A. Eidelman

On the universality of large-scale turbulence

Large-scale three-dimensional turbulence is a challenge to researchers, being one of the most complicated aspects of turbulence studies. The universal large scales behavior connected with the inverse energy cascade in two-dimensional turbulence has been known for about 35 years and studied experimentally and numerically. We have revealed the universality of three-dimensional large-scale turbulence properties experimentally and described it theoretically. A rigorous solution of this problem in the presence of an energy source gives scaling exponents −4/3 for velocity correlations and 1/3 for energy spectra of the large-scale turbulence. Such spectra are also observed in atmospheric air flows under different conditions—stable, convective, in cirrus clouds. The revealed physical phenomenon is important for the development of turbulence theory complementing the results obtained for its smaller scales.

Helicity of mean and turbulent flow with coherent structures in Rayleigh-Bénard convective cell

We present results of the study of a turbulent air flow with a large scale circulation in Rayleigh-Benard rectangular convective cell with a heated bottom wall and a cooled top wall. Velocity fields were measured using Particle Image Velocimetry in two sets of mutually perpendicular planes parallel to the vertical walls of the cell. Experiments revealed the existence of the main roll, having a length scale of the order of the size of the cell, and elongated eddy rings adjacent to the bottom and top of the main roll. The mean horizontal velocity of the main roll and the mean vorticity of eddy rings are almost aligned in a large part of the flow. The helicity of the mean flow is quite high, and is the source of turbulent helicity. Since helicity of the mean flow and turbulence is quite large, the flow in Rayleigh-Benard convective cell is well suited to study properties of helical turbulence. Spatial distribution of the turbulent kinetic energy is almost locally isotropic in the central region of the cell. ...

Sheared stably stratified turbulence and large-scale waves in a lid driven cavity

We investigated experimentally stably stratified turbulent flows in a lid driven cavity with a non-zero vertical mean temperature gradient in order to identify the parameters governing the mean and turbulent flows and to understand their effects on the momentum and heat transfer. We found that the mean velocity patterns (e.g., the form and the sizes of the large-scale circulations) depend strongly on the degree of the temperature stratification. In the case of strong stable stratification, the strong turbulence region is located in the vicinity of the main large-scale circulation. We detected the large-scale nonlinear oscillations in the case of strong stable stratification which can be interpreted as nonlinear internal gravity waves. The ratio of the main energy-containing frequencies of these waves in velocity and temperature fields in the nonlinear stage is about 2. The amplitude of the waves increases in the region of weak turbulence (near the bottom wall of the cavity), whereby the vertical mean temp...

Turbulent thermal diffusion in strongly stratified turbulence: Theory and experiments

Turbulent thermal diffusion is a combined effect of the temperature stratified turbulence and inertia of small particles. It causes the appearance of a non-diffusive turbulent flux of particles in the direction of the turbulent heat flux. This non-diffusive turbulent flux of particles is proportional to the product of the mean particle number density and the effective velocity of inertial particles. The theory of this effect has been previously developed only for small temperature gradients and small Stokes numbers (Phys. Rev. Lett. {\bf 76}, 224, 1996). In this study a generalized theory of turbulent thermal diffusion for arbitrary temperature gradients and Stokes numbers has been developed. The laboratory experiments in the oscillating grid turbulence and in the multi-fan produced turbulence have been performed to validate the theory of turbulent thermal diffusion in strongly stratified turbulent flows. It has been shown that the ratio of the effective velocity of inertial particles to the characteristic vertical turbulent velocity for large Reynolds numbers is less than 1. The effective velocity of inertial particles as well as the effective coefficient of turbulent thermal diffusion increase with Stokes numbers reaching the maximum at small Stokes numbers and decreases for larger Stokes numbers. The effective coefficient of turbulent thermal diffusion also decreases with the mean temperature gradient. It has been demonstrated that the developed theory is in a good agreement with the results of the laboratory experiments.

Peculiarities of turbulence in a flow with vortices

Abstract In the atmospheric boundary layer there exist groups of roll vortices contributing considerably to the momentum transfer, motion properties, etc. There are data pointing to an important role of such vortices in the formation of such a dangerous extreme weather event (EWE) as a tornado. It is known that helical turbulence mode is the cause of the similarity of atmospheric and magnetohydrodynamic turbulence. To clarify the peculiarities of EWE origination, experimental studies of MHD turbulence were carried out under laboratory conditions.

Influence of variations of dissipation and pressure on formation of coherent structures in geophysical media

Abstract In this work containing both reviewed and original results we analyze the behaviour of the Reynolds stress tensor in a helical turbulent medium taking into account: the relation between the direct and inverse transfer of the averaged motion parameters, the effects of higher moments of the turbulent field and helical fluctuations on the turbulent viscosity. We analyze the reasons of the helical structure localization due to: a) the medium inhomogeneity, b) the negative turbulent viscosity, c) the excess of the external pressure of the medium surrounding the region with helical turbulence. A possible structure of the tropical cyclone (TC) is discussed taking into account the helical inhomogeneity. Characteristic properties in the pressure behaviour at the TC origination are revealed and elucidated.

Experimental study of temperature fluctuations in forced stably stratified turbulent flows

We study experimentally temperature fluctuations in stably stratified forced turbulence in air flow. In the experiments with an imposed vertical temperature gradient, the turbulence is produced by two oscillating grids located nearby the side walls of the chamber. Particle image velocimetry is used to determine the turbulent and mean velocity fields, and a specially designed temperature probe with sensitive thermocouples is employed to measure the temperature field. We found that the ratio (� x ∇xT) 2 + (� y∇yT) 2 + (� z∇zT) 2 /� θ 2 � is nearly constant, is independent of the frequency of the grid oscillations, and has the same magnitude for both, stably and

Experimental Detection of the New Phenomenon of Turbulent Thermal Diffusion

A new phenomenon of turbulent thermal diffusion, which was predicted theoretically in [1,2], has been detected experimentally in oscillating grids turbulence with an imposed mean temperature gradient in air flow with a stable and unstable stratification. This effect implies an additional mean flux of particles in the direction opposite to the mean temperature gradient and results in formation of large-scale inhomogeneities in the spatial distribution of particles. We used Particle Image Velocimetry (PIV) to determine the turbulent velocity field and an Image Processing Technique to determine the spatial distribution of particles. Analysis of the intensity of laser light Mie scattering by particles showed that they are accumulated in the vicinity of the minimum of the mean temperature of the surrounding fluid due to the effect of turbulent thermal diffusion. Phenomenon of molecular thermal diffusion in gases was predicted by Enskog (1911) and confirmed experimentally by Chapman and Dootson (1917), and thermophoresis of particles was observed by Tyndall (1870). Equation for the number density n of particles taking into account this effect reads ∂n/∂t = −∇ · J M , where the flux of particles J M is given by J M = −D(∇n + kt∇T/T ). The first term in the formula for the flux of particles describes molecular diffusion, while the second term accounts for the flux of particles caused by the fluid temperature gradient ∇T (molecular thermal diffusion). Here D is the coefficient of molecular diffusion, kt ∝ n is the thermal diffusion ratio, and D M = Dkt is the coefficient of molecular thermal diffusion. In turbulent fluid flow at large Reynolds and Peclet numbers the nature of diffusion drastically changes, e.g., turbulence results in a sharp increase of the effective diffusion coefficient. It was found in [1,2] that in a low Mach number turbulent fluid flow with a nonzero mean temperature gradient there appears an additional mean flux of particles or gases in the direction opposite to the mean temperature gradient (the phenomenon of turbulent thermal diffusion). For large Reynolds and Peclet numbers the turbulent thermal diffusion is much stronger than the molecular thermal diffusion. The mechanism of this effect for solid particles is as follows. The inertia causes particles inside the turbulent eddies to drift out to the boundary regions between eddies (i.e., regions with low vorticity or high strain rate and maximum of fluid pressure). Thus, particles are accumulated in regions with the maximum pressure of the turbulent fluid. Similarly, there is an outflow of particles from regions with the minimum pressure of fluid. In a homogeneous and isotropic turbulence without imposed large-scale gradients of temperature a drift from regions with increased (decreased) concentration of particles by a turbulent flow of fluid is equiprobable in all directions. Therefore pressure (temperature) of the surrounding fluid is not correlated with turbulent velocity field and there exists only turbulent diffusion of particles. Situation drastically changes in a turbulent fluid flow with a mean temperature gradient. In this case the mean heat flux 〈uΘ〉 is not zero, i.e., fluctuations of fluid temperature Θ and velocity u of fluid are correlated. Fluctuations of temperature cause fluctuations of pressure of the fluid, and the pressure fluctuations result in fluctuations of the number density of particles. Indeed, increase (decrease) of the pressure of surrounding fluid is accompanied by accumulation (outflow) of the particles. Therefore, direction of mean flux of particles 〈un〉 coincides with that of heat flux, i.e., 〈un〉 ∝ 〈uΘ〉 ∝ −∇T̄ , where T̄ is the mean fluid temperature. The mean flux of particles is directed to the minimum of the mean temperature T̄ and the particles are accumulated in this region. Evolution of the number density n(t, r) of small particles in a turbulent flow is determined by equation: ∂n/∂t+∇·(nvp) = −∇·JM , where vp is the velocity field of the particles which they acquire in a turbulent fluid velocity field. Averaging this equation over turbulent velocity field we arrive at the equation for the mean number density of particles N̄ ≡ 〈n〉 :

Effect of the external magnetic field on the MHD turbulence spectra

The turbulent properties of conducting fluids in an external constant magnetic field are known to change with increasing field strength. A study is made of the behavior of the second-order structural function of the velocity field in a homogeneous incompressible turbulent fluid in the presence of an external uniform magnetic field. It is shown that, depending on the magnetic field strength, there may be different governing parameters of the system in both the inertial and dissipative intervals of turbulence. This leads to new spectral scalings that are consistent with experimental ones.