arXiv subjects

T. Elperin

Publications and source records attributed to T. Elperin.

At least 19 recordsLinked to original sources

arXiv2020

Detection of standing internal gravity waves in experiments with convection over a wavy heated wall

Convection over a wavy heated bottom wall in the air flow has been studied in experiments with the Rayleigh number $\sim 10^8$. It is shown that the mean temperature gradient in the flow core inside a large-scale circulation is directed upward, that corresponds to the stably stratified flow. In the experiments with a wavy heated bottom wall, we detect large-scale standing internal gravity waves excited in the regions with the stably stratified flow. The wavelength and the period of these waves are much larger than the turbulent spatial and time scales, respectively. In particular, the frequencies of the observed large-scale waves vary from 0.006 Hz to 0.07 Hz, while the turbulent time in the integral scale is about 0.5 s. The measured spectra of these waves contains several localized maxima, that implies an existence of waveguide resonators for the large-scale standing internal gravity waves. For comparisons, experiments with convection over a smooth plane bottom wall at the same mean temperature difference between bottom and upper walls have been also conducted. In these experiments various locations with a stably stratified flow are also found and the large-scale standing internal gravity waves are observed in these regions.

physics.flu-dyn↗

arXiv2017

Turbulent diffusion of chemically reacting flows: theory and numerical simulations

The theory of turbulent diffusion of chemically reacting gaseous admixtures developed previously (Phys. Rev. E {\bf 90}, 053001, 2014) is generalized for large yet finite Reynolds numbers, and the dependence of turbulent diffusion coefficient versus two parameters, the Reynolds number and Damköhler number (which characterizes a ratio of turbulent and reaction time scales) is obtained. Three-dimensional direct numerical simulations (DNS) of a finite thickness reaction wave for the first-order chemical reactions propagating in forced, homogeneous, isotropic, and incompressible turbulence are performed to validate the theoretically predicted effect of chemical reactions on turbulent diffusion. It is shown that the obtained DNS results are in a good agreement with the developed theory.

physics.flu-dyn↗

arXiv2017

Three-dimensional slow Rossby waves in rotating spherical density stratified convection

We develop a theory of three-dimensional slow Rossby waves in rotating spherical density stratified convection. The Rossby waves with frequencies which are much smaller than the rotating frequency, are excited by a non-axisymmetric instability from the equilibrium based on the developed convection. These waves interact with the inertial waves and the density stratified convection. The density stratification is taken into account using the anelastic approximation for very low-Mach-number flows. We study long-term planetary Rossby waves with periods which are larger than two years. We suggest that these waves are related to the Southern Oscillation and El Niño. The El Niño is an irregularly periodical variation in winds and sea surface temperatures over the tropical Pacific Ocean, while the Southern Oscillation is an oscillation in surface air pressure between the tropical eastern and the western Pacific Ocean. The strength of the Southern Oscillation is characterised by the Southern Oscillation Index (SOI). The developed theory is applied for the interpretation of the observed periods of the SOI. This study demonstrates a good agreement between the theoretical predictions and the observations.

physics.flu-dyn↗

arXiv2017

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.

physics.flu-dyn↗

arXiv2015

Acceleration of raindrops formation due to tangling-clustering instability in turbulent stratified atmosphere

Condensation of water vapor on active cloud condensation nuclei produces micron-size water droplets. To form rain, they must grow rapidly into at least 50-100 $μ$m droplets. Observations show that this process takes only 15-20 minutes. The unexplained physical mechanism of such fast growth, is crucial for understanding and modeling of rain, and known as "condensation-coalescence bottleneck in rain formation". We show that the recently discovered phenomenon of the tangling clustering instability of small droplets in temperature-stratified turbulence (Phys. Fluids 25, 085104, 2013) results in the formation of droplet clusters with drastically increased droplet number densities. The mechanism of the tangling clustering instability is much more effective than the previously considered by us the inertial clustering instability caused by the centrifugal effect of turbulent vortices. This is the reason of strong enhancement of the collision-coalescence rate inside the clusters. The mean-field theory of the droplet growth developed in this study can be useful for explanation of the observed fast growth of cloud droplets in warm clouds from the initial 1 micron size droplets to 40-50 micron size droplets within 15-20 minutes.

physics.ao-ph↗

arXiv2015

A hierarchy of energy- and flux-budget (EFB) turbulence closure models for stably stratified geophysical flows

In this paper we advance physical background of the energy- and flux-budget turbulence closure based on the budget equations for the turbulent kinetic and potential energies and turbulent fluxes of momentum and buoyancy, and a new relaxation equation for the turbulent dissipation time-scale. The closure is designed for stratified geophysical flows from neutral to very stable and accounts for the Earth rotation. In accordance to modern experimental evidence, the closure implies maintaining of turbulence by the velocity shear at any gradient Richardson number Ri, and distinguishes between the two principally different regimes: "strong turbulence" at Ri << 1 typical of boundary-layer flows and characterised by the practically constant turbulent Prandtl number; and "weak turbulence" at Ri > 1 typical of the free atmosphere or deep ocean, where the turbulent Prandtl number asymptotically linearly increases with increasing Ri (which implies very strong suppression of the heat transfer compared to the momentum transfer). For use in different applications, the closure is formulated at different levels of complexity, from the local algebraic model relevant to the steady-state regime of turbulence to a hierarchy of non-local closures including simpler down-gradient models, presented in terms of the eddy-viscosity and eddy-conductivity, and general non-gradient model based on prognostic equations for all basic parameters of turbulence including turbulent fluxes.

physics.ao-ph↗

arXiv2014

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 temperature gradient increases.

physics.flu-dyn↗

arXiv2013

Helicity of mean and turbulent flow with coherent structures in Rayleigh-Benard 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. 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.

physics.flu-dyn↗

arXiv2012

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 $\big[(\ell_x \nabla_x \bar{T})^2 + (\ell_y \nabla_y \bar{T})^2 + (\ell_z \nabla_z \bar{T})^2\big] / <θ^2 >$ is nearly constant, is independent of the frequency of the grid oscillations and has the same magnitude for both, stably and unstably stratified turbulent flows, where $\ell_i$ are the integral scales of turbulence along $x, y, z$ directions, $\bar{T}$ and $θ$ are the mean and turbulent fluctuations components of the fluid temperature. We demonstrated that for large frequencies of the grid oscillations, the temperature field can be considered as a passive scalar, while for smaller frequencies the temperature field behaves as an active field. The theoretical predictions based on the budget equations for turbulent kinetic energy, turbulent potential energy ($\propto <θ^2 >)$ and turbulent heat flux, are in a good agreement with the experimental results. Detailed comparison with experimental results obtained previously in unstably stratified forced turbulence is performed.

physics.flu-dyn↗

arXiv2011

Transition phenomena in unstably stratified turbulent flows

We study experimentally and theoretically transition phenomena caused by the external forcing from Rayleigh-Benard convection with the large-scale circulation (LSC) to the limiting regime of unstably stratified turbulent flow without LSC whereby the temperature field behaves like a passive scalar. In the experiments we use the Rayleigh-Bénard apparatus with an additional source of turbulence produced by two oscillating grids located nearby the side walls of the chamber. When the frequency of the grid oscillations is larger than 2 Hz, the large-scale circulation (LSC) in turbulent convection is destroyed, and the destruction of the LSC is accompanied by a strong change of the mean temperature distribution. However, in all regimes of the unstably stratified turbulent flow the ratio $\big[(\ell_x \nabla_x T)^2 + (\ell_y \nabla_y T)^2 + (\ell_z \nabla_z T)^2\big] / < θ^2 >$ varies slightly (even in the range of parameters whereby the behaviour of the temperature field is different from that of the passive scalar). Here $\ell_i$ are the integral scales of turbulence along x, y, z directions, T and θare the mean and fluctuating parts of the fluid temperature. At all frequencies of the grid oscillations we have detected the long-term nonlinear oscillations of the mean temperature. The theoretical predictions based on the budget equations for turbulent kinetic energy, turbulent temperature fluctuations and turbulent heat flux, are in agreement with the experimental results.

physics.flu-dyn↗

arXiv2010

Tangling clustering of inertial particles in stably stratified turbulence

We have predicted theoretically and detected in laboratory experiments a new type of particle clustering (tangling clustering of inertial particles) in a stably stratified turbulence with imposed mean vertical temperature gradient. In this stratified turbulence a spatial distribution of the mean particle number density is nonuniform due to the phenomenon of turbulent thermal diffusion, that results in formation of a gradient of the mean particle number density, \nabla N, and generation of fluctuations of the particle number density by tangling of the gradient, \nabla N, by velocity fluctuations. The mean temperature gradient, \nabla T, produces the temperature fluctuations by tangling of the gradient, \nabla T, by velocity fluctuations. These fluctuations increase the rate of formation of the particle clusters in small scales. In the laboratory stratified turbulence this tangling clustering is much more effective than a pure inertial clustering that has been observed in isothermal turbulence. In particular, in our experiments in oscillating grid isothermal turbulence in air without imposed mean temperature gradient, the inertial clustering is very weak for solid particles with the diameter 10 microns and Reynolds numbers Re =250. Our theoretical predictions are in a good agreement with the obtained experimental results.

physics.flu-dyn↗

arXiv2009

Turbulent Diffusion and Turbulent Thermal Diffusion of Aerosols in Stratified Atmospheric Flows

The paper analyzes the phenomenon of turbulent thermal diffusion in the Earth atmosphere, its relation to the turbulent diffusion and its potential impact on aerosol distribution. This phenomenon was predicted theoretically more than 10 years ago and detected recently in the laboratory experiments. This effect causes a non-diffusive flux of aerosols in the direction of the heat flux and results in formation of long-living aerosol layers in the vicinity of temperature inversions. We demonstrated that the theory of turbulent thermal diffusion explains the GOMOS aerosol observations near the tropopause (i.e., the observed shape of aerosol vertical profiles with elevated concentrations located almost symmetrically with respect to temperature profile). In combination with the derived expression for the dependence of the turbulent thermal diffusion ratio on the turbulent diffusion, these measurements yield an independent method for determining the coefficient of turbulent diffusion at the tropopause. We evaluated the impact of turbulent thermal diffusion to the lower-troposphere vertical profiles of aerosol concentration by means of numerical dispersion modelling, and found a regular upward forcing of aerosols with coarse particles affected stronger than fine aerosols.

physics.ao-ph↗

arXiv2009

Energy- and flux-budget turbulence closure model for stably stratified flows. Part II: the role of internal gravity waves

We advance our prior energy- and flux-budget turbulence closure model (Zilitinkevich et al., 2007, 2008) for the stably stratified atmospheric flows and extend it accounting for additional vertical flux of momentum and additional productions of turbulent kinetic energy, turbulent potential energy (TPE) and turbulent flux of potential temperature due to large-scale internal gravity waves (IGW). Main effects of IGW are following: the maximal value of the flux Richardson number (universal constant 0.2-0.25 in the no-IGW regime) becomes strongly variable. In the vertically homogeneous stratification, it increases with increasing wave energy and can even exceed 1. In the heterogeneous stratification, when IGW propagate towards stronger stratification, the maximal flux Richardson number decreases with increasing wave energy, reaches zero and then becomes negative. In other words, the vertical flux of potential temperature becomes counter-gradient. IGW also reduce anisotropy of turbulence and increase the share of TPE in the turbulent total energy. Depending on the direction (downward or upward), IGW either strengthen or weaken the total vertical flux of momentum. Predictions from the proposed model are consistent with available data from atmospheric and laboratory experiments, direct numerical simulations and large-eddy simulations.

physics.ao-ph↗

arXiv2009

Effect of large-scale coherent structures on turbulent convection

We study an effect of large-scale coherent structures on global properties of turbulent convection in laboratory experiments in air flow in a rectangular chamber with aspect ratios $A \approx 2$ and $A\approx 4$ (with the Rayleigh numbers varying in the range from $5 \times 10^6$ to $10^8$). The large-scale coherent structures comprise the one-cell and two-cell flow patterns. We found that a main contribution to the turbulence kinetic energy production in turbulent convection with large-scale coherent structures is due to the non-uniform large-scale motions. Turbulence in large Rayleigh number convection with coherent structures is produced by shear, rather than by buoyancy. We determined the scalings of global parameters (e.g., the production and dissipation of turbulent kinetic energy, the turbulent velocity and integral turbulent scale, the large-scale shear, etc.) of turbulent convection versus the temperature difference between the bottom and the top walls of the chamber. These scalings are in an agreement with our theoretical predictions. We demonstrated that the degree of inhomogeneity of the turbulent convection with large-scale coherent structures is small.

physics.flu-dyn↗

arXiv2009

Mixing at the external boundary of a submerged turbulent jet

We study experimentally and theoretically mixing at the external boundary of a submerged turbulent jet. In the experimental study we use Particle Image Velocimetry and an Image Processing Technique based on the analysis of the intensity of the Mie scattering to determine the spatial distribution of tracer particles. An air jet is seeded with the incense smoke particles which are characterized by large Schmidt number and small Stokes number. We determine the spatial distributions of the jet fluid characterized by a high concentration of the particles and of the ambient fluid characterized by a low concentration of the tracer particles. In the data analysis we use two approaches, whereby one approach is based on the measured phase function for the study of the mixed state of two fluids. The other approach is based on the analysis of the two-point second-order correlation function of the particle number density fluctuations generated by tangling of the gradient of the mean particle number density by the turbulent velocity field. This gradient is formed at the external boundary of a submerged turbulent jet. We demonstrate that PDF of the phase function of a jet fluid penetrating into an external flow and the two-point second-order correlation function of the particle number density do not have universal scaling and cannot be described by a power-law function. The theoretical predictions made in this study are in a qualitative agreement with the obtained experimental results.

physics.flu-dyn↗

arXiv2008

Turbulence energetics in stably stratified geophysical flows: strong and weak mixing regimes

Traditionally, turbulence energetics is characterized by turbulent kinetic energy (TKE) and modelled using solely the TKE budget equation. In stable stratification, TKE is generated by the velocity shear and expended through viscous dissipation and work against buoyancy forces. The effect of stratification is characterized by the ratio of the buoyancy gradient to squared shear, called Richardson number, Ri. It is widely believed that at Ri exceeding a critical value, Ric, local shear cannot maintain turbulence, and the flow becomes laminar. We revise this concept by extending the energy analysis to turbulent potential and total energies (TPE and TTE = TKE + TPE), consider their budget equations, and conclude that TTE is a conservative parameter maintained by shear in any stratification. Hence there is no "energetics Ric", in contrast to the hydrodynamic-instability threshold, Ric-instability, whose typical values vary from 0.25 to 1. We demonstrate that this interval, 0.25 >1, clarify principal difference between turbulent boundary layers and free flows, and provide basis for improving operational turbulence closure models.

physics.ao-ph↗

arXiv2007

Large-scale instability in a sheared nonhelical turbulence: formation of vortical structures

We study a large-scale instability in a sheared nonhelical turbulence that causes generation of large-scale vorticity. Three types of the background large-scale flows are considered, i.e., the Couette and Poiseuille flows in a small-scale homogeneous turbulence, and the "log-linear" velocity shear in an inhomogeneous turbulence. It is known that laminar plane Couette flow and antisymmetric mode of laminar plane Poiseuille flow are stable with respect to small perturbations for any Reynolds numbers. We demonstrate that in a small-scale turbulence under certain conditions the large-scale Couette and Poiseuille flows are unstable due to the large-scale instability. This instability causes formation of large-scale vortical structures stretched along the mean sheared velocity. The growth rate of the large-scale instability for the "log-linear" velocity shear is much larger than that for the Couette and Poiseuille background flows. We have found a turbulent analogue of the Tollmien-Schlichting waves in a small-scale sheared turbulence. A mechanism of excitation of turbulent Tollmien-Schlichting waves is associated with a combined effect of the turbulent Reynolds stress-induced generation of perturbations of the mean vorticity and the background sheared motions. These waves can be excited even in a plane Couette flow imposed on a small-scale turbulence when perturbations of mean velocity depend on three spatial coordinates. The energy of these waves is supplied by the small-scale sheared turbulence.

physics.flu-dyn↗

arXiv2007

Energy- and flux-budget (EFB) turbulence closure model for the stably stratified flows. Part I: Steady-state, homogeneous regimes

We propose a new turbulence closure model based on the budget equations for the key second moments: turbulent kinetic and potential energies: TKE and TPE (comprising the turbulent total energy: TTE = TKE + TPE) and vertical turbulent fluxes of momentum and buoyancy (proportional to potential temperature). Besides the concept of TTE, we take into account the non-gradient correction to the traditional buoyancy flux formulation. The proposed model grants the existence of turbulence at any gradient Richardson number, Ri. Instead of its critical value separating - as usually assumed - the turbulent and the laminar regimes, it reveals a transition interval, 0.1< Ri <1, which separates two regimes of essentially different nature but both turbulent: strong turbulence at Ri<<1; and weak turbulence, capable of transporting momentum but much less efficient in transporting heat, at Ri>1. Predictions from this model are consistent with available data from atmospheric and lab experiments, direct numerical simulation (DNS) and large-eddy simulation (LES).

physics.ao-ph↗