NUMERICAL SIMULATION OF TURBULENT DIFFUSION OVER A COMPLEX TERRAIN

A set of hydrostatic atmospheric thermodynamic equations and diffusion equation are solved numerically to simulate the flow,temperature and concentration fields over the Fenhe River Valley,Shanxi Province. The results are compared with the data observed in a tracer experiment carried out in February of 1984. The concentration distributions are calculated by three approaches:ordinary grid numerical model,nested grid model and Gaussian model.The comparison shows that the nested grid model gives the best results and needs only a little more computer time.

THE DISTRIBUTION OF SOLID PARTICLES SUSPENDED IN A TURBULENT FLOW:A STOCHASTIC APPROACH

Basic fluid mechanics and stochastic theories are applied to show that the concentration distribution of suspended solid particles in a direction normal to the mean streamlines of a two-dimensional turbulent flow is greatly influenced by the lift force exerted on them in the vicinity of the wall.Analytic solution shows that,when the direction of the mean flow is horizontal,the probability density function p(y,t)for random displacements of the particles will have a maximum value at a point from the wall where the perpendicular component of the lift force precisely balances particle gravity.Interpretation of experimental observations is presented using this theory.

ON DIFFUSION VELOCITY AND THE MASS CONSERVATION EQUATION FOR COMPONENTS

The mass migration velocity(absolute velocitv) of component i in a multicomponent flow is equal to the convection velocity (frame velocity) plus the diffusion velocity (relative velocity). The diffusion velocity as well as the corresponding diffusion coefficient depends on how the convection velocity is adopted.In turbulent flow, the mass migration velocity of component i is( muss-weighted time average velocity). The diffusion velocity consists of turbulent diffusion velocity and molecular diffusion velocity is the simple lime average velocity of component i and a is a certain convection velocity). So, the part of turbulent diffusion velocity is independent of what convection velocity is taken.In the mdss conservation equation for component i, the expression for the diffusion term on its right-hand side will change when the convection velocity on its left-hand side changes. In turbulent flow, there could be no diffusion terms, or a turbulent diffusion term only or both the turbulent and molecular diffusion terms when or any velocity other than these two is taken as the convection velocity. The case, in which there could he molecular diffusion only without turbulent diffusion, occurs in laminar flow. The molecular diffusion term always depends on the adoption of convection velocitv.In two-phase flow, the value of the molecular diffusion term is often near or even exceeds that of the turbulent diffusion term, which is quite different from the case in gas mixture flow.

Vertical multiple-layer structure of temperature and turbulent diffusivity in the South China Sea

We report field measurements of vertical profiles of the turbulent diffusivity and temperature at different stations in the South China Sea(SCS).Our study shows that the measured turbulent diffusivity follows a power-law distribution with a varying exponent in water layers.Similar multiple-layer scaling regimes were also observed from the temperature fluctuations.Combining turbulent diffusivity and temperature fluctuations,the vertical structure of temperature was revealed.Furthermore,we discussed the temperature profiles in each layer.A constant function of a dimensionless temperature profile was found in water layers that have identical turbulence conditions.Our results reveal the multiple-layer structure of temperature in the SCS.This study contributes to the understanding of the vertical structure of multiple layers in the SCS and provides clues for exploring the physical mechanism for maintaining the temperature structure.

Turbulent mixing in the upper ocean of the northwestern Weddell Sea, Antarctica

Turbulent mixing in the upper ocean（30-200 m） of the northwestern Weddell Sea is investigated based on profiles of temperature,salinity and microstructure data obtained during February 2014.Vertical thermohaline structures are distinct due to geographic features and sea ice distribution,resulting in that turbulent dissipation rates（ε） and turbulent diffusivity（K） are vertically and spatially non-uniform.On the shelf north of Antarctic Peninsula and Philip Ridge,with a relatively homogeneous vertical structure of temperature and salinity through the entire water column in the upper 200 m,both ε and K show significantly enhanced values in the order of O（10^（-7））-O（10^（-6）） W/kg and O（10^（-3））-O（10^（-2）） m^2/s respectively,about two or three orders of magnitude higher than those in the open ocean.Mixing intensities tend to be mild due to strong stratification in the Powell Basin and South Orkney Plateau,where s decreases with depth from O（10^（-8）） to O（10^（-9）） W/kg,while K changes vertically in an inverse direction relative to s from O（10^（-6）） to O（10^（-5）） m^2/s.In the marginal ice zone,K is vertically stable with the order of10^（-4） m^2/s although both intense dissipation and strong stratification occur at depth of 50-100 m below a cold freshened mixed layer.Though previous studies indentify wind work and tides as the primary energy sources for turbulent mixing in coastal regions,our results indicate weak relationship between K and wind stress or tidal kinetic energy.Instead,intensified mixing occurs with large bottom roughness,demonstrating that only when internal waves generated by wind and tide impinge on steep topography can the energy dissipate to support mixing.In addition,geostrophic current flowing out of the Weddell Sea through the gap west of Philip Passage is another energy source contributing to the local intense mixing.

Experimental Study of the Diffusion of a Confined Wall Jet through a Perforated Plate: Influence of the Porosity and the Geometry

This paper investigated lateral diffusion of a confined two-dimensional wall jet (air inlet height: 5 cm) through a perforated plate. We considered two plates with porosities of and . The plates were positioned at distances of 10 cm and 20 cm below the jet inlet. The experiments were realized using 2D Laser Doppler Anemometer (LDA). Different profiles of mean and fluctuating velocities are presented. The presence of a perforated plate strongly modified the airflow pattern compared to an empty enclosure. The velocities above and below the plate depend on several parameters, including the porosity and the plate’s position relative to the inlet slot and the longitudinal position. The difference between the flow velocity above and below the plates could not be related using a universal formula that depends on these parameters. We also investigated the influence of a porous media of a height of 20 cm (a stack of spheres having a diameter of 3.75 cm) located below the perforated plate. The results highlight that the porous medium strengthens the effects of the perforated plate on the flow.

Experimental and Numerical Investigation of the Diffusion of a Confined Wall Jet through a Perforated Plate

When performing numerical modeling of fluid flows where a clear medium is adjacent to a porous medium, a degree of difficulty related to the condition at the interface between the two media, where slip velocity exists, is encountered. A similar situation can be found when a jet flow interacts with a perforated plate. The numerical modeling of a perforated plate by meshing in detail each hole is most often impossible in a practical case (many holes with different shapes). Therefore, perforated plates are often modeled as porous zones with a simplified hypothesis based on pressure losses related to the normal flow through the plate. Nevertheless, previous investigations of flow over permeable walls highlight the impossibility of deducing a universal analytical law governing the slip velocity coefficient since the latter depends on many parameters such as the Reynolds number, porosity, interface structure, design of perforations, and flow direction. This makes the modeling of such a configuration difficult. The present study proposes an original numerical interface law for a perforated plate. It is used to model the turbulent jet flow interacting with a perforated plate considered as a fictitious porous medium without a detailed description of the perforations. It considers the normal and tangential effects of the flow over the plate. Validation of the model is realized through comparison with experimental data.

Analysis of High Concentration Spikes Appearing in Mass Plume in Nearly Homogeneous Turbulent Flow Based on the PDF Transport Equation

To evaluate the pollutant dispersion in background turbulent flows, most researches focus on statistical variation of concentrations or its fluctuations. However, those time-averaged quantities may be insufficient for risk assessment, because there emerge many high-intensity pollutant areas in the instantaneous concentration field. In this study, we tried to estimate the frequency of appearance of the high concentration areas in a turbulent flow based on the Probability Density Function (PDF) of concentration. The high concentration area was recognized by two conditions based on the concentration and the concentration gradient values. We considered that the estimation equation for the frequency of appearance of the recognized areas consisted of two terms based on each condition. In order to represent the two terms with physical quantities of velocity and concentration fields, simultaneous PIV (Particle Image Velocimetry) and PLIF (Planar Laser-Induced Fluorescence) measurement and PLIF time-serial measurement were performed in a quasi-homogeneous turbulent flow. According to the experimental results, one of the terms, related to the condition of the concentration, was found to be represented by the concentration PDF, while the other term, by the streamwise mean velocity and the integral length scale of the turbulent flow. Based on the results, we developed an estimation equation including the concentration PDF and the flow features of mean velocity and integral scale of turbulence. In the area where the concentration PDF was a Gaussian one, the difference between the frequencies of appearance estimated by the equation and calculated from the experimental data was within 25%, which showed good accuracy of our proposed estimation equation. Therefore, our proposed equation is feasible for estimating the frequency of appearance of high concentration areas in a limited area in turbulent mass diffusion.

Numerical Simulation of Water Exchange Characteristics of the Jiaozhou Bay Based on A Three-Dimensional Lagrangian Model

Based on theory of three-dimensional hydrodynamics, an Euler-Lagrangian particle model is established to study the transport and water exchange capability in the Jiaozhou Bay. The three-dimensional hydrodynamic model, driven by tide and wind, is used to study the effects of wetting and drying of estuarine intertidal flats by the dry-wet grid technology based on the Estuarine, Coastal and Ocean Model （ECOM）. The particle model includes the advection and the diffusion processes, of which the advection process is simulated with a certain method, and the diffusion process is simulated with the random walk method. The effect of the intertidal zone, the turbulent diffusion and the timescales of the water exchange are also discussed. The results show that a moving boundary model can simulate the transport process of the particle in the intertidal zone, where the particles are transported for a longer distance than that of the stationary result. Simulations with and without the turbulent random walk show that the effect of turbulent diffusion is very effective at spreading particles throughout the estuary and speeding up the particle movement. The spatial distribution of residence time is given to quantify the water exchange capability that has very important ramifications to water quality. The effect of wind on the water exchange is also examined and the southeasterly wind in summer tends to block the water exchange near the northeast coast, while the northerly wind in winter speeds up the transport process. These results indicate that the Lagrangian particle model is applicable and has a large potential to help understanding the water exchange capability in estuaries, which can also be useful to simulate the transport process of contaminant.

Mathematical Model of Combustion in Blunt Annular Ceramic Burner

The computer simulation of the combustion process in blast furnace(BF) stove has been studied by using the k-ε-g turbulent diffusion flame model.The combustion process in blunt annular ceramic burner was calculated by using the software.The profiles of gas and air velocity,temperature of the combustion products,concentration of the components,and the shape and length of the flame during combustion have been researched.Compared with the original annular ceramic burner,the new design of the blunt one improves the mixing of the gas and the air significantly,and shortened the length of the flame.

Physical oceanography of the Caroline M4 seamount in the tropical Western Pacific Ocean in summer 2017

Physical oceanography plays an important role in the formation of submarine sediments,and the distribution of nutriments and biocenoses in seamounts.The M4 seamount is located in the Caroline Island Ridge of the Western Pacific Ocean.The physical properties around M4 seamount are preliminarily analyzed based on the in-situ data obtained in summer 2017 in Caroline M4 seamount and open-sourced data.We found that the water in the upper 200 m is controlled by the westward North Equatorial Current(NEC),while the water between 300-1000 m is dominated by the eastward North Equatorial Undercurrent(NEUC).The current direction fluctuates significantly below 300 m at upstream stations.At the same depth of the lee sides,the current direction changes with the distance from seamount.These are likely caused by the obstacle of M4 seamount.The calculation results show that there is an anticyclonic cap above M4 seamount caused by tidal rectification.Tidal currents in M4 seamount are squeezed by the topography and amplified,and the amplified tidal currents play a dominant role in M4 seamount.First,the circulation system generated by the interaction of the amplified tidal current and M4 seamount drives the upward/downward movement of the isotherms.Secondly,the thickness of the surface turbulent layer is changed with the tidal phase.Thirdly,high turbulent diffusivities are found in the bottom of M4 seamount,and these are most likely attributed to the turbulent mixing induced by the mutual effect between semidiurnal tidal currents and steep bathymetry.This article of physical oceanography provides scientific basis for further analysis of the distribution of biological community and deposition mechanism in M4 seamount.

Observation of physical oceanography at the Y3 seamount (Yap Arc) in winter 2014

Seamounts aff ect the surrounding physical oceanography and form unique dynamic processes.The infl uences of these processes on biological and sedimentary distributions are quite diff erent in seamount areas at diff erent depths.The Y3 seamount is located in the Yap Arc of the tropical Western Pacifi c Ocean.The water depth of its summit is~280 m.Based on fi eld data obtained in December 2014 and other open-access data,the physical oceanography around the Y3 seamount was preliminarily analyzed.The results show that the upper layer(0-150 m)was under the infl uence of the westward-fl owing North Equatorial Current(NEC),while the eastward-fl owing North Equatorial Undercurrent(NEUC)controlled the water between 200-800 m.The NEC was strong and steady,but the NEUC was disturbed by the Y3 seamount.The cold dome above the Y3 seamount was not caused by a Taylor cap or tidal rectifi cation but probably by upwelling during the survey time.Tidal currents were squeezed against topography and greatly amplifi ed in the Y3 seamount.The thicknesses of the surface turbulent layers were greatly infl uenced by the spring-neap tidal cycle.The turbulent diff usivities in the sea surface layer above the Y3 seamount were much larger than those in the open ocean.Calculations showed that the surface wind stress greatly aff ected the turbulent mixing in the surface layer of the Y3 seamount.The reciprocal action between the amplifi ed tidal currents and topography was the most likely cause of the turbulent mixing near the bottom of the Y3 seamount.This study can provide a scientifi c basis for further study of biological and depositional characteristics at the Y3 seamount.

Application of the three-dimensional telegraph equation to cosmic-ray transport

An analytical solution to the three-dimensional telegraph equation is presented. This equation has recently received some attention but so far the treatment has been one-dimensional. By using the structural similarity to the Klein-Gordon equation, the telegraph equation can be solved in closed form. Illustrative examples are used to discuss the qualitative differences from the diffusion solution. A comparison with a numerical test-particle simulation reveals that some features of an intensity profile can be better explained using the telegraph approach.

Turbulent mass transfer model for simulating protein desorption in liquid-solid circulating fluidized bed risers

An integrated model,namely the two-equation turbulent model,is introduced to simulate mass transfer in a liquid-solid circulating fluidized bed(LSCFB)riser.Protein desorption is simulated and the proposed model is validated.The protein concentration profiles simulated with this model agree well with published experimental results.This model enables direct determination of turbulent mass diffusivity,removing the need to empirically guess a constant turbulent Schmidt number for simulating mass transfer in a turbulent flow.This model is useful when the turbulent mass diffusivity is not available for simulating mass transfer in an LSCFB riser.

Turbulent Transport Coefficients in Turbulent Flows of Liquid Sodium

The direct measurements of turbulent viscosity and effective magnetic diffusivity in turbulent flow of electro-conductive fluids under moderate magnetic Reynolds number,i.e.,1<Rm<Rm*,where Rm* denotes the dynamo threshold,are reported.The measurements are performed in a nonstationary turbulent flow of liquid sodium,generated in a closed toroidal channel.The peak level of the Reynolds number reached 3 000 000,which corresponds to magnetic Reynolds number about 30.

A numerical model for air concentration distribution in self-aerated open channel flows

The self-aeration in open channel flows, called white waters, is a phenomenon seen in spillways and steep chutes. The air distribution in the flow is always an important and fundamental issue. The present study develops a numerical model to predict the air concentration distribution in self-aerated open channel flows, by taking the air-water flow as consisting of a low flow region and an upper flow region. On the interface between the two regions, the air concentration is 0.5. In the low flow region where air concentration is lower than 0.5, air bubbles diffuse in the water flow by turbulent transport fluctuations, and in the upper region where air concentration is higher than 0.5, water droplets and free surface roughness diffuse in the air. The air concentration distributions obtained from the diffusion model are in good agreement with measured data both in the uniform equilibrium region and in the self-aerated developing region. It is demonstrated that the numerical model provides a reasonable description of the self-aeration region in open channel flows.