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.

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.

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.