A Modification to Vertical Distribution of Tidal Flow Reynolds Stress in Shallow Sea

Tidal flow is a periodic movement of unsteady and non-uniform, which has acceleration and deceleration process obviously, especially in coastal shallow waters. Many researches show that vertical distribution of tidal flow Reynolds stress deviated from linear distribution. The parabolic distribution of the tidal flow Reynolds stress was proposed by Song et al. （2009）. Although the model fills better with field observations and indoor experimental data, it has the lower truncated series expansion of tidal flow Reynolds stress, and the description of the distribution is not very comprehensive By introducing the motion equation of tidal flow and improving the parabolic distribution established by Song et al. （2009）, the cubic distribution of the tidal flow Reynolds stress is proposed. The cubic distribution is verified well by field data （Bowden and Fairbairn, 1952; Bowden et al., 1959; Rippeth et al., 2002） and experimental data （Anwar and Atkins, 1980）, is consistent with the numerical model results of Kuo et al. （1996）, and is compared with the parabolic distribution of the tidal flow Reynolds stress. It is shown that this cubic distribution is not only better than the parabolic distribution, but also can better reflect the basic features of Reynolds stress deviating from linear distribution downward with the tidal flow acceleration and upward with the tidal flow deceleration, for the foundation of further study on the velocity profile of tidal flow.

Edge Structure of Reynolds Stress and Poloidal Flow on the HL-1M Tokamak

The measurement on radial profile of electrostatic Reynolds stress, plasma poloidal rotations, radial and poloidal electric field have been performed in the plasma boundary region of the HL-IM Tokamak using a multi-array of Mach/Langmuir probes. In the experiments of Lower Hybrid Current Drive (LHCD), Supersonic Molecular Beam injection (SMBI), Multi-shot Pellet Injection (MPI) and Neutral Beam injection (NBI), the correlation between the Reynolds stress and poloidal flow in the edge plasma is presented. The results indicate that a sheared poloidal flow can be generated in Tokamak plasma due to radially varying Reynolds stress.

Vertical Distribution of Tidal Flow Reynolds Stress in Shallow Sea

Based on the results of the tidal flow Reynolds stresses of the field observations, indoor experiments, and numerical models, the parabolic distribution of the tidal flow Reynolds stress is proposed and its coefficients are determined theoretically in this paper. Having been well verified with the field data and experimental data, the proposed distribution of Reynolds stress is also compared with numerical model results, and a good agreement is obtained, showing that this distribution can well reflect the basic features of Reynolds stress deviating from the linear distribution that is downward when the tidal flow is of acceleration, upward when the tidal flow is of deceleration. Its dynamics cause is also discussed preliminarily and the influence of the water depth is pointed out from the definition of Reynolds stress, turbulent generation, transmission, and so on. The established expression for the vertical distribution of the tidal flow Reynolds stress is not only simple and explicit, but can also well reflect the features of the tidal flow acceleration and deceleration for further study on the velocity profile of tidal flow.

An iterative data-driven turbulence modeling framework based on Reynolds stress representation

Data-driven turbulence modeling studies have reached such a stage that the basic framework is settled,but several essential issues remain that strongly affect the performance.Two problems are studied in the current research:(1)the processing of the Reynolds stress tensor and(2)the coupling method between the machine learning model and flow solver.For the Reynolds stress processing issue,we perform the theoretical derivation to extend the relevant tensor arguments of Reynolds stress.Then,the tensor representation theorem is employed to give the complete irreducible invariants and integrity basis.An adaptive regularization term is employed to enhance the representation performance.For the coupling issue,an iterative coupling framework with consistent convergence is proposed and then applied to a canonical separated flow.The results have high consistency with the direct numerical simulation true values,which proves the validity of the current approach.

Effect of an adverse pressure gradient on the streamwise Reynolds stress profile maxima in a turbulent boundary layer

It is widely accepted that in a turbulent boundary layer （TBL） with adverse pressure gradient （APG） an outer peak usually appears in the profile of streamwise Reynolds stress. However, the effect of APG on this outer peak is not clearly understood. In this paper, the effect of APG is analysed using the numerical and experimental results in the literature. Because the effect of upstream flow is inherent in the TBL, we first analyse this effect in TBLs with zero pressure gradient on flat plates. Under the individual effect of upstream flow, an outer peak already appears in the profile of streamwise Reynolds stress when the TBL continues developing in the streamwise direction. The APG accelerates the appearance of the outer peak, instead of being a trigger.

Bias Effects on the Reynolds Stress Using the Multi-Purpose Probe in IR-T1 Tokamak

The effect of the positive bias on Reynolds stress （RS） and its effect on the radial turbulent transport at the edge plasma （r/a =0.9） and scrape-off layer （SOL） region of plasma in tokamak are investigated. The radial and poloidal electric fields （Sr, Ep） and ion saturation current （Is） are measured by multi-purpose probe （MPP）. This probe is fabricated and constructed for the first time in the IR-T1 tokamak. The most advantage of this probe is that the variations of Er and Ep can be measured in different radii at the single shot. Thus the information of different radii can be compared with high precision. The bias voltage is fixed at Vbias = 200 V and it has been applied with the limiter bias that is fixed in r/a = 0.9. Moreover, the phase difference between radial and poloidal electric fields, and temporal evolution of the RS .spectrum detected by MPP are calculated. RS magnitude on the edge （r/a = 0.9） is more than its value in the SOL （r/a = 1.02）. With the applied bias 200 V, ItS and the magnitude of the phase difference between Er and Ep are increased, while the radial turbulent transport is decreased simultaneously. Thus it can be concluded that RS affects radial turbulence. Temporal evolution of the RS spectrum shows that the frequency of RS is increased and reaches its highest value at r/a=0.9 in the presence of bias.

COMPUTATION OF RECIRCULATING SWIRLING FLOW WITH THE GLM REYNOLDS STRESS CLOSURE

A Reynolds stress closure based on the generalized Langevin model (GLM), developed by Haworth and Pope, is applied to the flow calculation with swirl-induced recirculation. The purpose of the work is to assess the performance of this model under the complex flow conditions caused by the presence of strong swirl which gives rise to both unconventional recirculation in the vicinity of the symmetry axis and strong anisotropy in the turbulence field. Comparison of the computational results are made both with the experimental data of Roback and Johnson and the computational results obtained with the typical isotropization of production model (IPM) and the k-∈ type Boussinesq viscosity model.

Derivation of a second-order model for Reynolds stress using renormalization group analysis and the two-scale expansion technique

With the two-scale expansion technique proposed by Yoshizawa,the turbulent fluctuating field is expanded around the isotropic field.At a low-order two-scale expansion,applying the mode coupling approximation in the Yakhot-Orszag renormalization group method to analyze the fluctuating field,the Reynolds-average terms in the Reynolds stress transport equation,such as the convective term,the pressure-gradient-velocity correlation term and the dissipation term,are modeled.Two numerical examples：turbulent flow past a backward-facing step and the fully developed flow in a rotating channel,are presented for testing the efficiency of the proposed second-order model.For these two numerical examples,the proposed model performs as well as the Gibson-Launder （GL） model,giving better prediction than the standard k-ε model,especially in the abilities to calculate the secondary flow in the backward-facing step flow and to capture the asymmetric turbulent structure caused by frame rotation.

Rotation invariant constitutive relation for Reynolds stress structure parameter

A new Reynolds stress constitutive formula is constructed using the first- order statistics of turbulent fluctuations instead of the mean strain rate. It includes zero empirical coefficients. The formula is validated with the direct numerical simulation （DNS） data of turbulent channel flow at Reτ=180. The Reynolds stresses given by the proposed formula agree very well with the DNS results. The good agreement persists even after the multi-angle rotation of the coordinate system, indicating the rotation in- variance of the formula. The autocorrelation of the fluctuating velocity rather than the mean strain rate is close to the essence of the Reynolds stress.

Computing mean fields with known Reynolds stresses at steady state

With the rising of modern data science,data-driven turbulence modeling with the aid of machine learning algorithms is becoming a new promising field.Many approaches are able to achieve better Reynolds stress prediction,with much lower modeling error(∈_(M)),than traditional Reynolds-averaged Navier-Stokes(RANS)models,but they still suffer from numerical error and stability issues when the mean velocity fields are estimated by solving RANS equations with the predicted Reynolds stresses.This fact illustrates that the error of solving the RANS equations(∈_(P))is also very important for a RANS simulation.In the present work,the error∈_(P)is studied separately by using the Reynolds stresses obtained from direct numerical simulation(DNS)/highly resolved large-eddy simulation to minimize the modeling error∈_(M),and the sources of∈_(P)are derived mathematically.For the implementations with known Reynolds stresses solely,we suggest to run an auxiliary RANS simulation to make a first guess onν_(t)^(*)and S_(ij)^(0).With around 10 iterations,the error of the streamwise velocity component could be reduced by about one-order of magnitude in flow over periodic hills.The present work is not to develop a new RANS model,but to clarify the facts that obtaining mean field with known Reynolds stresses is nontrivial and that the nonlinear part of the Reynolds stresses is very important in flow problems with separations.The proposed approach to reduce∈_(P)may be very useful for the a posteriori applications of the data-driven turbulence models.

Numerical simulation of fluid dynamics in the stirred tank by the SSG Reynolds Stress Model

The Speziale,Sarkar and Gatski Reynolds Stress Model(SSG RSM)is utilized to simulate the fluid dynamics in a full baffled stirred tank with a Rushton turbine impeller.Four levels of grid resolutions are chosen to determine an optimised number of grids for further simulations.CFD model data in terms of the flow field,trailing vortex,and the power number are compared with published experimental results.The comparison shows that the global fluid dynamics throughout the stirred tank and the local characteristics of trailing vortices near the blade tips can be captured by the SSG RSM.The predicted mean velocity components in axial,radial and tangential direction are also in good agreement with experiment data.The power number predicted is quite close to the designed value,which demonstrates that this model can accurately calculate the power number in the stirred tank.Therefore,the simulation by using a combination of SSG RSM and MRF impeller rotational model can accurately model turbulent fluid flow in the stirred tank,and it offers an alternative method for design and optimisation of stirred tanks.

Sand storms:CFD analysis of Reynolds stress and collision stress of particles near sand bed

Sand storm is a serious environmental threat to humans. Sand particles are transported by saltation and suspension, causing soil erosion in one place and deposition in another. In order to prevent and predict sand storms, the causes and the manners of particle motions must he studied in detail. In this paper a standard k-8 model is used for the gas phase simulation and the discrete element method （DEM） is used to predict the movements of particles using an in-house procedure. The data are summarized in an Eulerian-Eulerian regime after simulation to get the statistical particle Reynolds stress and particle collision stress. The results show that for the current case the Reynolds stress and the air shear stress predominate in the region 20-250 mm above the initial sand bed surface. However, in the region below 3 ram, the collision stress must be taken into account in predicting particle movement.

Effects of adverse pressure gradient on Reynolds stresses inturbulent boundary layers

The effects of adverse pressure gradient(APG)on Reynolds stresses in turbulent boundary layers(TBLs)with APG were analyzed.The difficulty of this work was attributable to the Reynolds stresses in TBLs with APG under two combined effects,i.e.:effect of upstream flow and effect of APG.The effect of upstream flow is an inherent effect no matter pressure gradient exists or not.The individual effect was analyzed from absolute developments of Reynolds stresses in TBLs with zero pressure gradient(ZPG)firstly.Effect of APG was then analyzed from absolute developments of Reynolds stresses in TBLs with APG.Result showed that,for absolute development of mean streamwise Reynolds stresses,APG accelerated its development in TBL with ZPG;for absolute development of mean normal or shear Reynolds stresses,APG increased their magnitude in the outer part,and decreased their extent of large value region.

Detrended analysis of Reynolds stress in a decaying turbulent flow in a wind tunnel with active grids

Multi-scale properties of Reynolds stress in decaying turbulence in a wind tunnel with high Reynolds number are investi-gated. Two filtering techniques i.e., the zeroth-order and first-order detrending methods are applied to the two velocity components, where the local mean value （resp. local linear trend） is removed in the former （latter） technique. Some basic statistics for thirty mea-surements show that the variation is very large at first two locations and relatively small at last two locations. Moderately good power law is found for the mean value of local Reynolds stress at last three measurement locations with scaling exponents approxi-mately being 1.0 and a dual power law exists for the mean value of standard deviation of local Reynolds stress at all four measureme-nt locations with scaling exponents being 0.53 and 0.58 for zeroth-and first-order filtering respectively. Present results about local Reynolds stress are useful to build and evaluate the model of sub-grid Reynolds stress in large eddy simulations.

Reynolds stress constrained large eddy simulation of separation flows in a U-duct

This paper presents Reynolds stress constrained large eddy simulation(RSC-LES)method applied to a U-duct flow.Different from traditional Reynolds-averaged Navier-Stokes/detached eddy simulation(RANS/DES)hybrid method(including DES method),the RSC-LES method solves the LES equations in the whole computation domain with the near-wall regions being constrained by a prescribed Reynolds stress.By doing so it is possible to overcome the log-law mismatch(LLM)problem in hybrid method.The RSC-LES results show better agreement with experiment result.Compared with RANS and DES,RSC-LES gives more accurate pressure coefficients and friction coefficients on the wall,because the RSC-LES method captures the separation point and reattachment point on the inner wall.The computation results show that the RSC-LES method has the potential to solve the log-law mismatch problem of RANS/DES hybrid method and predict complex phenomena of internal flow field.

Linear logistic regression with weight thresholding for flow regime classification of a stratified wake

A stratified wake has multiple flow regimes,and exhibits different behaviors in these regimes due to the competing physical effects of momentum and buoyancy.This work aims at automated classification of the weakly and the strongly stratified turbulence regimes based on information available in a full Reynolds stress model.First,we generate a direct numerical simulation database with Reynolds numbers from 10,000 to 50,000 and Froude numbers from 2 to 50.Order(100)independent realizations of temporally evolving wakes are computed to get converged statistics.Second,we train a linear logistic regression classifier with weight thresholding for automated flow regime classification.The classifier is designed to identify the physics critical to classification.Trained against data at one flow condition,the classifier is found to generalize well to other Reynolds and Froude numbers.The results show that the physics governing wake evolution is universal,and that the classifier captures that physics.

Velocity distribution of flow with submerged flexible vegetations based on mixing-length approach

By choosing a PVC slice to simulate flexible vegetation, we carried out experiments in an open channel with submerged flexible vegetation. A 3D acoustic Doppler velocimeter （micro ADV） was used to measure local flow velocities and Reynolds stress. The results show that hydraulic characteristics in non-vegetation and vegetation layers are totally different. In a region above the vegetation, Reynolds stress distribution is linear, and the measured velocity profile is a classical logarithmic one. Based on the concept of new-riverbed, the river compression parameter representing the impact of vegetation on river is given, and a new assumption of mixing length expression is made. The formula for time-averaged velocity derived from the expression requires less parameters and simple calculation, and is useful in applications.

A NEW PHENOMENON OF ACOUSTIC STREAMING

This paper describes a new phenomenon of acoustic streaming which takes place when a Helmholtz resonator is excited by an inside sound source with resonant frequency,and takes the form of a strong turbulent jet.The flow visualizations,hot wire and LDV measurements are combined to investigate the process of acoustic streaming.It is found that this kind of acoustic streaming results from the contribution of Reynolds stress.

MODELLING OF THE PRESSURE-VELOCITY CORRELATION IN TURBULENCE DIFFUSION

Most current computations of trubulent flows with second-moment closure adopt the diffusion mo- dels which neglect the effect of pressure-velocity correlation.ln the present paper the importance of this correlation effect is elucidated the neglect of this effect accounts for some major defects in the wide application of the se- cond-moment closures.Through the relation between and ,established by Lumley,we propose here a new turbulence diffusion model which takes into consideration the pressure effect.Applications of this new model in the computation of shearless turbulence mixing layer and plane-and round-jet flows show that the spreading rate of these flows can be satisfactorily captured.

Modelling of pressure-strain correlation in compressible turbulent flow

Previous studies carried out in the early 1990s conjectured that the main compressible effects could be associated with the dilatational effects of velocity fluctuation. Later, it was shown that the main compressibility effect came from the reduced pressure-strain term due to reduced pressure fluctuations. Although better understanding of the compressible turbulence is generally achieved with the increased DNS and experimental research effort, there are still some discrepancies among these recent findings. Analysis of the DNS and experimental data suggests that some of the discrepancies are apparent if the compressible effect is related to the turbulent Mach number, Mt. From the comparison of two classes of compressible flow, homogenous shear flow and inhomogeneous shear flow （mixing layer）, we found that the effect of compressibility on both classes of shear flow can be characterized in three categories corresponding to three regions of turbulent Mach numbers： the low-Mr, the moderate-Mr and high-Mr regions. In these three regions the effect of compressibility on the growth rate of the turbulent mixing layer thickness is rather different. A simple approach to the reduced pressure-strain effect may not necessarily reduce the mixing-layer growth rate, and may even cause an increase in the growth rate. The present work develops a new second-moment model for the compressible turbulence through the introduction of some blending functions of Mt to account for the compressibility effects on the flow. The model has been successfully applied to the compressible mixing layers.