Emily S.C. Ching

Emily S.C. Ching
The Chinese University of Hong Kong | CUHK · Department of Physics

PhD

About

118
Publications
5,013
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
2,604
Citations
Introduction
Current research interests include boundary layer analysis in turbulent convection and network reconstruction

Publications

Publications (118)
Article
In the study of biological networks, one of the major challenges is to understand the relationships between network structure and dynamics. In this paper, we model in vitro cortical neuronal cultures as stochastic dynamical systems and apply a method that reconstructs directed networks from dynamics [Ching and Tam, Phys. Rev. E 95, 010301(R) (2017)...
Preprint
Full-text available
In the study of biological networks, one of the major challenges is to understand the relationships between network structure and dynamics. In this paper, we model in vitro cortical neuronal cultures as stochastic dynamical systems and apply a method that reconstructs directed networks from dynamics [Ching and Tam, Phys. Rev. E 95, 010301(R), 2017]...
Article
Full-text available
How does the dynamics of neurons in a network respond to changes in synaptic weights? Answer to this question would be important for a full understanding of synaptic plasticity. In this article, we report our numerical study of the effects of changes in inhibitory synaptic weights on the spontaneous activity of networks of spiking neurons with cond...
Article
Using a closed set of boundary layer equations [E. S. C. Ching et al., Phys. Rev. Research 1, 033037 (2019)] for turbulent Rayleigh-Bénard convection, we derive analytical results for the dependence of the heat flux, measured by the Nusselt number (Nu), on the Reynolds (Re) and Prandtl (Pr) numbers and two parameters that measure fluctuations in th...
Article
Full-text available
In turbulent Rayleigh-Bénard convection, the boundary layers are nonsteady with fluctuations, the time-averaged large-scale circulating velocity vanishes far away from the top and bottom plates, and the motion arises from buoyancy. In this paper, we derive the full set of boundary layer equations for both the temperature and velocity fields from th...
Article
Much research effort has been devoted to developing methods for reconstructing the links of a network from dynamics of its nodes. Many current methods require the measurements of the dynamics of all the nodes to be known. In real-world problems, it is common that either some nodes of a network of interest are unknown or the measurements of some nod...
Article
The interaction of flexible polymers with fluid flows leads to a number of intriguing phenomena observed in laboratory experiments, namely drag reduction, elastic turbulence, and heat transport modification in natural convection, and is one of the most challenging subjects in soft matter physics. In this review, we examine our present knowledge on...
Article
Reconstructing the structure of complex networks from measurements of the nodes is a challenge in many branches of science. External influences are always present and act as a noise to the networks of interest. In this paper, we present a method for reconstructing networks from measured dynamics of the nodes subjected to correlated noise that canno...
Article
To predict the mean temperature profiles in turbulent thermal convection, the thermal boundary layer (BL) equation has to be solved. Starting from a thermal BL equation that takes into account fluctuations in terms of an eddy thermal diffusivity [Shishkina et al., Phys. Rev. Lett. 114 (2015)], we make use of the idea of Prandtl's mixing length mode...
Article
Full-text available
We investigate the effect of fluctuations in thermal boundary layer on heat transfer in turbulent Rayleigh–Bénard convection for Prandtl number greater than one in the regime where the thermal dissipation rate is dominated by boundary layer contribution and in the presence of a large-scale circulating flow.
Article
We address the long-standing challenge of how to reconstruct links in directed networks from measurements, and present a general method that makes use of a noise-induced relation between network structure and both the time-lagged covariance of measurements taken at two different times and the covariance of measurements taken at the same time. When...
Article
We study how polymers affect the heat flux in turbulent Rayleigh-Bénard convection at moderate Rayleigh numbers using direct numerical simulations with polymers of different relaxation times. We find that heat flux is enhanced by polymers and the amount of heat enhancement first increases and then decreases with the Weissenberg number, which is the...
Article
We study how heat transport is affected by finitely extensible polymers in a laminar boundary layer flow within the framework of the Prandtl–Blasius–Pohlhausen theory. The polymers are described by the finitely extensible nonlinear elastic-Peterlin model with a parameter $b^{2}$ , which is the ratio of the maximum to the equilibrium value of the...
Conference Paper
Many systems of interest in physics, biology or social science are complex networks. The links, their direction and weights or relative coupling strength of a network are important features that provide insights and fundamental understanding of the overall behavior and functionality of the network. Thus a method that can extract such information fr...
Article
We report a new thermal boundary layer equation for turbulent Rayleigh–Bénard convection for Prandtl number Pr>1 that takes into account the effect of turbulent fluctuations. These fluctuations are neglected in existing equations, which are based on steady-state and laminar assumptions. Using this new equation, we derive analytically the mean tempe...
Article
We present a method that reconstructs both the links and their relative coupling strength of bidirectional weighted networks. Our method requires only measurements of node dynamics as input. Using several examples, we demonstrate that our method can give accurate results for weighted random and weighted scale-free networks with both linear and nonl...
Article
Full-text available
We report a new thermal boundary layer equation for turbulent Rayleigh-Benard convection for Prandtl number Pr>1 that takes into account the effect of turbulent fluctuations. These fluctuations are neglected in existing equations, which are based on steady-state and laminar assumptions. Using this new equation, we derive analytically the mean tempe...
Chapter
The Rayleigh-Bénard convection system consists of a closed cell of fluid heated from below and cooled from above. Turbulent Rayleigh-Bénard convection is a fundamental problem of great research interest. In this monograph, we have discussed Rayleigh-Bénard convection exclusively in the Oberbeck-Boussinesq approximation, and focused on two issues of...
Chapter
We first introduce the local Bolgiano length, which depends on the vertical coordinate as a result of the inhomogeneity of the system. Based on the local Bolgiano length evaluated in numerical calculations, K41-OC scaling is expected in the central region and BO scaling is expected to exist only near the top and bottom plates. Then we discuss the e...
Chapter
The Rayleigh-Bénard convection system consists of a closed cell of fluid heated from below and cooled from above. We formulate the problem in this chapter. We first introduce the Oberbeck-Boussinesq approximation and derive the equations of motion under this approximation. The boundary conditions are then specified. The dimensionless parameters des...
Chapter
The statistics of the velocity and temperature differences, between measurements taken at two points separated by a distance \(l\), can reveal the structure of turbulence. These structure functions often exhibit power laws or scaling laws in \(l\). We introduce the important concept of energy cascade in turbulent flows and the different theories fo...
Chapter
We first introduce the basic statistical tools, including probability density functions (PDF) and conditional statistics, for studying fluctuations in general. Then we discuss the closure problem in turbulence. Because of this closure problem, exact implicit relations between different statistical quantities are useful. We derive two implicit resul...
Article
We study the effects of polymers in two-dimensional turbulent thermal convection using a shell model. In the absence of polymers, the inverse energy cascade in two dimensions leads to the observed Bolgiano-Obukhov scaling. When polymers are added, energy is extracted from the flow by the polymers, and as a result, the thermal balance between buoyan...
Article
We would like to correct a mistake in our paper. In the first sentence of the third paragraph in Sec. IV, we should add that in carrying out the procedure described in Sec. III to obtain the results presented in the paper, we have excluded d i (1) in the identification of m 0 (i) in step (2) since nodes of degree one are rather uncommon in general...
Article
In the study of networked systems, a method that can extract information about how the individual nodes are connected with one another would be valuable. In this paper, we present a method that can yield such information of network connectivity using measurements of the dynamics of the nodes as the only input data. Our method is built upon a noise-...
Article
Full-text available
We show that the nature of the scaling behavior can be revealed by studying the conditional structure functions evaluated at given values of the locally averaged thermal dissipation rate. These conditional structure functions have power-law dependence on the value of the locally averaged thermal dissipation rate, and such dependence for the Bolgian...
Article
It is found that in some cases the complete and irreducible scale invariants given by Ref.[1] are not independent. There are some implicit functional relations among them. The scale invariants for two different cases are calculated. The first case is an arbitrary second order tensor. The second case includes a symmetric tensor, an antisymmetric ten...
Article
The possible effects of a large-scale mean flow, represented as a non-zero mean velocity in the shell of the largest scale, are studied using a shell model of turbulent convection. In the regime where buoyancy is dynamically important, flow reversals are not observed. On the other hand, flow reversals are found in the regime where buoyancy is not d...
Article
Full-text available
Motivated by recent experimental observations, we consider a steady-state Prandtl-Blasius boundary layer flow with polymers above a slightly heated horizontal plate and study how the heat transport might be affected by the polymers. We discuss how a set of equations can be derived for the problem and how these equations can be solved numerically by...
Article
Full-text available
Using a homemade local temperature gradient probe, the instantaneous thermal dissipation rate T r , t is obtained in an aspect-ratio-one cylindrical convection cell filled with water. From the time series measurements, a locally averaged thermal dissipation r , t over a time interval is constructed. Herein we decompose r , t into three contribution...
Article
Mode-III fracture propagation in a two-dimensional continuum model is studied theoretically. The material is assumed to be isotropic and linearly elastic with a frictional dissipation, and the crack-tip region is modeled by a cohesive zone. As the externally applied load increases, the steady-state crack speed increases to a maximum value which can...
Article
Turbulent thermal convection is a well-studied problem with various issues of interest. In this paper, we review our work which shows the nature and origin of anomalous scaling and heat transport in the limit of very strong thermal forcing, can be gained by studying a dynamical model, known as shell model, of homogeneous turbulent thermal convectio...
Article
In this Letter, we explore the possible effects of polymer additives on heat transport in turbulent thermal convective flows. Using both direct numerical simulations and shell-model calculations, we show that polymer additives can significantly enhance the heat transport in homogeneous turbulent thermal convection, which mimics the bulk of turbulen...
Article
Full-text available
From the measured thermal dissipation rate in turbulent Rayleigh–Bénard convection in a cylindrical cell, we construct a locally averaged thermal dissipation rate χ f τ by averaging over a time interval τ . We study how the statistical moments (χ f τ) p depend on τ at various locations along the vertical axis of the convection cell. We find that (χ...
Article
Full-text available
We perform a systematic numerical study of the effects of the particle-size ratio $R \ge 1$ on the properties of jammed binary mixtures. We find that changing $R$ does not qualitatively affect the critical scaling of the pressure and coordination number with the compression near the jamming transition, but the critical volume fraction at the jammin...
Article
The shear modulus and yield stress of amorphous solids are important material parameters, with the former determining the rate of increase in stress under external strain and the latter being the stress value at which the material flows in a plastic manner. It is therefore important to understand how these parameters can be related to the interpart...
Article
Full-text available
The shear-modulus and yield-stress of amorphous solids are important material parameters, with the former determining the rate of increase of stress under external strain and the latter being the stress value at which the material flows in a plastic manner. It is therefore important to understand how these parameters can be related to the inter-par...
Article
The modification of turbulence due to the introduction of dilute fibres in a channel flow is analysed by means of Direct Numerical Simulation (DNS). Using a simplified rheological model it is possible to assess that the modification of turbulent structure is far simpler than in the flexible case. In fact, at a given fibre concentration some relevan...
Article
An interesting question in turbulent convection is how the heat transport depends on the strength of thermal forcing in the limit of very large thermal forcing. Kraichnan predicted [Phys. Fluids 5, 1374 (1962)] that for fluids with low Prandtl number (Pr), the heat transport measured by the Nusselt number (Nu) would depend on the strength of therma...
Article
A major challenge in turbulence research is to understand from first principles the origin of the anomalous scaling of velocity fluctuations in high-Reynolds-number turbulent flows. One important idea was proposed by Kolmogorov [J. Fluid Mech. 13, 82 (1962)], which attributes the anomaly to variations of the locally averaged energy dissipation rate...
Article
Full-text available
A major challenge in turbulence research is to understand from first principles the origin of anomalous scaling of the velocity fluctuations in high-Reynolds-number turbulent flows. One important idea was proposed by Kolmogorov [J. Fluid Mech. {\bf 13}, 82 (1962)], which attributes the anomaly to the variations of the locally averaged energy dissip...
Article
Different scaling behavior has been reported in various shell models proposed for turbulent thermal convection. In this paper, we show that buoyancy is not always relevant to the statistical properties of these shell models even though there is an explicit coupling between velocity and temperature in the equations of motion. When buoyancy is releva...
Article
Full-text available
Numerical simulations of turbulent channel flows, with or without additives, are limited in the extent of the Reynolds number (Re) and Deborah number (De). The comparison of such simulations to theories of drag reduction, which are usually derived for asymptotically high Re and De, calls for some care. In this paper we present a study of drag reduc...
Article
Anomalous scaling in the statistics of an active scalar is studied in a shell model of homogeneous turbulent convection. We extend refined similarity ideas for homogeneous and isotropic turbulence to homogeneous turbulent convection and attribute the origin of the anomalous scaling to variations of the entropy transfer rate. We verify the consequen...
Article
Human heart rate is known to display complex fluctuations. Evidence of multifractality in heart rate fluctuations in healthy state has been reported [Ivanov, Nature (London) 399, 461 (1999)]. This multifractal character could be manifested as the dependence of the probability density functions (PDFs) of the interbeat interval increments, which are...
Article
The possible effects of a large-scale mean flow, represented as a non-zero mean velocity in the shell of the largest scale, are studied using a shell model of turbulent convection. In the regime where buoyancy is dynamically important, flow reversals are not observed. On the other hand, flow reversals are found in the regime where buoyancy is not d...
Article
We study equilibrium phase separation of immiscible diblock copolymer chains, A-B and B-A, end-grafted to the interior surface of cylinders or spheres. We show that with the grafting surface curving moderately, the microphase separation pattern is qualitatively different from that for a flat surface. When h/R > ρc (h is the height of the polymer la...
Article
In confined turbulent thermal convection, the velocity is separated into two parts: one that is correlated with some function of the temperature fluctuations, and thus associated with the plume velocity, and the other part, the background velocity, which is uncorrelated with any function of the temperature fluctuations. As a result, one should focu...
Article
We study the streamlines of the velocity field produced by two unlinked vortex rings. We find that two vortex rings can produce chaos and observe a route to chaos directly from periodic orbits. From the case study of numerous ring configurations we give conditions for integrability of streamlines. We also find that near the larger ring or the stron...
Article
Full-text available
Drag reduction by polymers is bounded between two universal asymptotes, the von Kármán log law of the law and the maximum drag reduction (MDR) asymptote. It is theoretically understood why the MDR asymptote is universal, independent of whether the polymers are flexible or rodlike. The crossover behavior from the Newtonian von Kármán log law to the...
Article
We have studied the heat transport by steady circulating flows in two-dimensional rectangular cells of different values of the aspect ratio Γ. The cells are heated from below and cooled on top with a fixed temperature difference. These steady circulating flows mimic the mean large-scale circulating wind observed in turbulent Rayleigh–Bénard convect...
Article
It is interesting to understand the scaling behavior of velocity and temperature fields in turbulent thermal convection. Theoretical ideas suggest Bolgiano-Obukhov scaling when the turbulent dynamics are governed by a cascade of entropy. On the other hand, there were experimental and numerical studies of confined convection which showed results tha...
Article
Full-text available
We address the additive equivalence discovered by Virk and co-workers: drag reduction affected by flexible and rigid rodlike polymers added to turbulent wall-bounded flows is limited from above by a very similar maximum drag reduction (MDR) asymptote. Considering the equations of motion of rodlike polymers in wall-bounded turbulent ensembles, we sh...
Article
Full-text available
We present a scheme to extract the velocity of buoyant structures in turbulent thermal convection from simultaneous local velocity and temperature measurements. Applying this scheme to measurements taken at positions within the convection cell where the buoyant structures are dominated by plumes, we obtain the temperature dependence of the plume ve...
Article
We demonstrate, by using suitable shell models, that drag reduction in homogeneous turbulence is usefully discussed in terms of a scale-dependent effective viscosity. The essence of the phenomenon of drag reduction found in models that couple the velocity field to the polymers can be recaptured by an "equivalent" equation of motion for the velocity...
Article
Full-text available
We analyse simultaneous velocity and temperature measurements in turbulent thermal convection. Our results show the existence of a cross-scaling between the normalized velocity and temperature structure functions, as implied by the Bolgiano-Obukhov scaling, at the centre of the convection cell. We find that the cross-scaling exponents are, however,...
Article
The hierarchical structure of the She-Leveque (SL) form, which exists in the healthy and diseased human heart rate variability (HRV) was investigated. This structure implies further details in the HRV fractal scaling. The model allows to study the empirical law which appears to be universal and is capable of describing both healthy and congestive h...
Article
A simple model of the effect of polymer concentration on the amount of drag reduction in turbulence is presented, simulated, and analyzed. The qualitative phase diagram of drag coefficient versus Reynolds number (Re) is recaptured in this model, including the theoretically elusive onset of drag reduction and the maximum drag reduction (MDR) asympto...
Article
Both the velocity and temperature measurements taken in turbulent Rayleigh-B'enard convection experiments have been analyzed. It is found that both the velocity and temperature fluctuations are intermittent and can be well-described by the She-Leveque hierarchical structure. A positive correlation between the vertical velocity and the temperature d...
Article
Full-text available
We analyze velocity fluctuations in turbulent Rayleigh-Bénard convection. The velocity measurements were taken at the center of an aspect-ratio-one convection cell filled with water. The measured probability density functions of the velocity difference over a time interval tau are found to change with tau, indicating that the velocity fluctuations...
Article
It has been conjectured13 that the extended self-similarity measured in turbulent flows is an indication of the maximum velocity difference being scale-independent and thus the most intense velocity structures being shock-like. In this paper, we present analyses of velocity measurements in turbulent Rayleigh-Bénard convection that show further supp...
Conference Paper
It has been conjectured(13) that the extended self-similarity measured in turbulent flows is an indication of the maximum velocity difference being scale-independent and thus the most intense velocity structures being shock-like. In this paper, we present analyses of velocity measurements in turbulent Rayleigh-Benard convection that show further su...
Article
We have recently proposed that the statistics of active fields (which affect the velocity field itself) in well-developed turbulence are also dominated by the statistically preserved structures of auxiliary passive fields which are advected by the same velocity field. The statistically preserved structures are eigenmodes of eigenvalue 1 of an appro...
Article
We show that a generalization of the She-Leveque hierarchical structure [Z.S. She and E. Leveque, Phys. Rev. Lett. 72, 336 (1994)] together with a constant maximum magnitude of the velocity difference give rise to the extended self-similarity (ESS) [R. Benzi et al., Phy. Rev. E 48, R29 (1993)]. Our analysis thus suggests that the ESS measured in tu...
Article
Full-text available
We study numerically the dependence of heat transport on the maximum velocity and shear rate of physical circulating flows, which are prescribed to have the key characteristics of the large-scale mean flow observed in turbulent convection. When the side-boundary thermal layer is thinner than the viscous boundary layer, the Nusselt number (Nu), whic...
Article
The anomalous scaling of correlation functions in the turbulent statistics of active scalars (like temperature in turbulent convection) is understood in terms of an auxiliary passive scalar which is advected by the same turbulent velocity field. The even-order correlation functions of the two fields are the same to leading order (up to a trivial mu...
Article
We study the problem of heat transport by fluid flows with prescribed velocity fields. The advection-diffusion equation in two dimensions is solved for two velocity fields: (i). a circulation and (ii). a shear flow. These two flows focus separately on the two dominant features of the mean large-scale flow observed in turbulent convection experiment...
Article
We study the streamlines of the velocity field generated by two Helmholtz vortex rings which are fixed in space. Chaos can arise directly from a perturbation of periodic orbits. Trajectories are regular far away from linked vortex rings, and chaotic far away from unlinked vortex rings. Intersections of vortex rings produce intricate streamline topo...
Article
We study the problem of heat transport by fluid flows with prescribed velocity fields. The advection-diffusion equation in two dimensions is solved for two velocity fields: (i) a circulation and (ii) a shear flow. These two flows focus separately on the two dominant features of the mean large-scale flow observed in turbulent convection experiments....
Article
We find that the conditional statistics of temperature difference at fixed values of the locally averaged temperature dissipation rate in turbulent convection become Gaussian in the regime where the mixing dynamics is expected to be driven by buoyancy. Hence, intermittency of the temperature fluctuations in this buoyancy-driven regime can be solely...
Article
We find that the conditional statistics of temperature difference at fixed values df the locally averaged temperature dissipation rate in turbulent convection become Gaussian in the regime where the mixing dynamics is expected to be driven by buoyancy. Hence, intermittency of the temperature fluctuations in this buoyancy-driven regime can be solely...
Article
We propose a method to classify multifractal properties, which have been found in many systems. We then study the multifractal properties previously found in various models of fracture and fragmentation, and show explicitly that they indeed fall into the two classes proposed in our method. Several interesting features are also revealed.
Article
We study the statistics of the local temperature dissipation in high Rayleigh number convection. We find that its probability distribution deviates from a lognormal, although very low order moments can be approximated by a lognormal distribution. Instead, the moments satisfy a hierarchy similar to that proposed by She and Leveque [Phys. Rev. Lett....
Article
Fragmentation is studied using a simple numerical model. An object is taken to be two dimensional and consists of particles that interact pairwise via the Lennard–Jones potential while the effect of the fragmentation-induced forces is represented by some initial velocities assigned to the particles. As time evolves, the particles form clusters whic...
Article
We have performed an experimental study of impact fragmentation with a focus on the dependence on the energy input. Long glass rods were dropped horizontally onto the ground from seven diierent heights. We ÿnd that the energy dependence is better characterized by studying the diierential mass distribution rather than the cumulative mass distributio...
Article
The scaling behavior of the temperature structure functions in turbulent convection is found to be different for length scales below and above the Bolgiano scale. Both sets of the exponents are well described by log-Poisson statistics. The parameter beta(T) which measures the degree of intermittency is the same for the two regimes of scales and is...
Article
It is found that in some cases the complete and irreducible scale invariants given by Ref.[1] are not independent. There are some implicit functional relations among them. The scale invariants for two different cases are calculated. The first case is an arbitrary second order tensor. The second case includes a symmetric tensor, an antisymmetric ten...
Article
We use a two-dimensional lattice model to study the intermittency problem of a passive scalar advected by a velocity field of finite correlation time. The stream function generating the incompressible velocity field is modeled by a random Gaussian noise that is identically independently distributed at each lattice point and is updated every certain...
Article
We present a general formalism to characterize the probability density function of a set of dynamic variables in a stationary process using conditional expectations of kinematic observables on those variables. The formalism is exemplified with stochastic processes such as general Gaussian random processes and Brownian systems. We show that this for...
Article
In the study of turbulent fluid flows, one of the key issues is to understand the statistics of the fluctuations of the physical quantities of interest. Specifically, one would like to obtain results for the probability density function (PDF) which describes the statistics. One might attempt to derive the PDF directly from the equations of motion....
Article
We study fragmentation numerically using a simple model in which an object is taken to be a set of particles that interact pairwisely via a Lennard-Jones potential while the effect of the fragmentation-induced forces is represented by some initial velocities assigned to the particles. The motion of the particles, which is given by Newton's laws, is...
Article
Full-text available
An open system is not conservative because energy can escape to the outside. As a result, the time-evolution operator is not Hermitian in the usual sense and the eigenfunctions (factorized solutions in space and time) are no longer normal modes but quasinormal modes (QNMs) whose frequencies omega are complex. Qausinormal-mode analysis has been a po...
Article
We study the effects of a large-scale mean circulating flow on passive scalar statistics in turbulent advection using a two-dimensional lattice model. The incompressible advecting velocity field consists of a large-scale circulation plus fluctuations. The latter are modeled by a random Gaussian field that has a finite correlation time but is statis...
Article
For a passive scalar T(r, t) randomly advected by a statistically homogeneous flow, the probability density function (pdf) of its fluctuation can in general be expressed in terms of two conditional means: 2 T|T and |T|2|T. We find that in some special cases, either one of the two conditional means can be obtained explicitly from the equation of mot...
Article
Kolmogorov's refined similarity hypothesis (RSH) is extended to study the inertial-range scaling of a passive scalar advected by a rapidly changing incompressible velocity field in d dimensions. For zeta2>d, the non-negativity of the scalar dissipation rate constrains the 2nth order scaling exponents, zeta2n, to be linear in n asymptotically. With...
Article
We study numerically a model of random advection of a passive scalar by an incompressible velocity field of different prescribed statistics. Our focus is on the conditional statistics of the passive scalar and specifically on two conditional averages: the averages of the time derivative squared and the second time derivative of the scalar when its...
Article
One interesting feature of hard turbulence, a scaling regime in turbulent convection, is the presence of a large-scale mean circulating flow. Its effect on heat flux was studied by Shraiman and Siggia [Phys. Rev. A 42, 3650 (1990)], who approximated it as a shear flow near the boundaries. A constant shear rate was considered, which, in effect, assu...
Article
A general formula is derived for the probability density function (PDF) of fluctuating physical quantities measured in any stationary or statistically homogeneous process. For stationary processes, the formula relates the PDF to two conditional means: two averages involving a general function of the quantity and its time derivatives, the time deriv...
Article
Full-text available
We consider turbulent advection of a scalar field T(r), passive or active, and focus on the statistics of gradient fields conditioned on scalar differences DT(R) across a scale R. In particular we focus on two conditional averages ^¹2TuDT(R)& and ^u¹Tu2uDT(R)&. We find exact relations between these averages, and with the help of the fusion rules we...
Article
The equations of motion in fluid mechanics, be them for the velocity field u(r, t) or for a scalar field like the temperature T(r, t), contain interaction terms like u� ∇u or u � ∇T and dissipative terms like ν∇2u or κ∇2T, with ν and κ being the kinematic viscosity and the scalar dif- fusivity respectively. Accordingly, when one attempts to derive...
Article
Full-text available
Fusion rules in turbulence address the asympt