Turbulent Energy Transfer Research Articles

Improved vortex method for large-eddy simulation inflow generation

The generation of turbulent inflow conditions in large-eddy simulation (LES) is a key ingredient for general applications of LES in both academic turbulent flows and industrial designs with complicated engineering flows. This is because accurate predictions of the fluid behaviour are strongly dependent on the inflow conditions, particularly in turbulent flows at high turbulent Reynolds numbers. This paper aims at improving the vortex method (VM) of Sergent that demands long adaptive distances (12 times the half channel height, for a channel flow at Reτ=395) to achieve high quality turbulence, and evaluating the equilibrium of the flow field obtained in terms of both the equilibrium of the mean flow and that of the turbulence (inter-scale turbulent energy transfer). The mean flow equilibrium is checked with classic criteria such as the friction velocity. In order to assess the equilibrium of turbulence, we propose using the velocity-derivative skewness, because it associates with the balance of energy transfer between large- and small-scale fluid motions. Numerical tests with the optimised set of model parameters reveal that the IVM is very efficient, in terms of adaptive distance, in generating high-quality synthetic turbulent fluctuations over a moderate distance: 6h for channel flow and 21δ for flat-plate boundary layer, with h and δ being respectively the half channel height and the nominal boundary layer thickness.

Energy transfer in turbulence under rotation

It is known that rapidly rotating turbulent flows are characterized by the emergence of simultaneous upscale and downscale energy transfer. Indeed, both numerics and experiments show the formation of large-scale anisotropic vortices together with the development of small-scale dissipative structures. However the organization of interactions leading to this complex dynamics remains unclear. Two different mechanisms are known to be able to transfer energy upscale in a turbulent flow. The first is characterized by two-dimensional interactions among triads lying on the two-dimensional, three-component (2D3C) manifold, namely on the Fourier plane perpendicular to the rotation axis. The second mechanism is three-dimensional and consists of interactions between triads with the same sign of helicity (homochiral). Here, we present a detailed numerical study of rotating flows using a suite of high Reynolds number direct numerical simulations within different parameter regimes to analyze both upscale and downscale cascade ranges. We find that the upscale cascade at wave numbers close to the forcing scale is generated by increasingly dominant homochiral interactions which couple the three-dimensional bulk and the 2D3C plane. This coupling produces an accumulation of energy in the 2D3C plane, which then transfers energy to smaller wave numbers thanks to the two-dimensional mechanism. In the forward cascade range, we find that the energy transfer is dominated by heterochiral triads and is dominated primarily by interaction within the fast manifold where $k_z\ne0$. We further analyze the energy transfer in different regions in the real-space domain. In particular, we distinguish high-strain from high-vorticity regions and we uncover that while the mean transfer is produced inside regions of strain, the rare but extreme events of energy transfer occur primarily inside the large-scale column vortices.

Energy balance and partitioning and vertical profiles of turbulence characteristics during initial growth of a banana plantation in a screenhouse

This study focused on boundary layer characteristics and evapotranspiration in a cultivated screenhouse. The temporal course of latent and sensible heat fluxes, as well as vertical profiles of turbulence characteristics, below and above the screen were determined as the crop developed. The study was in a young banana plantation screenhouse, 5.5 m high, from June 17 (DOY 169) to August 8, 2016 (221), i.e. 53 days. Two masts measured simultaneously. A manually operated lifting tower mast near the eastern down-wind edge of the screenhouse operated either continuously at a fixed height or measured vertical profiles between 2.5 and 10.2 m height during the same day. The second ‘reference’ mast was 20 m north of the tower. Continuous measurements included latent and sensible heat fluxes above the plants and below the screen. During the experiment plant height increased from 1.7 to 4.1 m, LAI increased from 0.3 to 1.6 and the Bowen ratio, defined as the ratio between sensible and latent heat fluxes measured below the screen, decreased from 1.9 to 0.3. Energy balance closure, expressed as the slope of the relationship between half-hourly consumed and available energy for this period was 76% (R2 = 0.92); however, after summing up the fluxes over the whole period, the closure increased to 86%. Energy balance closure decreased with plant growth, presumably due to the more stable boundary layer associated with larger plants. During plant growth, ET per unit ground area increased linearly with LAI, but when calculated per unit leaf area it decreased, presumably due to increased mutual shading of leaves. Friction velocity below the screen was about 50% of that above the screen, illustrating the effect of the screen in absorbing momentum flux. Spectral energy slopes above the screen were close to the theoretical value typical of the inertial sub-range of steady state boundary layers, −5/3. Below the screen and within the canopy deviations from this theoretical value increased and the slope of spectra decay was higher than −5/3, indicating a higher rate of transfer of turbulent kinetic energy across scales. Integral length scale of turbulent vortices within and just above the canopy scaled with plant dimensions and between-plant distances, respectively; above the screen the integral length scale increased with height, as expected for fully developed turbulent flows over flat surfaces.

Kinetic energy transfer in compressible isotropic turbulence

Kinetic energy transfer in compressible isotropic turbulence is studied using numerical simulations with solenoidal forcing at turbulent Mach numbers ranging from 0.4 to 1.0 and at a Taylor Reynolds number of approximately 250. The pressure dilatation plays an important role in the local conversion between kinetic energy and internal energy, but its net contribution to the average kinetic energy transfer is negligibly small, due to the cancellation between compression and expansion work. The right tail of probability density function (PDF) of the subgrid-scale (SGS) flux of kinetic energy is found to be longer at higher turbulent Mach numbers. With an increase of the turbulent Mach number, compression motions enhance the positive SGS flux, and expansion motions enhance the negative SGS flux. Average of SGS flux conditioned on the filtered velocity divergence is studied by numerical analysis and a heuristic model. The conditional average of SGS flux is shown to be proportional to the square of filtered velocity divergence in strong compression regions for turbulent Mach numbers from 0.6 to 1.0. Moreover, the antiparallel alignment between the large-scale strain and the SGS stress is observed in strong compression regions. The inter-scale transfer of solenoidal and compressible components of kinetic energy is investigated by Helmholtz decomposition. The SGS flux of solenoidal kinetic energy is insensitive to the change of turbulent Mach number, while the SGS flux of compressible kinetic energy increases drastically as the turbulent Mach number becomes larger. The compressible mode persistently absorbs energy from the solenoidal mode through nonlinear advection. The kinetic energy of the compressible mode is transferred from large scales to small scales through the compressible SGS flux, and is dissipated by viscosity at small scales.

Energy transfer in compressible magnetohydrodynamic turbulence for isothermal self-gravitating fluids.

Three-dimensional, compressible, magnetohydrodynamic turbulence of an isothermal, self-gravitating fluid is analyzed using two-point statistics in the asymptotic limit of large Reynolds numbers (both kinetic and magnetic). Following an alternative formulation proposed by Banerjee and Galtier [Phys. Rev. E 93, 033120 (2016)2470-004510.1103/PhysRevE.93.033120; J. Phys. A: Math. Theor. 50, 015501 (2017)1751-811310.1088/1751-8113/50/1/015501], an exact relation has been derived for the total energy transfer. This approach results in a simpler relation expressed entirely in terms of mixed second-order structure functions. The kinetic, thermodynamic, magnetic, and gravitational contributions to the energy transfer rate can be easily separated in the present form. By construction, the new formalism includes such additional effects as global rotation, the Hall term in the induction equation, etc. The analysis shows that solid-body rotation cannot alter the energy flux rate of compressible turbulence. However, the contribution of a uniform background magnetic field to the flux is shown to be nontrivial unlike in the incompressible case. Finally, the compressible, turbulent energy flux rate does not vanish completely due to simple alignments, which leads to a zero turbulent energy flux rate in the incompressible case.

Morphing continuum analysis of energy transfer in compressible turbulence

Morphing continuum analysis of energy transfer in compressible turbulence

On the Statistical Properties of Turbulent Energy Transfer Rate in the Inner Heliosphere

The transfer of energy from large to small scales in solar wind turbulence is an important ingredient of the longstanding question about the mechanism of the interplanetary plasma heating. Previous studies have shown that magnetohydrodynamic (MHD) turbulence is statistically compatible with the observed solar wind heating as it expands in the heliosphere. However, in order to understand which processes contribute to the plasma heating, it is necessary to have a local description of the energy flux across scales. To this aim, it is customary to use indicators such as the magnetic field partial variance of increments (PVI), which is associated with the local, relative, scale-dependent magnetic energy. A more complete evaluation of the energy transfer should also include other terms, related to velocity and cross-helicity. This is achieved here by introducing a proxy for the local, scale dependent turbulent energy transfer rate epsilon_Dt(t), based on the third-order moment scaling law for MHD turbulence. Data from Helios 2 are used to determine the statistical properties of such a proxy in comparison with the magnetic and velocity fields PVI, and the correlation with local solar wind heating is computed. PVI and epsilon_Dt(t) are generally well correlated, however epsilon_Dt(t) is a very sensitive proxy that can exhibit large amplitude values, both positive and negative, even for low amplitude peaks in the PVI. Furthermore, epsilon_Dt(t) is very well correlated with local increases of temperature when large amplitude bursts of energy transfer are localized, thus suggesting an important role played by this proxy in the study of plasma energy dissipation.

On Cascade Energy Transfer in Convective Turbulence

The paper is devoted to specificities of the cascade processes in developed turbulence existing on a background of the density (temperature) gradient either parallel (turbulence in a stably stratified (SS) medium) or antiparallel (convective turbulence (CT)) to the gravitational force. Our main attention is paid to the Obukhov–Bolgiano (OB) regime, which presumes a balance between the buoyancy and nonlinear forces in a sufficiently extensive part of the inertial interval. Up to now, there has been no reliable evidence of the existence of the OB regime, although fragments of spectra with slopes close to–11/5 and–7/5 were detected in some works on the numerical simulations of convective turbulence. The paper presents a critical comparison of these data with the results obtained in this work using the cascade model of convective turbulence, which makes it possible to consider a wide range of control parameters. The cascade model is new and was obtained by the generalization of the class of helical cascade models to the case of turbulent convection. It is shown that, in developed turbulence, which is characterized by an interval with a constant spectral flux of kinetic energy, the buoyancy force cannot compete with nonlinear interactions and has no essential effect on the dynamics of the inertial interval. It is the buoyancy force that supplies the cascade process with energy in convective turbulence but only in the maximum scales. Under the SS conditions, the buoyancy forces reduce the energy of turbulent pulsations. In the case of stable stratification, the buoyancy force reduces the turbulence pulsation energy. The OB regime arises in none of these cases, but, in the scales beyond the inertial interval, Kolmogorov’s turbulence with the “–5/3” law, in which temperature behaves like a passive admixture, is established. The observed deviations from the “–5/3” spectrum, erroneously interpreted as the OB regime, are manifested in the case of insufficient separation of the macroscale of turbulence and the dissipative scale.

Exact relations for energy transfer in self-gravitating isothermal turbulence.

Self-gravitating isothermal supersonic turbulence is analyzed in the asymptotic limit of large Reynolds numbers. Based on the inviscid invariance of total energy, an exact relation is derived for homogeneous (not necessarily isotropic) turbulence. A modified definition for the two-point energy correlation functions is used to comply with the requirement of detailed energy equipartition in the acoustic limit. In contrast to the previous relations (S. Galtier and S. Banerjee, Phys. Rev. Lett. 107, 134501 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.134501; S. Banerjee and S.Galtier, Phys. Rev. E 87, 013019 (2013)PLEEE81539-375510.1103/PhysRevE.87.013019), the current exact relation shows that the pressure dilatation terms play practically no role in the energy cascade. Both the flux and source terms are written in terms of two-point differences. Sources enter the relation in a form of mixed second-order structure functions. Unlike the kinetic and thermodynamic potential energies, the gravitational contribution is absent from the flux term. An estimate shows that, for the isotropic case, the correlation between density and gravitational acceleration may play an important role in modifying the energy transfer in self-gravitating turbulence. The exact relation is also written in an alternative form in terms of two-point correlation functions, which is then used to describe scale-by-scale energy budget in spectral space.

Roughness effects on the second-order turbulence statistics in oscillatory flows

Effects of roughness on the near-bed turbulence characteristics in oscillatory flows are studied by means of particle-resolved direct numerical simulations (DNS). Two particle sizes of diameter 375 and 125 in wall units in a very rough turbulent flow regime are studied. A double-averaging technique is employed to study the nature of the wake field, i.e., the spatial inhomogeneity at the roughness length scale. This introduced dispersive stresses along with additional production and transport terms in the double-averaged Reynolds stress budget, indicating alternate pathways of turbulent energy transfer mechanisms. While overall nature of the elementary processes responsible for energy transport in both flow cases remains identical, there are some discernible differences with regards to the near-bed turbulence structure. It is shown that the roughness modulates the near-bed turbulence, distorts and breaks the streamwise horseshoe structures, and therefore reduces the large-scale anisotropy; a result of redistribution of energy from streamwise component to other two components of the Reynolds stress and is illustrated by studying their individual budgets. In comparison to the small diameter, such effects are found to be significant in the case of large diameter particle-bed. In addition, redistribution of energy in the large diameter particle case shows reduced dependence on the flow oscillations, while for the small diameter particle it is more pronounced towards the end of an acceleration cycle.

Energy transfer in compressible magnetohydrodynamic turbulence

Magnetic fields, compressibility, and turbulence are important factors in many terrestrial and astrophysical processes. While energy dynamics, i.e., how energy is transferred within and between kinetic and magnetic reservoirs, has been previously studied in the context of incompressible magnetohydrodynamic (MHD) turbulence, we extend shell-to-shell energy transfer analysis to the compressible regime. We derive four new transfer functions specifically capturing compressibility effects in the kinetic and magnetic cascade, and capturing energy exchange via magnetic pressure. To illustrate their viability, we perform and analyze four simulations of driven isothermal MHD turbulence in the sub- and supersonic regime with two different codes. On the one hand, our analysis reveals robust characteristics across regime and numerical method. For example, energy transfer between individual scales is local and forward for both cascades with the magnetic cascade being stronger than the kinetic one. Magnetic tension and magnetic pressure related transfers are less local and weaker than the cascades. We find no evidence for significant nonlocal transfer. On the other hand, we show that certain functions, e.g., the compressive component of the magnetic energy cascade, exhibit a more complex behavior that varies both with regime and numerical method. Having established a basis for the analysis in the compressible regime, the method can now be applied to study a broader parameter space.

The warm season characteristics of the turbulence structure and transfer of turbulent kinetic energy over alpine wetlands at the source of the Yellow River

This study focuses on the relationships between wind velocity, temperature, water vapour, CO2, and the stability parameters over an alpine wetland. The turbulence data collected by a suite of instruments in the Maduo wetland, which is located at the source of the Yellow River (from June to August 2014), were used to study the characteristics of turbulence transport, turbulence kinetic energy, humidity variance, temperature variance, CO2 variance, and turbulence intensity. The results show that the normalized standard deviation of the wind velocity components (σ u , σ v , and σ w ) generally satisfies a 1/3 power-law relation. The values of σ u,v,w /u * increase with increasing |(z − d)/L|. Moreover, the normalized standard deviation of the temperature, CO2, and water vapour is scatter under stable stratification at night. However, they increase as the absolute stability parameters decrease under unstable stratification. The results also indicate that the turbulent kinetic energy and turbulence intensity reach their peak values when the stability parameter is close to zero. When the wind velocity is less than 2 m/s, the turbulence intensities in the three directions decrease rapidly with increasing wind velocity. Moreover, the average value of C D (the overall momentum transfer coefficient) is significantly larger than those of C H (the sensible heat transfer coefficient) under different conditions. The bulk transport coefficient decreases as the stability increases. Finally, because of the high temperatures, the leaf stomata are nearly closed, and the pulse of the CO2 flux is very small at noon time. Meanwhile, the latent and sensible heat fluxes reach their maximum values.

The stratigraphic record and processes of turbidity current transformation across deep‐marine lobes

AbstractSedimentary facies in the distal parts of deep‐marine lobes can diverge significantly from those predicted by classical turbidite models, and sedimentological processes in these environments are poorly understood. This gap may be bridged using outcrop studies and theoretical models. In the Skoorsteenberg Formation (South Africa), a downstream transition from thickly bedded turbidite sandstones to argillaceous, internally layered hybrid beds, is observed. The hybrid beds have a characteristic stratigraphic and spatial distribution, being associated with bed successions which generally coarsen and thicken‐upward reflecting deposition on the fringes of lobes in a dominantly progradational system. Using a detailed characterization of bed types, including grain size, grain‐fabric and mineralogical analyses, a process‐model for flow evolution is developed. This is explored using a numerical suspension capacity model for radially spreading and decelerating turbidity currents. The new model shows how decelerating sediment suspensions can reach a critical suspension capacity threshold beyond which grains are not supported by fluid turbulence. Sand and silt particles, settling together with flocculated clay, may form low yield strength cohesive flows; development of these higher concentration lower boundary layer flows inhibits transfer of turbulent kinetic energy into the upper parts of the flow ultimately resulting in catastrophic loss of turbulence and collapse of the upper part of the flow. Advection distances of the now transitional to laminar flow are relatively long (several kilometres) suggesting relatively slow dewatering (several hours) of the low yield strength flows. The catastrophic loss of turbulence accounts for the presence of such beds in other fine‐grained systems without invoking external controls or large‐scale flow partitioning and also explains the abrupt pinch‐out of all divisions of these sandstones. Estimation of the point of flow transformation is a useful tool in the prediction of heterogeneity distribution in subsurface systems.

Experimental measurements of energy transfer and nonlinear interaction in turbulence at the sino-united spherical tokamak

The characteristics of the energy transfer and nonlinear coupling among edge electromagnetic turbulence have been dedicatedly studied in various discharge stages at the sino-united spherical tokamak using multiple Langmuir and magnetic probe arrays. The wavelet bispectral analysis and the modified Kim's method are applied to investigate turbulence properties and their linear growth/damping and nonlinear energy transfer rates, along with multi-field turbulence interactions. The results show diverse features in the linear growth and nonlinear energy transfer between multi-field fluctuations during the current ramp-up, stationary, and internal connection event discharge phases. The diversity implies the importance to develop more sophisticated multi-field models to directly estimate the energy transfer rate among multiple turbulent fields.

Compressibility effect on coherent structures, energy transfer, and scaling in magnetohydrodynamic turbulence

Compressible magnetohydrodynamic (MHD) turbulence, a model often used to study space and astrophysical plasmas, differs from incompressible magnetohydrodynamic and hydrodynamic (HD) turbulence in many ways. Here direct numerical simulations of mechanically forced compressible MHD turbulence are used to study the degree to which some turbulence theories proposed in the incompressible case remain applicable in the compressible one. Several aspects of compressible turbulence are studied: (i) Intermittency in the compressible case is studied by addressing flows driven with varying forcing mechanisms; these display different features, such as compression and coherent structures. The more compressive simulation is characterized by sheet-like current density structures and shocks, which lead to saturated scaling exponents of high order structure functions of density and compressive velocity. (ii) Further investigations employing conditional averages of different energy transfer fluxes reveal that the influence of shocks (or compressions) makes differences in energy cascade and magnetic amplification. (iii) Cascade is also studied by examining the validity of Yaglom-type relations that verify the scale invariant property within the inertial range, where the transfer is relatively free of the effect of pressure dilation.

Mechanism of kinetic energy transfer in homogeneous bidisperse gas-solid flow and its implications for segregation

Most gas–solid flows encountered in nature and industrial applications are polydisperse, and the segregation or mixing of particle classes in polydisperse gas–solid flows is a phenomenon of great practical importance. A statistically homogeneous gas–solid flow with a bidisperse distribution (in size or density) of particles is a canonical representation of polydisperse flows. A key feature that distinguishes the bidisperse flow from its monodisperse counterpart is the exchange of momentum and kinetic energy between the particle classes due to collisions, which are important for applications outside the very dilute regime. The average exchange of linear momentum between particle classes due to collisions occurs through the particle–particle drag term. The conservation equations for average momentum corresponding to each particle class can be used to deduce the average slip velocity between the particle size and density classes, which is the signature of particle segregation. In this canonical problem, the steady value of particle mean slip velocity results from a balance between three terms, each in turn involving the body force or the mean fluid pressure gradient, the gas–particle drag, and the particle–particle drag. The particle–particle drag depends on the particle velocity fluctuations in each class [Louge, M. Y. et al., “The role of particle collisions in pneumatic transport,” J. Fluid Mech. 231, 345–359 (1991)], thereby coupling the mean and second–moment equations. For monodisperse gas-solid flows the transfer of kinetic energy from the mean to second-moment equations was explained by Subramaniam and co-workers who proposed the conservation of interphase turbulent kinetic energy transfer principle [Xu, Y. and Subramaniam, S., “Consistent modeling of interphase turbulent kinetic energy transfer in particle-laden turbulent flows,” Phys. Fluids 19(8), 085101 (2007)], and this was subsequently verified by particle–resolved direct numerical simulation [Mehrabadi, M. et al., “Pseudo-turbulent gas-phase velocity fluctuations in homogeneous gas-solid flow: Fixed particle assemblies and freely evolving suspensions,” J. Fluid Mech. 770, 210–246 (2015)]. The principle shows that the power supplied to the mean flow to maintain the mean slip velocity between solid and gas phases partitions into transfer terms that supply power to maintain fluid and particle velocity fluctuations. One question this paper seeks to answer is what the role of particle–particle drag is in this transfer process in bidisperse flows, given that the particle–particle drag does not appear in the mixture mean momentum conservation equation for the solid phase. The conservation equations for mean momentum and kinetic energy in each particle class are coupled through interphase and interclass exchange terms. This coupling between the mean momentum and kinetic energy equations due to interphase and interclass interactions is explained by extending the conservation of interphase turbulent kinetic energy transfer principle originally proposed for monodisperse gas-solid flows to bidisperse suspensions. This explains the role of particle–particle drag in the partitioning of kinetic energy in velocity fluctuations between particle classes and provides insight into segregation and mixing of particle classes in industrial devices.

Collisional Scaling of the Energy Transfer in Drift-Wave Zonal Flow Turbulence.

The collisionality scaling of density and potential coupling together with zonal flow energy transfer and spectral power is investigated at the stellarator experiment TJ-K. With a poloidal probe array, consisting of 128 Langmuir probes, density and potential fluctuations are measured on four neighboring flux surfaces simultaneously over the complete poloidal circumference. By analyzing Reynolds stress and pseudo-Reynolds stress, it is found that, for increasing collisionality, the coupling between density and potential decreases which hinders the zonal flow drive. Also, as a consequence, the nonlinear energy transfer, as well as the zonal flow contribution to the complete turbulent spectrum, decreases the same way. This is in line with theoretical expectations and is a first experimental verification of the importance of collisionality for large-scale structure formation in magnetically confined toroidal plasmas.

Effect of helicity on turbulent energy transfer through pressure diffusion

Effect of helicity on turbulent energy transfer through pressure diffusion

The effect of stable stratification on vortex stretching in open channel flow

We present the results of direct numerical simulation of stably stratified open channel flow. The main goal of the paper is to check the effect of thermal stratification on the dynamics of vortex interactions. By comparing the vortex stretching in neutral and stratified cases we show that imposing the stratification leads to an increase of the ratio between positive and negative vortex stretching magnitudes in the flow. That indicates the change in spectral transfer of turbulent energy.

TURBULENT DYNAMO IN A CONDUCTING FLUID AND A PARTIALLY IONIZED GAS

ABSTRACT By following the Kazantsev theory and taking into account both microscopic and turbulent diffusion of magnetic fields, we develop a unified treatment of the kinematic and nonlinear stages of a turbulent dynamo process, and we study the dynamo process for a full range of magnetic Prandtl number P m and ionization fractions. We find a striking similarity between the dependence of dynamo behavior on P m in a conducting fluid and (a function of ionization fraction) in a partially ionized gas. In a weakly ionized medium, the kinematic stage is largely extended, including not only exponential growth but a new regime of dynamo characterized by a linear-in-time growth of magnetic field strength, and the resulting magnetic energy is much higher than the kinetic energy carried by viscous-scale eddies. Unlike the kinematic stage, the subsequent nonlinear stage is unaffected by microscopic diffusion processes and has a universal linear-in-time growth of magnetic energy with the growth rate as a constant fraction 3/38 of the turbulent energy transfer rate, showing good agreement with earlier numerical results. Applying the analysis to the first stars and galaxies, we find that the kinematic stage is able to generate a field strength only an order of magnitude smaller than the final saturation value. But the generation of large-scale magnetic fields can only be accounted for by the relatively inefficient nonlinear stage and requires longer time than the free-fall time. It suggests that magnetic fields may not have played a dynamically important role during the formation of the first stars.