Space-time correlations of passive scalar in Kraichnan model

We consider the two-point,two-time(space-time)correlation of passive scalar R(r,τ)in the Kraichnan model under the assumption of homogeneity and isotropy.Using the fine-gird PDF method,we find that R(r,τ)satisfies a diffusion equation with constant diffusion coefficient determined by velocity variance and molecular diffusion.Itssolution can be expressed in terms of the two-point,one time correlation of passive scalar,i.e.,R(r,0).Moreover,the decorrelation o R(k,τ),which is the Fourier transform of R(r,τ),is determined byR(k,0)and a diffusion kernal.

TRANSPORTATION OF PASSIVE SCALAR IN INHOMOGENEOUS TURBULENCE

The paper studies the transportation of passive scalar in the inhomogeneous turbulence by means of large eddy simulation. The prediction accuracy is verified by the well-known Comte-Bellot spectrum of the homogeneous turbulence. The mean transportation properties are predicted with satisfaction and the underestimation of the thermal flux by the phenomenological models has been disclosed. The high intermittence of the temperature fluctuations has been found in the inhomogeneous turbulence and it is the reason for the underestimation of turbulent thermal flux by the phenomenological model.

Anomalous scaling in a non-Gaussian random shell model for passive scalars

In this paper, we have introduced a shell-model of Kraichnan＇s passive scalar problem. Different from the original problem, the prescribed random velocity field is non-Gaussian and σ correlated in time, and its introduction is inspired by She and Levveque （Phys. Rev. Lett. 72, 336 （1994））. For comparison, we also give the passive scalar advected by the Gaussian random velocity field. The anomalous scaling exponents H（p） of passive scalar advected by these two kinds of random velocities above are determined for structure function with values of p up to 15 by Monte Carlo simulations of the random shell model, with Gear methods used to solve the stochastic differential equations. We find that the H（p） advected by the non-Gaussian random velocity is not more anomalous than that advected by the Gaussian random velocity. Whether the advecting velocity is non-Gaussian or Gaussian, similar scaling exponents of passive scalar are obtained with the same molecular diffusivity.

Probability Distribution Function of Passive Scalars in Shell Models

A shell-model version of passive scalar problem is introduced, which is inspired by the model of K. Ohkitani and M. Yakhot [K. Ohkitani and M. Yakhot, Phys. Rev. Lett. 60 （1988） 983; K. Ohkitani and M. Yakhot, Prog. Theor. Phys. 81 （1988） 329]. As in the original problem, the prescribed random velocity field is Gaussian and 5 correlated in time. Deterministic differential equations are regarded as nonlinear Langevin equation. Then, the Fokker-Planck equations of PDF for passive scalars are obtained and solved numerically. In energy input range （n 〈 5, n is the shell number.）, the probability distribution function （PDF） of passive scalars is near the Gaussian distribution. In inertial range （5≤ n ≤ 16） and dissipation range （n ≥ 17）, the probability distribution function （PDF） of passive scalars has obvious intermittence. And the scaling power of passive scalar is anomalous. The results of numerical simulations are compared with experimental measurements.

Influence of Velocity Shell Correlations on Anomalous Scaling Exponents of Passive Scalars in Shell Models

We propose a new approach to the old-standing problem of the anomaly of the scaling exponents of passive scalars of turbulence. Different to the original problem, the distribution function of the prescribed random velocity field is multi-dimensional normal and delta-correlated in time. Here, our random velocity field is spatially correlative. For comparison, we also give the result obtained by the Gaussian random velocity field without spatial correlation. The anomalous scaling exponents H（p） of passive scalar advected by two kinds of random velocity above are determined for structure function up to p= 15 by numerical simulations of the random shell model with Runge-Kutta methods to solve the stochastic differential equations. We observed that the H（p） ＇s obtained by the multi-dimeasional normal distribution random velocity are more anomalous than those obtained by the independent Gaussian random velocity.

Influence of velocity spatiotemporal correlations on the anomalous scaling exponents of passive scalars

In this paper, we consider spatial-temporal correlation functions of the turbulent velocities. With numerical simulations on the Gledzer-Ohkitani-Yamada （GOY） shell model, we show that the correlation function decays exponentially. The advecting velocity field is regarded as a colored noise field, which is spatially and temporally correlative. For comparison, we are also given the scaling exponents of passive scalars obtained by the Gaussian random velocity field, the multi-dimensional normal velocity field and the She-Leveque velocity field, introduced by She, et al. We observe that extended self-similarity sealing exponents H（p）/H（2） of passive scalar obtained by the colored noise field are more anomalous than those obtained by the other three velocity fields.

Passive scalar characteristics along inertial particle trajectory in turbulent non-isothermal flows

The momentum and heat coupling between carrier fluid and particles are a complex and challenge topic in turbulent reactive gas-solid flow modeling.Most observations on this topic,either numerical or experimental,are based on Eulerian framework,which is not enough for developing the probability density function(PDF) model.In this paper,the instantous behavior and multi-particle statistics of passive scalar along inertial particle trajectory,in homogenous isotropic turbulence with a mean scalar gradient,are investigated by using the direct numerical simulation(DNS).The results show that St^1.0 particles are easy to aggregate in high strain and low vorticity regions in the fluid field,where the scalar dissipation is usually much higher than the mean value,and that every time they move across the cliff structures,the scalar change is much more intensive.Anyway,the self-correlation of scalar along particle trajectory is significantly different from the velocities observed by particle,for which the prefer-concentration effect is evident.The mechanical-to-thermal time scale ratio averaged along the particles,<r> p,is approximately two times smaller than that computed in the Eulerian frame r,and stays at nearly 1.77 with a weak dependence on particle inertia.

STUDY ON NEW PASSIVE SCALAR FLUX MODEL WITH DIFFUSIVITY OF COMPLEX NUMBER

The turbulent passive scalar fluxes were studied by separately considering the contributions of small eddy motions and large eddy ones. Explicit algebraic approximation was achieved for both small eddy and large eddy scalar fluxes. Especially, the large eddy scalar flux was modelled with complex diffusivity. The singular difficulties in usual algebraic scalar models, do not occur any more in this model. In addition, this new model provides a new way to reasonably describe the negative transport phenomena appearing in asymmetric turbulent flows.

Numerical Modeling of Mass Transfer in the Interaction between River Biofilm and a Turbulent Boundary Layer

In this article dedicated to the modeling of vertical mass transfers between the biofilm and the bulk flow, we have, in the first instance, presented the methodology used, followed by the presentation of various results obtained through analyses conducted on velocity fields, different fluxes, and overall transfer coefficients. Due to numerical constraints (resolution of relevant spatial scales), we have restricted the analysis to low Schmidt numbers (Sc=0.1, Sc=1, and Sc=10) and a single roughness Reynolds number (Re*=150). The analysis of instantaneous concentration fields from various simulations revealed logarithmic concentration profiles above the canopy. In this zone, the concentration is relatively homogeneous for longer times. The analysis of results also showed that the contribution of molecular diffusion to the total flux depends on the Schmidt number. This contribution is negligible for Schmidt numbers Sc≥0.1, but nearly balances the turbulent flux for Sc=0.1. In the canopy, the local Sherwood number, given by the ratio of the total flux (within or above the canopy) to the molecular diffusion flux at the wall, also depends on the Schmidt number and varies significantly between the canopy and the region above. The exchange velocity, a purely hydrodynamic parameter, is independent of the Schmidt number and is on the order of 10% of in the present case. This study also reveals that nutrient absorption by organisms near the wall depends on the Schmidt number. Such absorption is facilitated by lower Schmidt numbers.

Stirring by anisotropic squirming

We consider a fluid stirred by the locomotions of squirmers through it and generalize the stochastic hydrodynamic model proposed by Thiffeault and Childress,Phys.Lett.A(2010)and Lin et al.,J.Fluid Mech.(2011)to the case in which the swimmers move in anisotropically random directions.A non-diagonal effective diffusivity tensor is derived with which the diffusive preference of a passive particle along any given direction can be computed to provide more details of the phenomena beyond scalar statistics.We further identify a fraction from the orthogonal decomposition of the drift-induced particle displacement to distinguish the underlying nonlinear mixing mechanism for different types of swimmers.Numerical simulations verify the analytical results with explicit examples of prescribed,anisotropic stirring motions.We also connect our formulation to several measures used in clinical medical research such as diffusion tensor imaging where anisotropic diffusion has a significant consequence.

Study on the Shear Effect on Dye Patches Diffused in Wall-Bounded Shear Flow

This paper focuses on the high intensity filaments (dye patches) embedded in dye plumes in a wall-bounded shear flow, to investigate the shear effect on the dye patch distribution. Motivated by the widely concerned inverse estimation of the source location, we try extracting useful information to know the source location from down-stream dye patches. Accordingly, we changed the dye injection location at different distances from the wall and made observations at different downstream (diffusion) distances from the source. The orientation angle and roundness of dye patches were concerned to examine the shear effect and dye patch characteristics. To capture the dye plume images, a planar laser induced fluorescence (PLIF) technique was used. The orientation and roundness of each dye patch were calculated by least-square fitting. The statistics of both the orientation angle and the roundness were compared with those in homogeneous turbulent cases to reveal the shear effect. Different from uniformly-orientated dye patches in the homogeneous flow, larger occurrence probabilities with positive orientation angles of dye patches are observed in wall-bounded shear flow, in particular, when the injection location is near the wall. As with information extraction for the inverse estimation of source location, it is found that the orientation distribution of dye patches is independent of the diffusion distance, but related with the injection location from the wall. While for the homogeneous flow cases, a strong dependence on the diffusion distance is observed in the orientation distribution profiles. As for the roundness, similar aspects are found regarding the dependencies on the injection location in shear flow and on diffusion distance in homogeneous flow.

Inverse Source Locating Method Based on Graphical Analysis of Dye Plume Images in a Turbulent Flow

The inverse estimation of a source location of pollutant released into a turbulent flow is a probability problem instead of a deterministic one, as the turbulent flow is chaotic and irreversible. However, researches can be conducted to provide helpful instructions to the possible source location with corresponding uncertainty. This study aims to propose a method of inverse estimation of a passive-scalar source location. Experimental investigation of the dye plume characteristics released into a fully-developed turbulent flow is performed in a water channel. A planar laser-induced fluorescence (PLIF) technique is used to obtain two-dimensional images of spreading dye plumes at a bulk Reynolds number of 20,000. The distributions of high concentration areas in the PLIF images are chosen as features that characterize the traveling (diffusion) distance or time from the dye source. Graphical analysis is used to extract these high concentration areas. The procedure of graphical analysis has three steps: 1) binarization using a threshold to extract high concentration dye patches;2) labeling individual high-concentration dye patches in the binarized images;and 3) pixel-counting to measure the area and perimeter of each dye patch. We examine the variations of fractal dimension of patches, and the fractal dimension is observed to be almost constant irrespective of the distance from the source. The kurtosis of the probability density function curve of the logarithm dimensionless dye patch areas is found to be related with the downstream diffusion distance, based on which an inverse estimation method to locate a passive-scalar point source is proposed and evaluated.

Diffusion Process of High Concentration Spikes in a Quasi-Homogeneous Turbulent Flow

When a mass spreads in a turbulent flow, areas with obviously high concentration of the mass compared with surrounding areas are formed by organized structures of turbulence. In this study, we extract the high concentration areas and investigate their diffusion process. For this purpose, a combination of Planar Laser Induced Fluorescence (PLIF) and Particle Image Velocimetry (PIV) techniques was employed to obtain simultaneously the two fields of the concentration of injected dye and of the velocity in a water turbulent channel flow. With focusing on a quasi-homogeneous turbulence in the channel central region, a series of PLIF and PIV images were acquired at several different downstream positions. We applied a conditional sampling technique to the PLIF images to extract the high concentration areas, or spikes, and calculated the conditional-averaged statistics of the extracted areas such as length scale, mean concentration, and turbulent diffusion coefficient. We found that the averaged length scale was constant with downstream distance from the diffusion source and was smaller than integral scale of the turbulent eddies. The spanwise distribution of the mean concentration was basically Gaussian, and the spanwise width of the spikes increased linearly with downstream distance from the diffusion source. Moreover, the turbulent diffusion coefficient was found to increase in proportion to the spanwise distance from the source. These results reveal aspects different from those of regular mass diffusion and let us conclude that the diffusion process of the spikes differs from that of regular mass diffusion.

Large-eddy-simulation of 3-dimensional Rayleigh-Taylor instability in incompressible fluids

The 3-dimensional incompressible Rayleigh-Taylor instability is numerically studied through the large-eddy-simulation ( LES) approach based on the passive scalar transport model. Both the instantaneous velocity and the passive scalar fields excited by sinusoidal perturbation and random perturbation are simulated. A full treatment of the whole evolution process of the instability is addressed. To verify the reliability of the LES code, the averaged turbulent energy as well as the flux of passive scalar are calculated at both the resolved scale and the subgrid scale. Our results show good agreement with the experimental and other numerical work. The LES method has proved to be an effective approach to the Rayleigh-Taylor instability.

Effect of Oscillation Structures on Inertial-Range Intermittence and Topology in Turbulent Field

Using the incompressible isotropic turbulent fields obtained from direct numerical simulation and large-eddy simulation,we studied the statistics of oscillation structures based on local zero-crossings and their relation with inertial-range intermittency for transverse velocity and passive scalar.Our results show that for both the velocity and passive scalar,the local oscillation structures are statistically scaleinvariant at high Reynolds number,and the inertial-range intermittency of the overall flow region is determined by the most intermittent structures characterized by one local zero-crossing.Local flow patterns conditioned on the oscillation structures are characterized by the joint probability density function of the invariants of the filtered velocity gradient tensor at inertial range.We demonstrate that the most intermittent regions for longitudinal velocity tend to lay at the saddle area,while those for the transverse velocity tend to locate at the vortex-dominated area.The connection between the ramp-cliff structures in passive scalar field and the corresponding saddle regions in the velocity field is also verified by the approach of oscillation structure classification.