegawa–Mima equation taking into account the backreaction of ZF velocity on DW turbulence. It is shown that the y-averaged enstrophy of DW turbulence and the velocity of ZF are intrinsically related. By utilizing this feature, a nonlinear stage of DW modulational instability is considered within the framework of the wave kinetic equation. It is shown that in this approximation, the nonlinear stage of the modulational instability results in the collapsing solutions, accompanied by the “wave breaking” phenomenon. Numerical simulations based on the Hasegawa–Mima equation show that for a weak DW turbulence, Φ̃=(eφ̃/Te) (Ln/ρs)⪝1, the collapsing-like features on both ZF and y-averaged enstrophy of DW turbulence decay in time and then re-emerge again at different locations. For the case of a strong DW turbulence, Φ̃&amp;gt;1, where nonlinear interactions of DW harmonics dominate, stable spatial structures of ZF and y-averaged enstrophy of DW turbulence emerge.

Modeling Bubble Entrainment and Transport for Ship Wakes: Progress Using Hybrid RANS/LES Methods

This article presents progress on modeling bubble entrainment and transport around ships using hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/ LES) methods. Previous results using a Boltzmann-based polydisperse bubbly flow model show that LES perform better than RANS in predicting transport of bubbles to depth, a very important process to predict bubbly wakes. However, standard DES-type models fail to predict proper turbulent kinetic energy (TKE) and dissipation, needed by bubble entrainment, breakup, and coalescence models. We propose different approaches to obtain TKE and dissipation in LES regions and evaluate them for cases of increasing complexity, including decay of isotropic turbulence, a flat plate boundary layer, and the flow in the wake of the research vessel Athena. An exponential weighted average is used to estimate statistics and obtain the averaged quantities in regions with resolved turbulence. The TKE is satisfactorily predicted in the cases tested. A modified ω equation in the SST model is proposed to implicitly compute the dissipation, showing superior results than the standard DES models, although further improvements are necessary. A hybrid RANS/LES approach is proposed, which focused at conserving total TKE as the flow crosses RANS/LES interfaces, as previously performed for zonal approaches but attempting a DES-like detection of regions suitable for LES, critical for large-scale computations of bubbly flows involving complex geometries. A general form of a dynamic forcing term is derived to transfer the modeled TKE to resolved TKE with a controller to guarantee proper conservation of the energy transferred. It was verified that the model is not sensitive to grid size or time step. Improvements to DDES and the proposed TKE-conserving hybrid RANS/ LES method show encouraging results, although remaining challenges are discussed.