ONE of the main goals in the development of theory of chaotic dynamical system has been to make progress in understanding of turbulence. The attempts to related turbulence to chaotic motion got strong impetus from the celebrated paper by Ruelle and Takens . Considerable success has been achieved mainly in the area: the onset of turbulence. For fully developed turbulence, many questions remain unanswered. The aim of this letter is to show that there are dynamical systems that are much simpler than the Navier-Stokes equations but that can still have turbulent states and for which many concepts developed in the theory of dynamical systems can be successfully applied. In this connection we advocate a broader use of the universal properties of a wide range of isotropic turbulence phenomena. Even for the case of fully developed turbulence, which contains an extreme range of relevant length scales, it is possible, by using the present model, to reproduce a surprising variety of relevant features, such as multifractal cascade, intermittency. This letter reverts to possible applications of the Navier-Stokes equations to studies of the nature of turbulence.
We treat a turbulent velocity field as a message in the same way as a book or a picture. All messages can be described by their entropy per symbol $h$, defined as in Shannon's theory of communication. In a turbulent flow, as the Reynolds number $Re$ increases, more correlated degrees of freedom are excited and participate in the turbulent cascade. Experiments in a turbulent soap film suggest that the spatial entropy density $h$ is a decreasing function of $Re$, namely $h \propto -\log Re$ + const. In the logistic map, also analyzed here, increasing the control parameter $r$ increases $h$. A mo…
We investigate the effect of cooperative interactions in an ensemble of microorganisms, modelled as self-propelled disk-like and rod-like particles, in a three-dimensional turbulent flow to show flocking as an emergent phenomenon. Building on the work by Choudhary, et al. [Europhys. Lett. 112, 24005 (2015)] for two-dimensional systems, and combining ideas from active matter and turbulent transport, we show that non-trivial correlations between the flow and individual dynamics are essential for the microorganisms to flock in, for example, a turbulent three-dimensional, marine environment. Our r…
We study the spatial distribution of gyrotactic microorganisms transported by a three-dimensional turbulent flow generated by direct numerical simulations. We find that gyrotaxis combines with turbulent fluctuations to produce small scales (multi-)fractal clustering. We explain this result by showing that gyrotactic swimming cells behave like tracers in a compressible flow. The effective compressibility is derived in the limits of fluid acceleration much larger and smaller than the gravity.
Inspired by the lotus effect, many studies in the last decade have focused on micro- and nano-patterned surfaces. They revealed that patterns at the micro-scale combined with high contact angles can significantly reduce skin drag. However, the mechanisms and parameters that control drag reduction, e.g. Reynolds number and pattern geometry, are still unclear. We propose an effective medium representation of the micro-features, that treats the latter as a porous medium, and provides a framework to model flow over patterned surfaces in both Cassie and Wenzel states. Our key result is a closed-for…
The motility of microorganisms is often biased by gradients in physical and chemical properties of their environment, with myriad implications on their ecology. Here we show that fluid acceleration reorients gyrotactic plankton, triggering small-scale clustering. We experimentally demonstrate this phenomenon by studying the distribution of the phytoplankton Chlamydomonas augustae within a rotating tank and find it to be in good agreement with a new, generalized model of gyrotaxis. When this model is implemented in a direct numerical simulation of turbulent flow, we find that fluid acceleration…
Solvent exchange is a process involving mixing between a good solvent with dissolved solute and a poor solvent. The process creates local oversaturation which causes the nucleation of minute solute droplets. Such ternary systems on a macro-scale have remained unexplored in the turbulent regime. We experimentally study the solvent exchange process by injecting mixtures of ethanol and trans-anethole into water, forming a turbulent buoyant jet in upward direction. Locally, turbulent mixing causes oversaturation of the trans-anethole following turbulent entrainment. We optically measure the concen…
We develop an adversarial-reinforcement learning scheme for microswimmers in statistically homogeneous and isotropic turbulent fluid flows, in both two (2D) and three dimensions (3D). We show that this scheme allows microswimmers to find non-trivial paths, which enable them to reach a target on average in less time than a naive microswimmer, which tries, at any instant of time and at a given position in space, to swim in the direction of the target. We use pseudospectral direct numerical simulations (DNSs) of the 2D and 3D (incompressible) Navier-Stokes equations to obtain the turbulent flows.…
New insight into the contribution of the microscale vortex evolution towards convection heat transfer in porous media is presented in this paper. The objective is to determine how the microscale vortices influence convection heat transfer in turbulent flow inside porous media. The microscale temperature distribution is analyzed using flow visualization in 2D using streamlines and in 3D using Q structures. The pertinent observations are supplemented with the comparison of surface skin friction and heat transfer using: (1) surface skin friction lines and (2) joint PDF of pressure and skin fricti…
Single-point hot-wire measurements in the bulk of a turbulent channel have been performed in order to detect and quantify the phenomenon of preferential bubble accumulation. We show that statistical analysis of the bubble-probe colliding-times series can give a robust method for investigation of clustering in the bulk regions of a turbulent flow where, due to the opacity of the flow, no imaging technique can be employed. We demonstrate that micro-bubbles (radius R_0 ~ 0.1 mm) in a developed turbulent flow, where the Kolmogorov length-scale is, eta ~ R_0, display preferential concentration in s…
Drag reduction by microbubbles is a promising engineering method for improving ship performance. A fundamental theory of the phenomenon is lacking however, making actual design quite uphazard. We offer here a theory of drag reduction by microbubbles in the limit of very small bubbles, when the effect of the bubbles is mainly to normalize the density and the viscosity of the carrier fluid. The theory culminates with a prediction of the degree of drag reduction given the concentration profile of the bubbles. Comparisons with experiments are discussed and the road ahead is sketched.
Many aquatic microorganisms are able to swim. In natural environments they typically do so in the presence of flows. In recent years it has been shown that the interplay of swimming and flows can give rise to interesting and biologically relevant phenomena, such as accumulation of microorganisms in specific flow regions and local alignment with the flow properties. Here, we consider a mechanical model for elongated microswimmers in a Kolmogorov flow, a prototypic shear flow, both in steady and in turbulent conditions. By means of direct numerical simulations, supported by analytical calculatio…
Microswimmer suspensions self-organize into complex spatio-temporal flow patterns, including vortex lattices and mesoscale turbulence. Here we explore the consequences for the motion of passive tracers, based on a continuum model for the microswimmer velocity field. We observe two qualitatively different regimes distinguished via the dimensionless Kubo number $K$. At advection strengths right above the transition to turbulence, the flow field evolves very slowly ($K \gg 1$) and the spatial vortex structures lead to dominant trapping effects. In contrast, deep in the turbulent state, much faste…
Obstacle-aware navigation of smart microswimmers in a turbulent flow
Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）；Department of Physics, Maulana Azad National Institute of Technology (MANIT)（莫拉纳·阿扎德国立理工学院物理系）；Institute of Scientific Computing, TU Dresden（德累斯顿工业大学科学计算研究所）
Micromixer is a key element in lab on a chip for broad applications in the analysis and measurement of chemistry and engineering. Previous investigations reported electrokinetic (EK) turbulence could be realized in a Y-type micromixer with a cross-sectional dimension of 100 $μ$m order. Although the ultrafast turbulent mixing can be generated at a bulk flow Reynolds number of O(1), the micromixer has not been optimized. In this investigation, we systematically investigated the influence of electric field intensity, AC frequency, electric conductivity ratio, and channel width at the entrance on …
The object of this paper is to study the influence of dispersed micrometer size particles on turbulent heat transfer mechanisms in wall-bounded flows. The strategic target of the current research is to set up a methodology to size and design new-concept heat transfer fluids with properties given by those of the base fluid modulated by the presence of dynamically-interacting, suitably-chosen, discrete micro- and nano- particles. We run Direct Numerical Simulation (DNS) for hydrodynamically fully-developed, thermally-developing turbulent channel flow at shear Reynolds number Re=150 and Prandtl n…
Mass-Transfer Control With Microbubbles in Highly Turbulent Decaying Flows
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology（乔治·W·伍德拉夫机械工程学院，佐治亚理工学院）；Renewable Bioproducts Institute, Georgia Institute of Technology（可再生生物制品研究所，佐治亚理工学院）
It is shown that the Truncated Euler Equations, i.e. a finite set of ordinary differential equations for the amplitude of the large-scale modes, can correctly describe the complex transitional dynamics that occur within the turbulent regime of a confined 2D Navier-Stokes flow with bottom friction and a spatially periodic forcing. In particular, the random reversals of the large scale circulation on the turbulent background involve bifurcations of the probability distribution function of the large-scale circulation velocity that are described by the related microcanonical distribution which dis…
Turbulent motions enhance the diffusion of large-scale flows and temperature gradients. Such diffusion is often parameterized by coefficients of turbulent viscosity ($ν_{\rm t}$) and turbulent thermal diffusivity ($χ_{\rm t}$) that are analogous to their microscopic counterparts. We compute the turbulent diffusion coefficients by imposing large-scale velocity and temperature gradients on a turbulent flow and measuring the response of the system. We also confirm our results using experiments where the imposed gradients are allowed to decay. To achieve this, we use weakly compressible three-dime…
The Rouse number is commonly used to estimate the mode of the sediment transports in turbulent flows with large Reynolds number. However, in microchannels such as in modern inkjet systems, the liquid flows are usually laminar. In this paper, I modify the Rouse number by expanding it to the case of weakly turbulent and laminar flows and construct a calculator to estimate the modes of sediment transport in microchannels. To illustrate the applicability of the modified Rouse number, I apply it to the transport of sediments in an inkjet system and compare theoretical results with experimental obse…
We study the laminar and turbulent channel flow over a viscous hyper-elastic wall and show that it is possible to sustain an unsteady chaotic turbulent-like flow at any Reynolds number by properly choosing the wall elastic modulus. We propose a physical explanation for this effect by evaluating the shear stress and the turbulent kinetic energy budget in the fluid and elastic layer. We vary the bulk Reynolds number from 2800 to 10 and identify two distinct mechanisms for turbulence production. At moderate and high Reynolds numbers, turbulent fluctuations activate the wall oscillations, which, i…
Experiments are presented that demonstrate how liquid-infused surfaces can reduce turbulent drag significantly in Taylor-Couette flow. The test liquid was water, and the test surface was composed of square microscopic grooves measuring 100 $μ$m to 800 $μ$m, filled with alkane liquids with viscosities from 0.3 to 1.4 times that of water. We achieve drag reduction exceeding 35\%, four times higher than previously reported for liquid-infused surfaces in turbulent flow. The level of drag reduction increased with viscosity ratio, groove width, fluid area fraction, and Reynolds number. The optimum g…
Phytoplankton patchiness, namely the heterogeneous distribution of microalgae over multiple spatial scales, dramatically impacts marine ecology. A spectacular example of such heterogeneity occurs in thin phytoplankton layers (TPLs), where large numbers of photosynthetic microorganisms are found within a small depth interval. Some species of motile phytoplankton can form TPLs by gyrotactic trapping due to the interplay of their particular swimming style (directed motion biased against gravity) and the transport by a flow with shear along the direction of gravity. Here we consider gyrotactic swi…
We combine a DEM simulation with a stochastic process to model the movement of spherical particles in a turbulent channel flow. With this model we investigate the mixing properties of two species of particles flowing through the channel. We find a linear increase of the mixing zone with the length of the pipe. Flows at different Reynolds number are studied. Below a critical Reynolds number at the Taylor microscale of around $R_{c} \approx 300$ the mixing rate is strongly dependent on the Reynolds number. Above $R_{c}$ the mixing rate stays nearly constant.
We investigate the effects of turbulent fluctuations on the Lagrangian statistics of absorption of a scalar field by tracer particles, as a model for nutrient uptake by suspended non-motile microorganisms. By means of extensive direct numerical simulations of an Eulerian-Lagrangian model we quantify, in terms of the Sherwood number, the increase of the scalar uptake induced by turbulence and its dependence on the Peclet and Reynolds numbers. Numerical results are compared with classical predictions for a stationary shear flow extended here to take into account the presence of a restoring scala…
Turbulent flows frequently accompany physical, chemical and biological processes, such as mixing, two-phase flow, combustion and even foraging by bacteria and plankton larvae, all of which are in principle subject to thermal fluctuations already on scales of several microns. Nevertheless the large separation between the millimeter scale at which turbulent fluctuations begin to be strongly damped and the mean free path of the fluid has been generally assumed to imply that thermal fluctuations are irrelevant to the turbulent dissipation range. Here we use statistical mechanical estimates to show…
We study experimentally 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 a 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 have been measured with a temperature probe equipped with 12 E thermocouples. Spatial distributions…
By varying the oil volume fraction, the microscopic droplet size and the macroscopic rheology of emulsions are investigated in a Taylor-Couette (TC) turbulent shear flow. Although here oil and water in the emulsions have almost the same physical properties (density and viscosity), unexpectedly, we find that oil-in-water (O/W) and water-in-oil (W/O) emulsions have very distinct hydrodynamic behaviors, i.e., the system is clearly asymmetric. By looking at the micro-scales, the average droplet diameter hardly changes with the oil volume fraction neither for O/W nor for W/O. However, for W/O it is…
We observe electro-hydrodynamically driven turbulent flows at low Reynolds numbers in a two-fluid emulsion consisting of micron-scale droplets. In the presence of electric fields, the droplets produce interacting hydrodynamic flows which result in a dynamical organization at a spatial scale much larger than the size of the individual droplets. We characterize the dynamics associated with these structures by both video imaging and a simultaneous, in situ, measurement of the time variation of the bulk Reynolds stress with a rheometer. The results display scale invariance in the energy spectra in…
The arrangement of brine above water across a micro porous permeable membrane is used to study high Rayleigh Number($10^{11}- 10^{10}$) high Schmidt number(650)turbulent convection. The flux shows 4/3$^{rd}$ scaling with line plume as the near wall coherent structures. Shifting of multiple large scale flow cells result in changing near membrane mean shear directions for large aspect ratios. Lower aspect ratios show single large scale flow cell and constant sense of mean shear.
Liquid-infused surfaces (LIS) can reduce friction drag in both laminar and turbulent flows. However, the heat transfer properties of such multi-phase surfaces have still not been investigated to a large extent. We use numerical simulations to study conjugate heat transfer of liquid-filled grooves. It is shown that heat transfer can increase for both laminar and turbulent liquid flows due to recirculation in the surface texture. For the increase to be substantial, the thermal conductivity of the solid must be similar to the thermal conductivity of the fluids, and the recirculation in the groove…
We study the effect of turbulence on marine life by performing numerical simulations of motile microorganisms, modelled as prolate spheroids, in isotropic homogeneous turbulence. We show that the clustering and patchiness observed in laminar flows, linear shear and vortex flows, are significantly reduced in a three-dimensional turbulent flow mainly because of the complex topology; elongated micro-orgamisms show some level of clustering in the case of swimmers without any preferential alignment whereas spherical swimmers remain uniformly distributed. Micro-organisms with one preferential swimmi…
Emulsions are omnipresent in the food industry, health care, and chemical synthesis. In this Letter the dynamics of meta-stable oil-water emulsions in highly turbulent ($10^{11}\leq\text{Ta}\leq 3\times 10^{13}$) Taylor--Couette flow, far from equilibrium, is investigated. By varying the oil-in-water void fraction, catastrophic phase inversion between oil-in-water and water-in-oil emulsions can be triggered, changing the morphology, including droplet sizes, and rheological properties of the mixture, dramatically. The manifestation of these different states is exemplified by combining global to…
Due to its very low viscosity, cryogenic helium has been used for years to generate high Reynolds turbulent flows. The measurement of velocity fluctuations in such high Reynolds flows is however a challenging issue, as it is necessary to develop small size (typically micron-length), robust sensors, to measure the whole spectrum of fluctuations of the velocity, which may extend to hundreds of kHz and possibly higher. SBT has developed for years different facilities, in particular taking benefit of the refrigeration capacities available at CEA Grenoble. In this article we present the current sta…
Rotating fans are the prevalent forced cooling method for heat generating equipment and buildings. As the concentration of atmospheric pollutants has increased, the accumulation of microscale and nanoscale particles on surfaces due to advection-diffusion has led to adverse mechanical, chemical and electrical effects that increase cooling demands and reduce the reliability of electronic equipment. Here, we uncover the mechanisms leading to enhanced deposition of particle matter (PM$_{10}$ and PM$_{2.5}$) on surfaces due to turbulent axial fan flows operating at Reynolds numbers, $Re \sim 10^5$.…
In this paper we explore a possibility that all transport turbulent models are contained in a coarse-grained kinetic equation. Building on a recent work by H.Chen et al (2004), we account for fluctuations of a single -point probability density in turbulence, by introducing a``two-level'' (${\bf c,v}$)-phase-space, separating microscopic (${\bf c'\equiv c_{micro}= c-v}$) and hydrodynamic (${\bf v'=v-V}$) modes. Unlike traditional kinetic theories, with hydrodynamic approximations derived in terms of small deviations from thermodynamic equilibrium, the theory developed in this work, is based on …
In their way to/from turbulence, plane wall-bounded flows display an interesting transitional regime where laminar and turbulent oblique bands alternate, the origin of which is still mysterious. In line with Barkley's recent work about the pipe flow transition involving reaction-diffusion concepts, we consider plane Couette flow in the same perspective and transform Waleffe's classical four-variable model of self-sustaining process into a reaction-diffusion model. We show that, upon fulfillment of a condition on the relative diffusivities of its variables, the featureless turbulent regime beco…
Estimation of the initial state of turbulent channel flow from limited data is investigated using an adjoint-variational approach. The data are generated from a reference direct numerical simulation (DNS) which is sub-sampled at different spatiotemporal resolutions. When the velocity data are at 1/4096 the spatiotemporal resolution of DNS, the correlation coefficient between the true and adjoint-variational estimated state exceeds 99 percent. The robustness of the algorithm to observation noise is demonstrated. In addition, the impact of the spatiotemporal density of the data on estimation qua…
Compressed copper powder has a very large electrical resistance (1MOhm), due to the oxide layer on grains (100 micro m). We observe that its voltage-current U-I characteristics are nonlinear, and undergo an instability, from an insulating to a conductive state at relatively small applied voltages. Current through the powder is then noisy, and the noise has interesting self-similar properties, including intermittency and scale invariance. We show that heat dissipation plays an essential role in the physics of the system. One piece of evidence is that the instability threshold always corresponds…
Almost 50 years ago Bob Brodkey and his student, Corino, conceived of and carried out a visualization experiment for the very near wall region of a turbulent pipe flow that, together with the turbulent boundary layer visualization of Kline et al., excited the turbulence research community. Using a high speed movie camera mounted on a lathe bed that recorded magnified images in a frame of reference moving with the flow, they observed the motions of sub-micron particles in the sub-, buffer- and log-layers. Surprisingly, these motions were not nearly so locally random as was the general view of t…
This paper presents a new theory of turbulent mixing in stirred reactors. The degree of homogeneity of a mixed fluid may be characterized by the Kolmogorov micro-scale. The smaller its value, the better homogeneity. The micro-scale scales inversely with the fourth root of the energy dissipation rate in the stirring process. The higher this rate, the smaller lambda, and the better the homogeneity in the reactor. This is true for Newtonian fluids. In non-Newtonian fluids the situation is different. For instance, in shear-thickening fluids it is plausible that high shear rates thicken the fluid a…
Many plankton species undergo daily vertical migration to large depths in the turbulent ocean. To do this efficiently, the plankton can use a gyrotactic mechanism, aligning them with gravity to swim downwards, or against gravity to swim upwards. Many species show passive mechanisms for gyrotactic stability. For example, bottom-heavy plankton tend to align upwards. This is efficient for upward migration in quiescent flows, but it is often sensitive to turbulence which upsets the alignment. Here we suggest a simple, robust active mechanism for gyrotactic stability, which is only lightly affected…
The focus of this paper is to systematically study the influence of solid obstacle surface roughness in porous media on the microscale flow physics and report its effect on macroscale drag and Nusselt number. The Reynolds averaged flow field is numerically simulated for a flow through a periodic porous medium consisting of an in-line arrangement of square cylinders with square roughness particles on the cylinder surface. Two flow regimes are identified with respect to the surface roughness particle height: fine and coarse roughness regimes. The effect of the roughness particles in the fine rou…
We investigate calcium carbonate scale formation at high Reynolds numbers in a large pipe rig facility. The calcium carbonate solution is produced from the injection, at a T-joint inlet, of pH-stabilized sodium carbonate and calcium chloride aqueous solutions. A scanning electron microscopy analysis of the deposited mass along the pipe indicates that after an initial transient regime of ion-by-ion crystal growth, calcium carbonate scale is dominated by particulate deposition. While limescale formation in regions that are closer to the pipe's entrance can be described as the heterogeneous surfa…
Peculiarities of the turbulent two phase and multiphase flows of the mutually immiscible liquids and averaged differential equations for their modeling are considered based on the approach, which was first developed and proposed by Prof. A.I. Nakorchevski as an alternative to a number of the well known averaged multiphase dynamics equations. The main difference of the new method was in an averaging of the Navier Stokes equations by phases and components in time instead of the widely spread spatial averaging in multiphase mechanics. What was more, introduction of the so called function indicato…
