Mathematical modeling of turbulent jets of deep-water sewage discharge into coastal basins

The basic properties of the dynamic model of a turbulent jet formed by a deep-water sewage discharge into the stratified environment of coastal regions are considered. The model developed was used to estimate the parameters of a floating-up jet of deep wastewater discharge from Sand Island into the basin of Mamala Bay (Hawaii) depending on the season and discharge operation mode. The estimates of the float-up depths of the jet and the initial dilution of the jet were estimated on the basis of model calculations using experimental data on the vertical profiles of the water temperature and salinity under the actual conditions of stratification in the study region. It is shown that the further propagation of the wastewater jet depends on tidal events and internal waves generated by tides. The appearance of turbulent jets at the sea surface was recorded. The model estimates of the parameters of the wastewater discharge were compared with the results of experimental measurements. Good agreement was found, which indicates that the physical mechanisms of the propagation of turbulent jets in a stratified medium are adequately described by the model.     

On the effect that the direction of geostrophic wind has on turbulence and quasiordered large-scale structures in the atmospheric boundary layer

The dependence that the structure and intensity of turbulent and large-scale quasiordered eddies in the atmospheric boundary layer (ABL) have on the direction of geostrophic wind has been studied on the basis of a series of numerical experiments with a three-dimensional nonstationary model of high spatial resolution. The presence of the meridional component of the angular velocity of the Earth’s rotation results in a significant intensification of velocity fluctuations in a neutrally stratified turbulent flow during the easterly and northeasterly winds and in their decay during the westerly and southwesterly winds. This, in turn, results in significant variations in the mean velocity profile. It is shown that these variations are associated with the largest scale fluctuations and are comparable (in scale) to the depth of Ekman’s turbulent layer. It is found that, in the neutrally stratified ABL bounded in height and under stable stratification inside the ABL, the wind-direction dependence significantly decreases. The possibilities of parameterizing these effects in locally one-dimensional ABL models are discussed.     

A two-fluid model of turbulent two-phase flow for simulating turbulent stratified flows

In this paper, a two-fluid model of turbulent two-phase flow is used to simulate turbulent stratified flows. This is a unified multi-fluid model for the motion of each phase in the flow, whose turbulent transport is closed by a two-phase k– model. The exchanges of mass, momentum and energy between the two phases are fully accounted for in the simulation. For illustration, a case of turbulent stratified flow with strong buoyancy effects, for which extensive experimental data are available, is selected for examination. It is shown that the numerical results agree well with the experimental data.     

Transport of waste heat from a nuclear power plant into coastal water

A numerical and experimental modeling is presented for studying the transport of waste heat from a nuclear power plant into coastal water by using a full-field physical model with scale distortion, a local physical model with normal scale and a depth-averaged k− turbulence model with a modified second-order upwind scheme. Field investigations are also used to provide the calibration and validation of the modeling. A case study simulating the turbulent tidal flow and waste heat transport in the coastal water near Daya Bay Nuclear Power Plant in Southern China was conducted. The experimental result of the case study shows that the water temperature in coastal water was a little oversimulated near the surface and was a little undersimulated near the bottom of heated-water layer by the full-field physical model. The numerical study shows that the depth-averaged k− turbulence model presented a satisfied prediction of turbulent tidal flow and far-field temperature distribution in coastal water, although the near-field stratification due to the heated water effluent was not accounted for. The result of the effect of scale distortion on physical model shows that a full-field physical model with a scale distortion of 10 produced a satisfied result of temperature distribution in the present case study.     

Nutrient transport from an artificial upwelling of deep sea water

The transport of nutrient-rich, deep sea water from an artificial upwelling pipe has been simulated. A numerical model has been built within a commercial Computational Fluid Dynamics (CFD) package. The model considers the flow of the deep sea water after it is ejected from the pipe outlet in a negatively buoyant plume (densimetric Froude number = −2.6), within a stably stratified ocean environment subject to strong ocean current cross flow. Two cross-flow profiles were tested with momentum flux ratios equal to 0.92 and 3.7. The standard k-ε turbulence model has been employed and a range of turbulent Schmidt and Prandtl numbers tested. In all cases the results show that the rapid diffusion of heat and salinity at the pipe outlet causes the plume to attain neutral buoyancy very rapidly, preventing strong fountain-like behavior. At the higher momentum flux ratio fountain-like behavior is more pronounced close to the pipe outlet. The strong cross-current makes horizontal advection the dominant transport process downstream. The nutrient plume trajectory remains largely within one relatively thin stratified layer, making any ocean cross-flow profile less important. Very little unsteady behavior was observed. The results show that the nutrient is reduced to less than 2% of its inlet concentration 10 meters downstream of the inlet and this result is largely independent of turbulent Prandtl or Schmidt number. Initial results would suggest that if such an artificial upwelling were to be viable for an ocean farming project, a large number of upwelling pipes would be necessary. Further work will have to determine the minimum nutrient concentration required to sustain a viable phytoplankton population and the required spacing between upwelling pipes.     

Numerical Modeling of a Round Jet Discharged into Random Waves

Coastal disposal of waste water can be idealized as the problem of a jet under random waves. Understanding of this phenomenon is important for engineering design and environmental impact assessment. The present study aims to simulate such phenomenon by using a 3D numerical model based on the solution of the spatially filtered and σ-transformed Navier–Stokes equations with dynamic sub-grid scale model of turbulence. The numerical solution procedures are split into three steps: advection, diffusion and pressure propagation, and a Lagrange–Euler method is used to track the free surface. Cases of vertical jet in stagnant water, pure random waves and vertical jet in random waves are simulated with the same grid system for comparative study. Different methods of generating jet inflow turbulence have been tested and the method of jet azimuthal modes is found to be the optimum. The numerical results reproduce the distinct characteristics of jet in waves, including faster decay of centerline velocity, wider lateral spreading and the occurrence of wave tractive mechanism.     

Experimental Investigation of the Decay from A Ship’s Propeller

In the present study,an experimental investigation of the decay of the maximum velocity and its turbulent characteristics behind a ship propeller,in "bollard pull" condition(zero speed of advance),is reported.Velocity measurements were performed in laboratory by use of a Laser Doppler Anemometry(LDA) measurement system.Earlier researchers described that the maximum axial velocity is constant at the initial stage of a ship’s propeller jet(Fuehrer and Rmisch,1977;Blaauw and van de Kaa,1978;Berger et al.,1981;Verhey,1983) as reported in a pure water jet(Albertson et al.,1950;Lee et al.,2002;Dai,2005),but a number of researchers disagreed with the constant velocity assumption.The present study found that the maximum axial velocity decays in the zone of flow establishment and the zone of established flow with different rates.The investigation provides an insight into the decays of both the maximum velocity and the maximum turbulent fluctuation in axial,tangential and radial components and the decay of the maximum turbulent kinetic energy.Empirical equations are proposed to allow coastal engineers to estimate the jet characteristics from a ship’s propeller.     

Turbulent mixing in stably stratified flows of the environment: The current state of the problem (Review)

Specific features of the turbulent transfer of the momentum and heat in stably stratified geophysical flows, as well as possibilities for including them into RANS turbulence models, are analyzed. The momentum (but not heat) transfer by internal gravity waves under conditions of strong stability is, for example, one such feature. Laboratory data and measurements in the atmosphere fix a clear dropping trend of the inverse turbulent Prandtl number with an increasing gradient Richardson number, which must be reproduced by turbulence models. Ignoring this feature can cause a false diffusion of heat under conditions of strong stability and lead, in particular, to noticeable errors in calculations of the temperature in the atmospheric boundary layer. Therefore, models of turbulent transfer must include the effect of the action of buoyancy and internal gravity waves on turbulent flows of the momentum. Such a strategy of modeling the stratified turbulence is presented in the review by a concrete RANS model and original results obtained during the modeling of stratified flows in the environment. Semiempirical turbulence models used for calculations of complex turbulent flows in deep stratified bodies of water are also analyzed. This part of the review is based on the data of investigations within the framework of the large international scientific Comparative Analysis and Rationalization of Second-Moment Turbulence Models (CARTUM) project and other publications of leading specialists. The most economical and effective approach associated with modified two-parameter turbulence models is a real alternative to classical variants of these models. A class of test problems and laboratory and full-scale experiments used by the participants of the CARTUM project for the approbation of numerical models are considered.     

On the turbulent prandtl number in a stably stratified atmospheric boundary layer

The results obtained from both atmospheric and laboratory measurements and from LES data show that, in the stably stratified flows of the atmospheric boundary layer, turbulent mixing occurs at gradient Richardson numbers Ri _g that significantly exceed one: the inverse turbulent Prandtl number Pr _t ⁻¹ decreases with an increase in the thermal flow stability. The decreasing trend of the inverse turbulent Ptandtl number is reproduced in a stably stratified atmospheric boundary layer in agreement with measurement data with the aid of an improved three-parameter turbulence model. In this model, a modified model that takes into account the effect of stratification in the expression for the time scale of the scalar field is used for the pressure-scalar correlation.     

Numerical experiment on <Emphasis Type="Italic">Kyucho</Emphasis> around the Tango Peninsula induced by Typhoon 0406

A numerical experiment using a three dimensional level model was performed to clarify the mechanism generating a strong coastal current, Kyucho, induced by the passage of Typhoon 0406 around the tip of the Tango Peninsula, Japan in June 2004. Wind stress accompanied by Typhoon 0406 was applied to the model ocean with realistic bottom topography and stratification condition. The model well reproduced the characteristics of Kyucho observed by Kumaki et al. (2005), i.e., the strong alongshore current with maximum velocity of 53 cm s⁻¹ and its propagation along the peninsula with propagation speed of about 0.6 m s⁻¹ one half-day after the typhoon’s passage. Coastal-trapped waves (CTW) accompanied by downwelling were induced along the northwest coast of the peninsula by the alongshore wind stress. The energy density flux due to the CTW flowed eastward along the coast, and indicated scattering of the CTW around the eastern coast of the peninsula. In addition, significant near-inertial internal gravity waves were also caused in the offshore region from the west of the Noto Peninsula to the north of the Tango Peninsula by the typhoon’s passage. The energy flux density of the near-inertial fluctuations flowed southward off the Fukui coast, and part of the energy flux was trapped on the tip of the Tango Peninsula, flowing with the coast on its right. It was found that the strong current, Kyucho, at the northeastern tip of the Tango Peninsula was generated by superposition of the near-inertial internal gravity waves and subinertial CTW.     

Theoretical models of the height of the atmospheric boundary layer and turbulent entrainment at its upper boundary

The planetary boundary layer (PBL), which directly interacts with the underlying surface, differs significantly in its nature from the low-turbulent stably stratified free atmosphere. Fluctuations of the Earth’s surface heat balance immediately affect the PBL and assimilate there owing to the effective mechanism of turbulent heat transfer. In this case the upper boundary of the PBL plays the role of a cover, preventing the direct penetration of thermal effects and contaminants into an overlying atmospheric layer. In view of this, air pollution is especially dangerous when associated with shallow PBL. In addition, local peculiarities of climate change are mainly determined by the PBL height due to the high sensitivity of thin stably stratified PBLs to the thermal effects. Deep convective PBLs are not very sensitive to weak thermal effects, but they significantly affect the formation of convective cloudiness and the climate system as a whole by means of the turbulent entrainment of the thermal energy, humidity, aerosols, and other admixtures through the upper boundary. The PBL height and turbulent entrainment must be calculated when simulating and forecasting air pollution, abnormal frosts and heat, and other hazardous phenomena. In this paper we discuss the state-of-the-art knowledge in the area of PBL height simulation and suggest a new model of turbulent entrainment for convective PBLs.     

Dynamic analysis of tension leg platform for offshore wind turbine support as fluid-structure interaction

Tension leg platform (TLP) for offshore wind turbine support is a new type structure in wind energy utilization.The strong-interaction method is used in analyzing the coupled model,and the dynamic characteristics of the TLP for offshore wind turbine support are recognized.As shown by the calculated results:for the lower modes,the shapes are water’s vibration,and the vibration of water induces the structure’s swing;the mode shapes of the structure are complex,and can largely change among different members;the mode shapes of the platform are related to the tower’s.The frequencies of the structure do not change much after adjusting the length of the tension cables and the depth of the platform;the TLP has good adaptability for the water depths and the environment loads.The change of the size and parameters of TLP can improve the dynamic characteristics,which can reduce the vibration of the TLP caused by the loads.Through the vibration analysis,the natural vibration frequencies of TLP can be distinguished from the frequencies of condition loads,and thus the resonance vibration can be avoided,therefore the offshore wind turbine can work normally in the complex conditions.     

Estimation of the long-term variability of hydrophysical characteristics of the Black Sea based on the assimilation of the climatic hydrological fields L and altimetry data

To study the long-term variability of the thermohaline and dynamic characteristics of the Black Sea, we use three versions of climatic fields, namely, the fields reconstructed in the model according to the old (1903–1982) and new (1903–2003) hydrological climatic data arrays of temperature and salinity and according to the data of satellite altimetry. The analysis of the altimetry-based climatic fields confirms the distinctions (established earlier according to the old and new data arrays) in the seasonal variability of the integral characteristics of temperature and salinity and in the structures of hydrophysical fields in the sea. It is shown that, in the winter-spring season, the thermohaline fields reconstructed according to the new and altimetry data arrays are characterized by a small elevation of the halocline (pycnocline) and the upper boundary of the cold intermediate layer. In all seasons, the altimetry-based surface geostrophic currents contain numerous mesoscale eddies with different signs of rotation. Moreover, in all seasons, the Rim Current reconstructed according to the altimetry data is characterized by a narrower jet almost along the entire its length. This jet is especially intense near the coasts of West Anatolia. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 4, pp. 3–17, July–August, 2006.     

Modeling of decadal variations in the Black-Sea ecosystem

We consider the decadal evolution of the Black-Sea ecosystem on the basis of a three-dimensional coupled model consisting of the Black-Sea circulation model and a biogeochemical block. The circulation model is based on the widely used POM (Princeton Ocean Model) model. The calculated hydrophysical fields are interpolated then to levels of the biogeochemical model, which covers the upper 150-m layer. We demonstrate the close relationship between the interannual variation of hydrophysical fields and the evolution of the main elements of the ecosystem. The period under consideration (1992–2001) is characterized by the warming of the Black-Sea upper layer, which can be traced by the trend of a growing surface temperature. It follows from the results of modeling that the process of warming is also revealed in the subsurface hydrophysical characteristics and the dynamics of the main elements of the Black-Sea ecosystem.     

Reconstruction of the seasonal climate of the Black Sea on the basis of available hydrological data

We analyze the seasonal variability of the climatic hydrophysical fields of the Black Sea reporduced in three numerical experiments carried out according to the model of circulation. The numerical predictions are performed for a period of 12.5 yr on the basis of the hydrological data accumulated in 1983–1995. The monthly average climatic fields of the current speed are reconstructed according to the data on the climatic fields of temperature and salinity by the method of hydrodynamic adaptation (standard). It is shown that, in prognostic calculations, the seasonal variability of temperature and salinity is qualitatively close to the “standard” dependence. At the same time, the quantitative difference between the climatic behavior of the model and the standard dependence may be significant. The annual cycle of the currents is characterized by the intensification of the Main Black-Sea Current in winter. The structure of the hydrophysical fields of the sea in the model becomes much more realistic if it is based on the actual hydrological data. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Laboratory testing of mathematical models for high-concentration fluid mud turbidity currents

The propagation characteristics of fluid mud turbidity currents were investigated experimentally and theoretically. Parameterizations for propagation phase transition times from slumping to self-similar and self-similar to viscous phases are proposed. Predictive capabilities of different mathematical models that fall into three different modeling approaches (force-balance, box, shallow water) were evaluated for fluid mud turbidity current propagation using our experimental observations. For the slumping and self-similar phases, the box and force-balance models showed superior predictive capabilities than the one-layer shallow water models with deep ambient condition. Fluid mud turbidity currents have a non-Newtonian rheology and their transition and propagation characteristics in the viscous phase differ vastly from the Newtonian currents. We derived and presented a viscous force-balance expression for the propagation of a non-Newtonian power-law fluid current. We then experimentally evaluated the predictive capability of this force-balance and the viscous shallow water model by Di Federico et al. (2006). Both models' predictions are observed to be in notably good agreement with the experimental data. The results of this study are expected to be useful for preliminary swift calculations of the fluid mud turbidity current propagation characteristics as well as in deciding whether more detailed calculations at the expense of complexity are required.     

Integral bubble and jet models with pressure forces

Modifications of integral bubble and jet models including the pressure force are proposed. Exact solutions are found for the modified model of a stationary convective jet from a point source of buoyancy and momentum. The exact solutions are compared against analytical solutions of the integral models for a stationary jet that are based on the approximation of the vertical boundary layer. It is found that the modified integral models of convective jets retain the power-law dependences on the altitude for the vertical velocity and buoyancy obtained in classical models. For a buoyant jet in a neutrally stratified atmosphere, the inclusion of the pressure force increases the amplitude of buoyancy and decreases the amplitude of vertical velocity. The total amplitude change is about 10%. It is shown that in this model there is a dynamic invariant expressing the law of a uniform distribution of the potential and kinetic energy along the jet axis. For a spontaneous jet rising in an unstably stratified atmosphere, the inclusion of the pressure force retains the amplitude of buoyancy and increases the amplitude of vertical velocity by about 15%. It is shown that in the model of a spontaneous jet there is a dynamic invariant expressing the law of a uniform distribution of the available potential and kinetic energy along the jet axis. The results are of interest for the problems of anthropogenic pollution diffusion in the air and water environments and the formulation of models for statistical and stochastic ensembles of thermals in a mass-flux parameterization of turbulent moments.     

Thermodynamic characteristics of water in natural water bodies with a high mineralization

To adequately describe the hydrophysical processes in water bodies with a high mineralization, it is necessary to take into account the dependence that the thermodynamic characteristics of water have on the amount of salts contained in it. This work investigates some widely known formulas for calculating a number of thermodynamic parameters of mineralized water. The density, freezing temperature, specific heat of evaporation, and relative pressure of saturated vapor over the surface are considered. The possibilities of using these formulas when modeling hydrophysical processes in water bodies with salinity in the range of 0–250 pro mille are analyzed. It is shown that the formulas under consideration should be used when the salinity does not exceed 100 pro mille. If the mineralization is higher, it is necessary to elaborate more suitable formulas on the basis of an approximation of in situ data or data from handbooks.     

The calculation of turbulent characteristics in a shallow sea

Turbulent characteristics and current velocity are calculated in the framework of a quasistationary model for a shallow sea, using the equations for Reynolds stress transport and for the rate of dissipation. The paper shows that the ‘negative viscosity’ effect manifests itself in the near-bottom layer, related to energy transfer from pulse motions of turbulent flow to the mean ones. Translated by Vladimir A. Puchkin.     

Certain results of numerical simulation of processes in the Arctic Ocean

Variations in hydrophysical parameters in the Arctic Ocean and the North Atlantic are studied on the basis of numerical simulation with the use of an ocean circulation model (including ice formation and drift). The main circulation and ice-drift modes have been ascertained depending on atmospheric cycles. The possibilities of the parameterization of intermediate and deep water formation in numerical models of polar ocean dynamics are considered. The effect of the interannual variability of the discharge of Siberian rivers on the distribution and propagation of fresh water in this region are estimated from numerical experiments. The simulation results of the propagation of the dissolved methane from Siberian rivers are presented.