Taylor Microscale Reynolds Number Research Articles

Finite Reynolds Number Effect on Small-Scale Statistics in Decaying Grid Turbulence

Since about 1997, the realisation that the finite Reynolds number (FRN) effect needs to be carefully taken into account when assessing the behaviour of small-scale statistics came to the fore. The FRN effect can be analysed either in the real domain or in the spectral domain via the scale-by-scale energy budget equation or the transport equation for the energy spectrum. This analysis indicates that the inertial range (IR) is established only when the Taylor microscale Reynolds number Reλ is infinitely large, thus raising doubts about published power-law exponents at finite values of Reλ, for either the second-order velocity structure function (δu)2¯ or the energy spectrum. Here, we focus on the transport equation of (δu)2¯ in decaying grid turbulence, which represents a close approximation to homogeneous isotropic turbulence. The effect on the small-scales of the large-scale forcing term associated with the streamwise advection decreases as Reλ increases and finally disappears when Reλ is sufficiently large. An approach based on the dual scaling of (δu)2¯, i.e., a scaling based on the Kolmogorov scales (when the separation r is small) and another based on the integral scales (when r is large), yields (δu)2¯∼r2/3 when Reλ is infinitely large. This approach also yields (δu)n¯∼rn/3 when Reλ is infinitely large. These results seem to be supported by the trend, as Reλ increases, of available experimental data. Overall, the results for decaying grid turbulence strongly suggest that a tendency towards the predictions of K41 cannot be dismissed at least at Reynolds numbers which are currently beyond the reach of experiments and direct numerical simulations.

Machine learning-based vorticity evolution and super-resolution of homogeneous isotropic turbulence using wavelet projection

A wavelet-based machine learning method is proposed for predicting the time evolution of homogeneous isotropic turbulence where vortex tubes are preserved. Three-dimensional convolutional neural networks and long short-term memory are trained with a time series of direct numerical simulation (DNS) data of homogeneous isotropic turbulence at the Taylor microscale Reynolds number 92. The predicted results are assessed by using the flow visualization of vorticity and statistics, e.g., probability density functions of vorticity and enstrophy spectra. It is found that the predicted results are in good agreement with DNS results. The small-scale flow topology considering the second and the third invariants of the velocity gradient tensor likewise shows an approximate match. Furthermore, we apply the pre-trained neural networks to coarse-grained vorticity data using super-resolution. It is shown that the super-resolved flow field well agrees with the reference DNS field, and thus small-scale information and vortex tubes are well regenerated.

Heat transport in a non-homothermal turbulent particle-laden flow in the collisional regime

In this investigation, we explore the impact of particle collisions on turbulent heat flux within a temporally developing thermal mixing layer arising from the interaction of two homothermal regions driven by a statistically homogeneous and isotropic velocity field. Employing two-way thermally coupled Eulerian-Lagrangian Direct Numerical Simulations (DNSs) at a Taylor microscale Reynolds number up to 124, we examine the influence of particle collisions for a Stokes number from 0.2 to 3, maintaining a fixed thermal to kinetic relaxation times ratio of 4.43. Our study quantifies the reduction in average heat transport induced by particle-to-particle collisions, which disrupt the temperature-velocity correlation created by the initial temperature difference. Notably, while collisions diminish this correlation, our analysis reveals their overall impact remains minor, even at the highest simulated Stokes number. Additionally, we present statistics of the temperature difference among colliding particles across various flow conditions.

A universal scaling law for Lagrangian snowflake accelerations in atmospheric turbulence

We use a novel experimental setup to obtain the vertical velocity and acceleration statistics of snowflakes settling in atmospheric surface-layer turbulence, for Taylor microscale Reynolds numbers (Reλ) between 400 and 67 000, Stokes numbers (St) between 0.12 and 3.50, and a broad range of snowflake habits. Despite the complexity of snowflake structures and the non-uniform nature of the turbulence, we find that mean snowflake acceleration distributions can be uniquely determined from the value of St. Ensemble-averaged snowflake root mean square (rms) accelerations scale nearly linearly with St. Normalized by the rms value, the acceleration distribution is nearly exponential, with a scaling factor for the (exponent) of −3/2 that is independent of Reλ and St; kurtosis scales with Reλ, albeit weakly compared to fluid tracers in turbulence; gravitational drift with sweeping is observed for St < 1. Surprisingly, the same exponential distribution describes a pseudo-acceleration calculated from fluctuations of snowflake terminal fall speed in still air. This equivalence suggests an underlying connection between how turbulence determines the trajectories of particles and the microphysics determining the evolution of their shapes and sizes.

Dual scaling and the n-thirds law in grid turbulence

A dual scaling of the turbulent longitudinal velocity structure function $\overline {{(\delta u)}^n}$ , i.e. a scaling based on the Kolmogorov scales ( $u_K$ , $\eta$ ) and another based on ( $u'$ , $L$ ) representative of the large scale motion, is examined in the context of both the Kármán–Howarth equation and experimental grid turbulence data over a significant range of the Taylor microscale Reynolds number $Re_\lambda$ . As $Re_\lambda$ increases, the scaling based on ( $u'$ , $L$ ) extends to increasingly smaller values of $r/L$ while the scaling based on ( $u_K$ , $\eta$ ) extends to increasingly larger values of $r/\eta$ . The implication is that both scalings should eventually overlap in the so-called inertial range as $Re_\lambda$ continues to increase, thus leading to a power-law relation $\overline {{(\delta u)}^n} \sim r^{n/3}$ when the inertial range is rigorously established. The latter is likely to occur only when $Re_\lambda \to \infty$ . The use of an empirical model for $\overline {{(\delta u)}^n}$ , which complies with $\overline {{(\delta u)}^n} \sim r^{n/3}$ as $Re_\lambda \to \infty$ , shows that the finite Reynolds number effect may differ between even- and odd-orders of $\overline {{(\delta u)}^n}$ . This suggests that different values of $Re_\lambda$ may be required between even and odd values of $n$ for compliance with $\overline {{(\delta u)}^n} \sim r^{n/3}$ . The model describes adequately the dependence on $Re_\lambda$ of the available experimental data for $\overline {{(\delta u)}^n}$ and supports indirectly the extrapolation of these data to infinitely large $Re_\lambda$ .

Deciphering the dynamics of distorted turbulent flows: Lagrangian particle tracking and chaos prediction through transformer-based deep learning models

Turbulent flow is a complex and vital phenomenon in fluid dynamics, as it is the most common type of flow in both natural and artificial systems. Traditional methods of studying turbulent flow, such as computational fluid dynamics and experiments, have limitations such as high computational costs, experiment costs, and restricted problem scales and sizes. Recently, artificial intelligence has provided a new avenue for examining turbulent flow, which can help improve our understanding of its flow features and physics in various applications. Strained turbulent flow, which occurs in the presence of gravity in situations such as combustion chambers and shear flow, is one such case. This study proposes a novel data-driven transformer model to predict the velocity field of turbulent flow, building on the success of this deep sequential learning technique in areas such as language translation and music. The present study applied this model to experimental work by Hassanian et al., who studied distorted turbulent flow with a specific range of Taylor microscale Reynolds numbers 100<Reλ<120. The flow underwent a vertical mean strain rate of 8 s−1 in the presence of gravity. The Lagrangian particle tracking technique recorded every tracer particle's velocity field and displacement. Using this dataset, the transformer model was trained with different ratios of data and used to predict the velocity of the following period. The model's predictions significantly matched the experimental test data, with a mean absolute error of 0.002–0.003 and an R2 score of 0.98. Furthermore, the model demonstrated its ability to maintain high predictive performance with less training data, showcasing its potential to predict future turbulent flow velocity with fewer computational resources. To assess the model, it has been compared to the long short-term memory and gated recurrent units model. High-performance computing machines, such as JUWELS-DevelBOOSTER at the Juelich Supercomputing Center, were used to train and run the model for inference.

Experimental study of two side-by-side decaying grid turbulent fields at different mean velocities

A Hot-wire anemometry experiment is conducted to investigate how two turbulent fields decaying with different mean velocities interact at their interface. A grid with different mesh sizes and solidities on either side of the grid centerline is used to generate two turbulent fields. It is found that the resulting turbulent shear layer created at the interface of the two fields evolves in a self-preserving manner. Further, the Taylor microscale Reynolds number, increases linearly while and become constants as the distance x downstream of the grids increases. Off the centerline one observes the classical decay of turbulence, e.g. varies like (n is negative) and decreases. It is observed that the transport equation for is dominated by the production and pressure-velocity correlation in the central region of the turbulent shear layer while production, dissipation, and turbulent diffusion of the transport equation for dominate in the central part of the shear layer. The pressure-velocity correlation term for is negligible on the centreline of the shear layer and important on the edges. The measurements of the scale-by-scale (SBS) energy terms on the shear layer centerline reveal that the energy transfer from large to small scales occurs in a non-trivial manner.

Approach towards local isotropy in statistically stationary turbulent shear flows

We analyse the approach towards local isotropy in statistically stationary turbulent shear flows using the transport equations for the fourth-order moments of the velocity derivative. It is found that terms of these equations representing the large-scale contribution associated with the uniform mean velocity gradient gradually decrease as the Taylor microscale Reynolds number $Re_\lambda$ increases, and finally disappear when $Re_\lambda$ is sufficiently large. This gradual weakening of the large-scale effect is accompanied by a gradual approach towards local isotropy of the small-scale motion. The rate at which local isotropy is approached depends on the weakening of the large-scale forcing, which is controlled by the magnitude of the non-dimensional velocity shear parameter $S^*$ ( $\equiv \overline {u_1^2}({{\partial {{\bar U}_1}}}/{{\partial {x_2}}})/{\bar {\varepsilon }_{iso}}$ , where $\bar {\varepsilon }_{iso}$ is the isotropic mean turbulent energy dissipation rate, $\overline {u_1^2}$ is the streamwise velocity variance, and ${\partial {{\bar U}_1}/\partial {x_2}}$ is the uniform mean velocity gradient in the transverse direction). In particular, we show that the approach towards local isotropy can be recast in the form $C\, Re_\lambda ^{-1}$ , where $C$ is the product of $S^*$ and a ratio of transverse-to-streamwise velocity derivative variances. This is consistent with the behaviour of the normalized third-order moments of transverse velocity derivatives. With the further use of the transport equations for the eighth- and twelfth-order velocity derivative moments, it is found that the even moments of transverse velocity derivatives can significantly affect the rate at which local isotropy is approached, especially for higher orders.

Heat Transfer in a Non-Isothermal Collisionless Turbulent Particle-Laden Flow

To better understand the role of particle inertia on the heat transfer in the presence of a thermal inhomogeneity, Eulerian–Lagrangian direct numerical simulations (DNSs) have been carried out by using the point–particle model. By considering particles transported by a homogeneous and isotropic, statistically steady turbulent velocity field with a Taylor microscale Reynolds number from 37 to 124, we have investigated the role of particle inertia and thermal inertia in one- and two-way coupling collisionless regimes on the heat transfer between two regions at uniform temperature. A wide range of Stokes numbers, from 0.1 to 3 with a thermal Stokes-number-to-Stokes-number ratio equal to 0.5 to 4.43 has been simulated. It has been found that all moments always undergo a self-similar evolution in the interfacial region between the two uniform temperature zones, the thickness of which shows diffusive growth. We have determined that the maximum contribution of particles to the heat flux, relative to the convective heat transfer, is achieved at a Stokes number which increases with the ratio between thermal Stokes and Stokes number, approaching 1 for very large ratios. Furthermore, the maximum increases with the thermal Stokes-to-Stokes number ratio whereas it reduces for increasing Reynolds. In the two-way coupling regime, particle feedback tends to smooth temperature gradients by reducing the convective heat flux and to increase the particle turbulent heat flux, in particular at a high Stokes number. The impact of particle inertia reduces at very large Stokes numbers and at larger Reynolds numbers. The dependence of the Nusselt number on the relevant governing parameters is presented. The implications of these findings for turbulence modelling are also briefly discussed.

Deep Learning Forecasts a Strained Turbulent Flow Velocity Field in Temporal Lagrangian Framework: Comparison of LSTM and GRU

The subject of this study presents an employed method in deep learning to create a model and predict the following period of turbulent flow velocity. The applied data in this study are extracted datasets from simulated turbulent flow in the laboratory with the Taylor microscale Reynolds numbers in the range of 90 < Rλ< 110. The flow has been seeded with tracer particles. The turbulent intensity of the flow is created and controlled by eight impellers placed in a turbulence facility. The flow deformation has been conducted via two circular flat plates moving toward each other in the center of the tank. The Lagrangian particle-tracking method has been applied to measure the flow features. The data have been processed to extract the flow properties. Since the dataset is sequential, it is used to train long short-term memory and gated recurrent unit model. The parallel computing machine DEEP-DAM module from Juelich supercomputer center has been applied to accelerate the model. The predicted output was assessed and validated by the rest of the data from the experiment for the following period. The results from this approach display accurate prediction outcomes that could be developed further for more extensive data documentation and used to assist in similar applications. The mean average error and R2 score range from 0.001–0.002 and 0.9839–0.9873, respectively, for both models with two distinct training data ratios. Using GPUs increases the LSTM performance speed more than applications with no GPUs.

Scale-to-scale turbulence modification by small settling particles

Despite decades of investigations, there is still no consensus on whether inertial particles augment or dampen turbulence. Here, we perform the first experimental study in which the particle concentration is varied systematically across a broad range of volume fractions $\varPhi _{v}$ , from nominally one-way coupled to heavily two-way coupled regimes, keeping all other parameters constant. We utilize a zero-mean flow chamber where steady, homogeneous and approximately isotropic air turbulence is realized, with a Taylor-microscale Reynolds number $Re_{\lambda } = 150\unicode{x2013}300$ . We consider spherical solid particles of two sizes, both much smaller than the Kolmogorov length, and yielding Stokes numbers $St_{\eta } = 0.3$ and 2.6 based on the Kolmogorov time scale. By adjusting the turbulent intensity, the settling velocity parameter is kept constant for both cases, $Sv_{\eta } = V_{t}/u_{\eta }\approx 3$ (where $V_{t}$ is the still-air terminal velocity, and $u_{\eta }$ is the Kolmogorov velocity scale). Unlike previous studies focused on massively inertial particles, we find that the turbulent kinetic energy increases with particle loading, being more than doubled at $\varPhi _{v} =5\times 10^{-5}$ . This is attributed to the energy input associated with gravitational settling: the particles release their potential energy into the fluid and increase its dissipation rate, while the time scale associated with the inter-scale energy transfer is not strongly changed. Two-point statistics indicate that the energy-containing eddies become vertically elongated in the presence of falling particles, and that the latter redistribute the energy more homogeneously across the scales compared to unladen turbulence. This is rooted in an enhanced cascade, as shown by the nonlinear inter-scale energy transfer rate.

Forcing in DNS of stationary isotropic turbulence and its effects on the closure of diffusion current in the PDF kinetic equation for high-inertia particle pairs

The relative motion of inertial, monodisperse particle pairs in stationary isotropic turbulence is investigated by evolving the Langevin stochastic differential equations governing the pair relative velocities and separations in the limit of Stokes number ≫1. The stochastic force in the Langevin equations is evaluated from the pair relative-velocity-space diffusivity that is equal to 1/τv2 multiplied by the time integral of the Eulerian two-time correlation of fluid velocity differences seen by particle pairs that are nearly stationary (τv is the particle viscous relaxation time). The Eulerian two-time correlation of the fluid velocity-difference field is computed using direct numerical simulation (DNS) of isotropic turbulence seeded with fixed particles. Since numerical forcing of the energy-containing eddies is employed to achieve stationarity in DNS, the impact of the forcing scheme on the two-time correlation is quantified as a function of separation r and the Taylor micro-scale Reynolds number Reλ. As the DNS-computed correlation is needed to evaluate the stochastic force in Langevin simulations (LS), a key objective is to quantify the effects of forcing scheme on the LS predictions of pair relative motion. Deterministic forcing (DF) and stochastic forcing (SF) are employed to achieve stationarity in the DNS runs. In SF, one needs to specify the time scale Tf of the Uhlenbeck–Ornstein processes that constitute the forcing. The Eulerian two-time correlations were computed using both DNS with DF and DNS with SF, the latter for Tf=TE/4,TE/2,TE,2TE, and 4TE, where TE is the large-eddy turnover time obtained from the corresponding DNS with DF. It is seen that the correlations obtained from DNS with DF are higher than those from DNS with SF for all five Tf’s, the differences being substantially more pronounced at larger separations and for higher Reλ. The two-time correlations computed using DNS with DF and DNS with SF were then utilized to perform Langevin simulations for particle Stokes numbers based on Kolmogorov time scale, Stη≥10. For Reλ=80, the pair relative-velocity variances predicted by the Langevin simulations based on DF were not significantly different from those predicted by the Langevin simulations based on SF. However, for Reλ=130 and Stη=10,20, the variances obtained from LS based on DF were significantly higher than the variances from LS based on SF. The overprediction of relative velocity variances by LS-DF may be attributed to the slower decay of Eulerian two-time correlations when deterministic forcing is employed. The effects of forcing scheme on the radial distribution function (RDF) computed from the Langevin simulations are less pronounced compared to its effects on the variances. Nevertheless, for Reλ=130 and separations r=L/2 and L, where L is the integral length scale, the RDF values obtained from LS based on DF were higher than those from LS based on SF.

Taylor Microscale and Effective Reynolds Number near the Sun from PSP

The Taylor microscale is a fundamental length scale in turbulent fluids, representing the end of fluid properties and onset of dissipative processes. The Taylor microscale can also be used to evaluate the Reynolds number in classical turbulence theory. Although the solar wind is weakly collisional, it approximately behaves as a magnetohydrodynamic (MHD) fluid at scales larger than the kinetic scale. As a result, classical fluid turbulence theory and formalisms are often used to study turbulence in the MHD range. Therefore, a Taylor microscale can be used to estimate an effective Reynolds number in the solar wind. NASA’s Parker Solar Probe (PSP) has reached progressively closer to the Sun than any other spacecraft before. The collected data have revealed many new findings in the near-Sun solar wind. Here, we use the PSP data to estimate the Taylor microscale and effective Reynolds number near the Sun. We find that the Taylor microscale and Reynolds number are small compared to the corresponding near-Earth values, indicating a solar wind that has been less processed by turbulence, with very small-scale dissipative processes near the Sun.

Diffusion of turbulence following both stable and unstable step stratification perturbations

The evolution of a two-phase, air and unsaturated water vapor, time-decaying, shearless, and turbulent layer has been studied in the presence of both stable and unstable perturbations of the normal temperature lapse rate. The top interface between a warm vapor cloud and clear air in the absence of water droplets was considered as the reference dynamics. Direct, three-dimensional, and numerical simulations were performed within a 6 × 6-m-wide and 12-m-high domain, which was hypothesized to be located close to an interface between the warm cloud and clear air. The Taylor microscale Reynolds number was 250 inside the cloud portion. The squared Froude's number varied over intervals of [0.4; 981.6] and [−4.0; −19.6]. A sufficiently intense stratification was observed to change the mixing dynamics. The formation of a sublayer inside the shearless layer was observed. The sublayer, under a stable thermal stratification condition, behaved like a pit of kinetic energy. However, it was observed that kinetic energy transient growth took place under unstable conditions, which led to the formation of an energy peak just below the center of the shearless layer. The scaling law of the energy time-variation inside the interface region was quantified: this is an algebraic law with an exponent that depends on the perturbation stratification intensity. The presence of an unstable stratification increased the differences in statistical behavior among the longitudinal velocity derivatives, compared with the unstratified case. Since the mixing process is suppressed in stable cases, small-scale anisotropy is also suppressed.

Effects of Numerical Forcing on the Two-Time Correlation of Fluid Velocity Differences in Stationary Isotropic Turbulence

In direct numerical simulations (DNS) of homogeneous isotropic turbulence, numerical forcing is needed to achieve statistically stationary velocity fields. The Eulerian two-time correlation tensor of the fluid velocity difference field, Δu(r,t)=u(x+r,t)−u(x,t), characterizes the temporal evolution of turbulent eddies whose sizes scale with separation r=|r|. In this study, we investigate the effects of two spectral forcing schemes on the temporal decay of the Eulerian two-time correlation of fluid velocity differences ⟨Δu(r,t′)Δu(r,t)⟩. Accordingly, DNS of homogeneous isotropic turbulence were performed for two grid sizes, 1283 and 5123, corresponding to the Taylor micro-scale Reynolds numbers Reλ≈80 and 210, respectively. Statistical stationarity was achieved by employing deterministic and stochastic spectral forcing schemes. In the stochastic scheme, one needs to specify the time scale, Tf, of the Uhlenbeck–Ornstein (UO) processes that constitute the forcing. We considered four values of the UO time scale (Tf=TE/4,TE,2TE, and 4TE) for each Reλ, where TE is the large-eddy time scale obtained from the DNS run with deterministic forcing at the same Reλ. It is seen that the correlations ⟨Δu(r,t′)Δu(r,t)⟩ obtained from the deterministic-forcing DNS runs decay more slowly than those from stochastic-forcing DNS runs of all four Tf values. The slower decay of correlations in deterministic DNS runs is more pronounced at larger separations and for higher Reλ.

Hot-Wire Investigation of Turbulence Topology behind Blades at Different Shape Qualities

The scope of this paper is to perform a detailed experimental investigation of the shape error effect on the turbulence evolution behind NACA 64-618 airfoil. This airfoil is 3D-printed with predefined typical shape inaccuracies. A high-precision optical 3D scanner was used to assess the shape and surface quality of the manufactured models. The turbulent flow was studied using hot-wire anemometry. The developed force balance device was provided to measure the aerodynamic characteristics of the airfoil. Experimental studies were carried out for three angles of attack, +10∘, 0∘, −10∘, and different chord-based Reynolds numbers from 5.3×104 to 2.1×105. The obtained results show that the blunt trailing edge and rough surface decline the aerodynamic performance of the blades. In addition, the experimental results revealed a strong sensitivity of the Taylor microscale Reynolds number to the type of shape inaccuracy, especially at Re≈1.7×105. We also discuss the evolution of the Reynolds stress components, the degree of flow anisotropy, and the power spectrum distributions depending on the airfoil inaccuracies.

Unsteady forcing of turbulence by a randomly actuated impeller array

We investigate the unsteady forcing of turbulent flow in a well-stirred reactor using opposing arrays of pitched-blade impellers which randomly and independently reverse rotation. We systematically explore the dependence of the large-scale motions and the homogeneity and isotropy of the turbulence upon the forcing. We identify three dimensionless control parameters: the source fraction (the fraction of time spent in clockwise motion), the dimensionless forcing period and an impeller Reynolds number. We find the timescale of unsteady motion corresponds to the forcing period T, the average period of impeller reversal, independently of the impeller angular speed varOmega and source fraction. As in jet-stirred tanks, unsteady forcing substantially increases the unsteady kinetic energy, energy dissipation, integral length scale and Taylor microscale Reynolds number (R_lambda) and improves the homogeneity and isotropy of the flow, provided the source fraction is chosen optimally and the forcing period is sufficiently large (varOmega T > 10^3); impeller Reynolds number has a relatively small influence. The forcing period must be matched to angular speed: decreasing the forcing period below this threshold results in a less intense, more inhomogeneous turbulent flow. Spectra of two-point velocity increments demonstrate that unsteady energy injection is dominated by axial shear generated across impellers and becomes less prominent at smaller scales. However, even at R_lambda approx 354, the signature of this unsteady forcing can still be detected in near-dissipation-range statistics. These observations provide insight into optimisation of forcing and the mechanism of energy transfer when using unsteady forcing to generate turbulence in confined vessels.Graphical abstract

Transport equations for the normalized nth-order moments of velocity derivatives in grid turbulence

Transport equations for the normalized moments of the longitudinal velocity derivative ${F_{n + 1}}$ (here, $n$ is $1, 2, 3\ldots$ ) are derived from the Navier–Stokes (N–S) equations for shearless grid turbulence. The effect of the (large-scale) streamwise advection of ${F_{n + 1}}$ by the mean velocity on the normalized moments of the velocity derivatives can be expressed as $C_1 {F_{n + 1}}/Re_\lambda$ , where $C_1$ is a constant and $Re_\lambda$ is the Taylor microscale Reynolds number. Transport equations for the normalized odd moments of the transverse velocity derivatives ${F_{y,n + 1}}$ (here, $n$ is 2, 4, 6), which should be zero if local isotropy is satisfied, are also derived and discussed in sheared and shearless grid turbulence. The effect of the (large-scale) streamwise advection term on the normalized moments of the velocity derivatives can also be expressed in the form $C_2 {F_{y,n + 1}}/Re_\lambda$ , where $C_2$ is a constant. Finally, the contribution of the mean shear in the transport equation for ${F_{n + 1}}$ can be modelled as $15 B/Re_\lambda$ , where $B$ ( $=S^*{S_{s,n + 1}}$ ) is the product of the non-dimensional shear parameter $S^*$ and the normalized mixed longitudinal-transverse velocity derivatives ${{S_{s,n + 1}}}$ ; if local isotropy is satisfied, $S_{s,n + 1}$ should be zero. These results indicate that if ${F_{n + 1}}$ , ${F_{y,n + 1}}$ and $B$ do not increase as rapidly as $Re_\lambda$ , then the effect of the large-scale structures on small-scale turbulence will disappear when $Re_\lambda$ becomes sufficiently large.

Geometry and dynamics of passive scalar structures in compressible turbulent mixing

We present a structure-based numerical analysis of passive scalar mixing in decaying homogeneous isotropic turbulence (DHIT) and shock-turbulence interaction canonical configurations. The analysis focuses on the temporal evolution of ensembles of passive scalar structures, initialized as spheres of different sizes relative to the Taylor microscale. An algorithm is introduced to track the evolution of each individual structure and the interactions with other structures in the ensemble, relating changes in the surface geometry and the underlying physical processes (turbulent transport, scalar dissipation, and shock compression). The tracking algorithm is applied to datasets from shock-capturing direct numerical simulations of DHIT, with Taylor microscale Reynolds number Reλ=40 and turbulence Mach number Mt=0.2, and STI cases in which the turbulence is processed by a shock wave at Mach numbers M = 1.5 and 3.0. Temporal surface convolution increases for initially larger structures, resulting in a higher probability of locally hyperbolic geometries where breakup into smaller structures occurs. Shock-induced deformation of the structures amplifies breakup processes, enhancing mixing, particularly for larger structures. Mixing enhancement by the shock is manifested as an amplification of the surface-averaged scalar gradient, which increases for initially larger structures. The alignment between the scalar gradient and the most extensional strain-rate eigendirection on the scalar isosurfaces also increases across the shock. Larger magnitudes of the scalar gradient and its alignment with the most compressive strain-rate eigendirection correlate with flatter surface regions. Shock-induced structure compression increases the area coverage of flat regions, where the amplification of scalar gradient is localized.

Study of the interaction of two decaying grid-generated turbulent flows

Hot-wire measurements are carried out in a decaying turbulence downstream of a grid made up of two juxtaposed perforated plates with different mesh sizes but same solidity. The two perforated plates generate two interacting (quasi–) homogeneous and isotropic decaying turbulent flows with distinct turbulence intensities and integral length scales. The interaction between these two flows leads to the development of a shearless turbulent mixing layer (STML). The main focus is on the decay of the turbulence centerline of the STML. Along the downstream distance x, the Taylor microscale Reynolds number, Reλ, remains constant, the streamwise velocity variance behaves like x−1, and the Taylor microscale (λ) varies as x1/2. This indicates that the turbulence on the centerline of the STML decays in a perfectly self-preserving manner at all scales of motion. This is further supported by the very good collapse of the velocity spectra, second-, and third-order velocity structure functions.