Avi Levy

We investigate the phenomenon of turbulent thermal diffusion of inertial solid particles in laboratory experiments with convective turbulence forced by one or two oscillating grids in the air. Turbulent thermal diffusion causes a non-diffusive contribution to the turbulent flux of particles described in terms of an effective drift velocity directed opposite to the gradient of the mean fluid temperature. For inertial particles, this effective drift velocity depends on the Stokes and Reynolds numbers. In the experiments, fluid velocity and spatial distribution of inertial particles are measured using a particle image velocimetry system, and the temperature field is measured in many locations by a temperature probe equipped with 12 thermocouples. Measurements of temperature and particle number density spatial distributions have demonstrated the formation of large-scale clusters of inertial particles in the vicinity of the mean temperature minimum due to turbulent thermal diffusion. In the experiments, the effective drift velocity caused by turbulent thermal diffusion which results in the formation of large-scale clusters of inertial particles (having a diameter 10 μm), is in 1.5–2.5 times larger than that for noninertial particles (having the diameter 0.7 μm) depending on the level of turbulence. This is in agreement with the theoretical predictions.

We develop a mechanistic thin-film theory for the instability and rupture of micrometer-scale liquid films subjected to high-frequency acoustic forcing. Starting from the compressible Navier–Stokes equations, a controlled multiscale expansion yields an averaged momentum balance in which acoustic radiation pressure and steady streaming stresses arise from a unified quadratic momentum flux. A lubrication reduction produces a closed evolution equation for the film thickness. Linear stability analysis identifies a finite-wavelength instability governed by an effective acoustic forcing that competes with capillarity and gravity, and a weakly nonlinear reduction distinguishes regimes of saturation and rupture within the thin-film limit. The framework yields scaling relations connecting viscous penetration, forcing amplitude, and a pre-rupture correlation length, clarifying that excitation frequency enters indirectly through penetration and acoustic efficiency rather than acting as a universal droplet-size selector.

We investigate properties of turbulence and turbulent transport of non-inertial particles described in terms of turbulent thermal diffusion in strongly inhomogeneous and anisotropic convection forced by two similar turbulence generators with an oscillating membrane and a steady grid in the air flow (with the Rayleigh number about 108). Velocity field and spatial distribution of particles are measured using the particle image velocimetry system. The temperature distribution is measured in many locations using a temperature probe equipped with 12 E-thermocouples. In the forced convection, the gradients of the mean temperature field and the particle number density in the horizontal direction in the core flow are much stronger than in the vertical direction. The mean fluid velocity structure shows a transition between a single-roll pattern for isothermal turbulence to double-roll patterns with an increase in the temperature difference between the bottom and upper walls of the chamber. For larger temperature differences, the mean fluid velocity structure returns to a single-roll pattern. In the turbulent regions with large mean temperature gradients, the dominant effect of the large-scale particle clustering is turbulent thermal diffusion, resulting in the maximum of the mean particle number density being located in the regions with the minimum of the mean temperature and vice versa. Deviations from this feature are observed in the regions with strong mean fluid velocities where the mean temperature gradients are small.

Based on a mean-field theory of a non-rotating turbulent convection [T. Elperin et al., Phys. Rev. E 66, 066305, (2002)], we perform mean-field simulations (MFS) of sheared convection that takes into account an effect of modification of the turbulent heat flux by the non-uniform large-scale motions. This effect is caused by the production of additional essentially anisotropic velocity fluctuations generated by tangling of the mean-velocity gradients by small-scale turbulent motions due to the influence of the inertial forces during the lifetime of turbulent eddies. These anisotropic velocity fluctuations contribute to the turbulent heat flux. As the result of this effect, there is an excitation of large-scale convective-shear instability, which causes the formation of large-scale semi-organized structures in the form of rolls. The lifetimes and spatial scales of these structures are much larger compared to the turbulent scales. By means of MFS performed for stress-free and no-slip vertical boundary conditions, we determine the spatial and temporal characteristics of these structures. Our study demonstrates that the modification of the turbulent heat flux by non-uniform flows leads to a strong reduction of the critical effective Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the formation of the large-scale rolls. During the nonlinear stage of the convective-shear instability, there is a transition from a two-layer vertical structure with two rolls in the vertical direction before the system reaches steady-state to a one-layer vertical structure with one roll after the system reaches steady state. This effect is observed for all effective Rayleigh numbers. We find that inside the convective rolls, the spatial distribution of the mean potential temperature includes regions with a positive vertical gradient of the potential temperature caused by the mean heat flux of the convective rolls. This study might be useful for understanding the origin of large-scale rolls observed in atmospheric convective boundary layers, as well as in numerical simulations and laboratory experiments.

We investigate experimentally the phenomenon of turbulent thermal diffusion of micrometer-size solid particles in an inhomogeneous convective turbulence forced by one vertically oriented oscillating grid in an air flow. This effect causes the formation of large-scale inhomogeneities in particle spatial distributions in a temperature-stratified turbulence. We perform detailed comparisons of the experimental results with those obtained in our previous experiments with an inhomogeneous and anisotropic stably stratified turbulence produced by a one oscillating grid in the air flow. Since the buoyancy increases the turbulent kinetic energy for convective turbulence and decreases it for stably stratified turbulence, the measured turbulent velocities for convective turbulence are larger than those for stably stratified turbulence. This tendency is also seen in the measured vertical integral turbulent length scales. Measurements of temperature and particle number density spatial distributions show that particles are accumulated in the vicinity of the minimum of the mean temperature due to the phenomenon of turbulent thermal diffusion. This effect is observed in both convective and stably stratified turbulence, where we find the effective turbulent thermal diffusion coefficient for micrometer-size particles. The obtained experimental results are in agreement with theoretical predictions.

It has been previously shown [Elperin et al., “Formation of large-scale semi-organized structures in turbulent convection,” Phys. Rev. E 66, 066305 (2002)] that a non-rotating turbulent convection with nonuniform large-scale flows contributes to the turbulent heat flux. As a result, the turbulent heat flux depends explicitly not only on the gradients of the large-scale temperature, but also on the gradients of the large-scale velocity. This is because the nonuniform large-scale flows produce anisotropic velocity fluctuations, which modify the turbulent heat flux. This effect causes an excitation of a convective-wind instability and formation of large-scale semi-organized coherent structures (large-scale convective cells). In the present study, we perform mean-field numerical simulations of shear-free convection, which take into account the modification of the turbulent heat flux by nonuniform large-scale flows. We use periodic boundary conditions in horizontal direction as well as stress-free or no-slip boundary conditions in vertical direction. We show that the redistribution of the turbulent heat flux by the nonuniform large-scale motions in turbulent convection plays a crucial role in the formation of the large-scale semi-organized coherent structures. In particular, this effect results in a strong reduction of the critical effective Rayleigh number (based on the eddy viscosity and turbulent temperature diffusivity) required for the formation of the large-scale convective cells. We demonstrate that the convective-wind instability is excited when the scale separation ratio between the height of the convective layer and the integral turbulence scale is large. The level of the mean kinetic energy at saturation increases with the scale separation ratio. We also show that inside the large-scale convective cells, there are local regions with the positive vertical gradient of the potential temperature, which implies that these regions are stably stratified.

In this study, we developed a model of convective heat and mass transfer of an acoustically levitated slurry droplet that evaporates in an atmosphere of air, water vapor, and soluble gas. The advanced model considered the effects of acoustic streaming, forced convection, and non-isothermal gas absorption on the evaporation rate of a liquid droplet containing small solid particles. It is shown that the time of porous shell formation decreases with the increase of sound pressure level (SPL) and increases with the increase in frequency. Adding soluble gas to the gaseous phase shortens the time required for porous shell formation during slurry droplet drying. As shown by numerical calculations, in a gas mixture containing air with an ammonia content of 30%, at a temperature of 293 K and a humidity of 50%, with an acoustic field frequency of 2π·45 kHz and an SPL of 140 dB, the time of porous shell formation of a silica-water slurry droplet with the initial radius of 250 µm is about half shorter than that in a gas mixture not containing an active gas. The prediction of the developed model was in good agreement with the experimental results available in literature.

Since leaf temperature (LT) is not a trivial measurement, deep-neural networks (DNN) and machine learning (ML) models were evaluated in this study as tools for estimating foliage temperature. Two DNN methods were used. The first DNN used convolutional layers, while the second DNN was based on fully-connected layers and was trained by cross-validation techniques. The machine learning used the K-nearest neighbors (KNN) method for LT estimation. All models used the meteorological and microclimatic parameters (hereafter referred to as features) of the examined greenhouses to determine the average foliage temperature. The models were trained on 75% of the collected data and tested on the remaining 25%. RMS and absolute error were used to evaluate the performance of the different models compared to the LT values measured by a thermal camera. In addition, after finding the correlation of each feature to the leaf temperature, the models were trained based on the high-correlated features only. The machine learning model was superior to DNN when all available features were used and when only high-correlated features were used, resulting in errors of 0.7 °C and 0.8 °C, respectively.

We experimentally studied the turbulent thermal diffusion of small particles in inhomogeneous and anisotropic stably stratified turbulence produced by one oscillating grid in the air flow. The velocity fields have been measured using Particle Image Velocimetry (PIV). We have determined various turbulence characteristics: the mean and turbulent velocities, two-point correlation functions of the velocity field, and an integral scale of turbulence from the measured velocity fields. The temperature field has been measured with a temperature probe equipped with 12 E thermocouples. Spatial distributions of micrometer-sized particles have been determined by a PIV system using the effect of the Mie light scattering by particles in the flow. The experiments have demonstrated that particles are accumulated at the minimum of mean fluid temperature due to the phenomenon of turbulent thermal diffusion. Using measured spatial distributions of particles and temperature fields, we have determined the effective turbulent thermal diffusion coefficient of particles in inhomogeneous temperature-stratified turbulence. This experimental study has clearly detected the phenomenon of turbulent thermal diffusion in inhomogeneous turbulence.