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Results are described from a combined numerical and laboratory model study of the turbulent flow in a true 3D blade passage of a Francis hydro-turbine. The large eddy simulation (LES) is applied to investigate the intrinsic features and the spatial and temporal variations of the flow structures in the blade passage with strong wakes in inflow sweeping and the turbulence-induced blade vibration. The flow passes through the vibrating boundaries. Therefore, the system under consideration is in a dynamic fluid–structure interaction (FSI). In the simulation, one-coefficient dynamic sub-grid scale (SGS) model is incorporated in LES with Reynolds number 148 400 to better describe the energy exchange mechanism between large and small scales under the influences of strong geometrical curvature and vibrating boundaries. The governing equation of the blade vibration with FSI has been established by generalized variational principle combining the fluid and the structure. The vibration analysis is carried out by using Wilson-θ method. Separate iteration schemes are applied to solve the flow and the vibration in turn. The pressures on the wall sides of the blade and its vibrating accelerations are simultaneously measured. The numerical results show that the temporal and spatial distributions of turbulence in the 3D blade passage are significantly influenced by the curvature of blade configuration, the blade vibration, and the distorted wakes generated by flow passing through guide vanes. The influences of the vibration on the near-wall flow structures are quite remarkable. The simulated results are favourably compared with the measurements. Copyright © 2006 John Wiley & Sons, Ltd.

The properties and morphology of nanosilica modified with silane coupling agent, methacryloxypropyltrimethoxysilane (MPS), were characterized by fourier transform infrared, zeta potentials, thermogravimetric analysis, and transmission electron microscopy. The results showed that the grafting ratio of MPS on the surface of nanosilica increased with the MPS content. MPS-silica/PBA/PMMA core-shell latexes (MPS-Si/ACR) were prepared by seeded emulsion polymerization. Then they were used to mix with PVC resin. The outer layer (PMMA) enhanced the dispersibility of MPS-Si/ACR in the PVC matrix by increasing the interfacial interaction of these composite particles with PVC. The notched impact strengths of the blends were influenced by the weight ratio of MPS to silica, the concentration of emulsifier (SDS), and the MPS-Si/ACR content. The relationships between the mechanical properties and the core-shell composite structures were elaborated. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2008

A two-dimensional numerical model is developed to study the propagation of a solitary wave in the presence of a steady current flow. The numerical model is based on the Reynolds-averaged Navier-Stokes (RANS) equations with a k-e turbulence closure scheme and an internal wave-maker method. To capture the air-water interface, the volume of fluid (VOF) method is used in the numerical simulation. The current flow is initialized by imposing a steady inlet velocity on one computational domain end and a constant pressure outlet on the other end. The desired wave is generated by an internal wave maker. The propagation of a solitary wave traveling with a following/opposing current is simulated. The effects of the current velocity on the solitary-wave motion are investigated. The results show that the solitary wave has a smaller wave height, larger wave width, and higher traveling speed after interacting with a following current. Contrariwise, the solitary wave becomes higher with a smaller wave width and l...

It is a routine task in metabolic engineering to introduce multicomponent pathways into a heterologous host for production of metabolites. However, this process sometimes may take weeks to months due to the lack of standardized genetic tools. Here, we present a method for the design and construction of biological parts based on the native genes and regulatory elements in Saccharomyces cerevisiae. We have developed highly efficient protocols (termed YeastFab Assembly) to synthesize these genetic elements as standardized biological parts, which can be used to assemble transcriptional units in a single-tube reaction. In addition, standardized characterization assays are developed using reporter constructs to calibrate the function of promoters. Furthermore, the assembled transcription units can be either assayed individually or applied to construct multi-gene metabolic pathways, which targets a genomic locus or a receiving plasmid effectively, through a simple in vitro reaction. Finally, using β-carotene biosynthesis pathway as an example, we demonstrate that our method allows us not only to construct and test a metabolic pathway in several days, but also to optimize the production through combinatorial assembly of a pathway using hundreds of regulatory biological parts.

Model studies have been undertaken to study the spatial and temporal development of a brackish pool within an impoundment supplied by a freshwater inflow and bounded by an impermeable barrier that is overtopped periodically by a tidally generated saline water inflow. The results demonstrate the relative influence of the freshwater inflow and downstream tidal conditions in controlling the temporal development of this pool. In particular, the experimental data illustrate that the dimensions of the brackish pool reach equilibrium after a specific number of tidal cycles, with the normalized thickness of the pool being dependent primarily on the strength of the freshwater inflow. The density structure of the water within the impoundment is interpreted in terms of two contributory processes, namely, (1) turbulent entrainment of fresh receiving water into the saline intrusion; and (2) shear-induced interfacial erosion of the brackish water by the overriding fresh water during receding tidal conditions. A scaling analysis shows that the temporal growth of the brackish pool thickness can be parameterized successfully in terms of a volume ratio representing the dilution capacity of the freshwater stored in the impoundment during the saline intrusion phase.

Results are described from a combined laboratory and analytical study of the dense, deep-water flow through the Faroe Bank Channel. Archival field data have been used to specify the velocity and density field conditions in an idealized, distorted laboratory model in which the spatial and temporal development of a turbulent, dense source flow has been studied parametrically in terms of the source Rossby and Froude numbers, respectively. Measurements are presented to show that the flow (i) maintains geostrophic balance within the topographically varying channel and (ii) adjusts on the Ekman time scale to changing flow conditions. The outflow structure is shown to consist of a dominant axial (i.e., along channel) core component, with a significant transverse (i.e., side slope) secondary circulation driven by Ekman drainage and topographic divergence processes. Density field measurements are presented to show the mixing occurring between the turbulent outflow and the overlying water mass. Buoyancy anomaly data are derived to quantify the spatial variations of mixing processes along and across the channel. An analytical model based on Ekman dynamics is developed for flow in the channel, and the predictions of the dimensions of the outflow in terms of the external flow and topographic parameters are shown to agree well with the laboratory data.

Free overfall is treated by using two-dimensional steady potential flow theory. Based on the theory of the boundary value problem of analytical function and the substitution of variables we derive the boundary integral equations in the physical plane for solving the free overfall in a rectangular channel. A numerical iterative method has been developed to solve these boundary integral equations. The free water surface profiles, pressure distribution, and the end-depth ratio are calculated for a wide range of bed slopes, bed roughness, and incoming upstream Froude number. The computed results agree well with the available experimental data.

Results are described from a series of laboratory experiments in which the effects of a localized two-dimensional region of turbulence on the spatial development of a round, turbulent jet have been investigated. The evolution of the jet has been studied for respective cases with and without background turbulence in the receiving environment. For the former flow configuration, the breakdown of the jet by the presence of background turbulence (generated by an oscillating grid) has been investigated parametrically for a range of values of the source specific momentum flux J0 of the jet and the grid action K. Measurements of the location of the breakdown point of the jet, as detected by (i) a significant local increase in the jet spreading angle and (ii) the simultaneous decrease and increase in the magnitude of the axial and horizontal velocity components, respectively, of the flow field, confirm scaling predictions showing that the jet is destroyed significantly by the background turbulence when the background turbulence intensity is of the same order as the local turbulence intensity of the jet.

A series of laboratory experiments has been carried out to investigate the passage of an internal solitary wave of depression over a bottom ridge, in a two-layer fluid system for which the upper and lower layer is linearly-stratified and homogeneous respectively. Density, velocity and vorticity fields induced by the wave propagation over the ridge have been measured simultaneously at three locations, namely upstream, downstream and over the ridge crest, for a wide range of model parameters. Results are presented to show that wave breaking may occur for a sufficiently large wave amplitude and a strong ridge blockage factor, with accompanying mixing and overturning. Density field data are presented (i) to illustrate the overturning and mixing processes that accompany the wave breaking and (ii) to quantify the degree of mixing in terms of the wave and ridge parameters. For weak encounters, good agreement is obtained between the laboratory experimental results (velocity and vorticity fields induced by the wave propagation) and the predictions of a recently-developed fully nonlinear theory. Discrepancies between theory and experiment are discussed for cases in which breaking and mixing occur.

Results are presented from a series of model studies of the transient exchange flow resulting from the steady descent of an impermeable barrier separating initially-quiescent fresh and saline water bodies having density ρ0 and ρ0+(Δρ)0, respectively. A set of parametric laboratory experiments has been carried out (i) to determine the characteristic features of the time-dependent exchange flow over the barrier crest and (ii) to quantify the temporal increase in the thickness and spatial extent of the brackish water reservoir formed behind the barrier by the outflowing, partly-mixed saline water. The results of the laboratory experiments have been compared with the predictions of a theoretical model adapted from the steady, so-called maximal exchange flow case and good qualitative agreement between theory and experiment has been demonstrated. The comparisons indicate that head losses of between 7% and 3% are applicable to the flow over the ridge crest in the early and late stages, respectively, of the barrier descent phase, with these losses being attributed to mixing processes associated with the counterflowing layers of fresh and saline water in the vicinity of the ridge crest. The experimental data show (and the theoretical model predictions confirm) that (i) the dimensionless time of detection t det(g′/H b)1/2 of the brackish water pool fed by the dense outflow increases (at a given distance from the barrier) with increasing values of the descent rate parameter g'H b/(dh b/dt)2 and (ii) the normalised thickness δ(x,t)/H b of the pool at a given reference station increases monotonically with increasing values of the modified time (t−t det)/(H b/g′)1/2, with the rate of thickening decreasing with increasing values of the descent rate parameter g'H b(dh b/dt)2. Here, g′=(g/ρ0)(Δρ)0 is the modified gravitational acceleration, H b is the mean depth of the water and dh b/dt denotes the rate of descent of the barrier height h b with elapsed time t after the two water bodies are first brought into contact.

A series of laboratory experiments were carried out to investigate the response of a bar-blocked, saltwedge estuary to the imposition of both steady freshwater inflows and transient inflows that simulate storm events in the catchment area or the regular water releases from upstream reservoirs. The trapped salt water forms a wedge within the estuary, which migrates downstream under the influence of the freshwater inflow. The experiments show that the wedge migration occurs in two stages, namely (i) an initial phase characterized by intense shear-induced mixing at the nose of the wedge, followed by (ii) a relatively quiescent phase with significantly reduced mixing in which the wedge migrates more slowly downstream. Provided that the transition time t T between these two regimes satisfies t T >g′h 4 L/q 3 α, as was the case for all our experiments and is likely to be the case for most estuaries, then the transition occurs at time t T =1.2(gα 3 L 6 /g′ 3 q 2 ) 1/6 , where g′=gΔρ/ρ0 is the reduced gravity, g the acceleration due to gravity, Δρ the density excess of the saline water over the density ρ 0 of the freshwater, q the river inflow rate per unit width, and L and α are the length and bottom slope of the estuary, respectively. A simple model, based on conversion of the kinetic energy of the freshwater inflow into potential energy to mix the salt layer, was developed to predict the displacement xw over time t of the saltwedge nose from its initial position. For continuous inflows subject to t T , the model predicts the saltwedge displacement as x w /h=1.1 (t/τ) 1/3 , where the normalizing length and time scales are h=(q 2 /g) 1/3 and τ=g′α 2 h4L/q 3 , respectively. For continuous inflows subject to t>tT, the model predicts the displacement as xw/h=0.45N1/6(t/τ)1/6/α, where N=q 2 /g′h 2 L is a non-dimensional number for the problem. This model shows very good agreement with the experiments. For repeated, pulsed discharges subject to t T , the saltwedge displacement is given by (xw/h)3−(x0/h)(xw/h)2=1.3t/τ, where x 0 is the initial displacement following one discharge event but prior to the next event. For pulsed discharges subject to t>t T , the displacement is given by (xw/h) 6 −(x0/h)(xw/h) 5 =0.008N(t/τ)/α 6 . This model shows very good agreement with the experiments for the initial discharge event but does systematically underestimate the wedge position for the subsequent pulses. However, the positional error is less than 15%.

Laboratory model experiments have been conducted to investigate the interaction of a tidally forced stratified flow with a continental shelf. Results collected from a wide range of parametric experiments covering sub-, critical and super-critical tidal forcing are presented to show that the resulting flow regimes can be classified conveniently by the dimensionless parameters Fr=Usb/cw and μ=ω2/N02α, where Usb is the maximum velocity at the shelf break of slope angle α, cw is the long-wave speed of the lowest internal mode, ω is the frequency of the forcing and N0 is the buoyancy frequency of the initial undisturbed flow. Three distinct and characteristic flow regimes are observed, namely (i) shelf break eddies, (ii) intense downslope jets associated with offshore filamentary transport and (iii) pure up- and down-slope oscillatory jet flow, the occurrence of each of which is well-determined within Fr:μ parameter space. Measurements show a monotonic increase in eddy size (normalised by the amplitude A of the tidal forcing) with increasing Fr, while the thickness of the up- and downslope jet is shown to scale with A and to have no significant dependence on Fr. Measurements of the perturbation density field show significant intra-cycle variability in the local mixing and overturning parameters such as the buoyancy anomaly g′(zi), the available potential energy function ξ and the r.m.s. density ρr.m.s., with evidence of weak mixing and overturning (but significant internal wave activity) at slack tide conditions. Maximum values of both ξ and ρr.m.s. within a cycle show monotonic increases with increasing Fr and a strong dependence upon α and offshore location. Overall qualitative agreement with aspects of related numerical model results of Xing and Davies (J. Phys. Oceanogr. 27 (1997) 2100) and Holloway and Barnes (Cont. Shelf Res. 18 (1998) 31) is shown to be encouraging.

An experimental laboratory study has been carried out to investigate the propagation of an internal solitary wave of depression and its distortion by a bottom ridge in a two-layer stratified fluid system. Wave profiles, density fields and velocity fields have been measured at three reference locations, namely upstream, downstream and over the ridge. Experiments have been performed with wave amplitudes in the range 0.2– 1.9 times the depth of the upper layer, and a ratio between the lower and the upper layer in the range 3.0–8.5. The ridge slope was varied from 0.1 to 0.33 and the maximum ridge height was two-thirds of the thicker fluid layer. Over the ridge, the flow has been classified into: (i) cases when the bottom ridge has little influence on the propagation and spatial structure of the internal solitary wave, (ii) cases where the internal solitary wave is significantly distorted by the blocking effect of the ridge (though no wave breaking occurs), and (iii) cases for which the internal solitary wave is broken as it encounters and passes over the bottom ridge. A detailed description of the processes leading to wave breaking is given. Breaking has been found to take place when the fluid velocity in the lower layer exceeds 0.7 of a local nonlinear wave speed, defined at the top of the ridge. The breaking condition is also expressed in terms of the amplitude of the incident wave, the layer thickness ratio and the relative height of the ridge. The wave breaking can be determined from the input parameters of the experiment. The transmitted waves have been found to always consist of a leading pulse (solitary wave) followed by a dispersive wavetrain. The (solitary) wave amplitude is significantly reduced only when breaking takes place at the ridge. Internal waves of mode two are generated in cases with strong breaking.

Results are presented from a series of laboratory modelling studies carried out as part of the international multidisciplinary project CANIGO. The focus of interest has been the phenomenon of flow adjustment within the Gulf of Cadiz of the Mediterranean outflow plume, modelled by a turbulent, negatively-buoyant jet discharging into a rotating stratified reservoir scaled to the idealised topography of the Gulf. The results show that the fully developed flow pattern that forms close to the entrance to the Gulf consists of a relatively intense jet that divides when it encounters the southern Iberian coastal boundary; part of the jet is deflected westwards to form a boundary current at intermediate depth along the coastline and part is deflected eastwards and back towards the Strait to form a closed weak circulation near the diverging right wall of the Gulf. Within this closed circulation (the typical horizontal dimensions of which scale with the source Froude number when normalised with the inertial radius), small-scale eddy features are embedded. The degree of entrainment into the descending turbulent jet is seen to be determined primarily by the receiving water Froude number (and is relatively insensitive to the Burger and Rossby numbers of the flow), resulting in the formation of a boundary current of intermediate density that follows the Iberian coastal boundary with a typical velocity determined primarily by the effective driving head at the source and weakly by the Burger number of the flow.

The energy loss in hydraulic turbine is the most direct factor that affects the efficiency of the hydraulic turbine. Based on the analysis theory of inner energy loss of hydraulic turbine, combining the measurement data of the Francis-99, this paper calculates characteristic parameters of inner energy loss of the hydraulic turbine, and establishes the calculation model of the hydraulic turbine power. Taken the start-up test conditions given by Francis-99 as case, characteristics of the inner energy of the hydraulic turbine in transient and transformation law are researched. Further, analyzing mechanical friction in hydraulic turbine, we think that main ingredients of mechanical friction loss is the rotation friction loss between rotating runner and water body, and defined as the inner mechanical friction loss. The calculation method of the inner mechanical friction loss is given roughly. Our purpose is that explore and research the method and way increasing transformation efficiency of water flow by means of analysis energy losses in hydraulic turbine.

The accurate prediction of the dilution and motion of the produced denser water (e.g., discharge of concentrated brine generated during solution mining and desalination) is of importance for environmental protection. Boundary conditions and ambient stratification can significantly affect the dilution and motion of gravity currents. In this study, a multiphase model was applied to simulate the gravity current descending a slope into a linearly stratified ambient. The k-ω turbulence model was used to better simulate the near-bed motion. The mathematical model, the initial and boundary conditions, and the details of the numerical scheme are described here. The time-dependent evolution of the gravity current, the flow thickness, and the velocity and density field were simulated for a range of flow parameters. Simulations show that the Kelvin–Helmholtz (K-H) billows are generated at the top of the trailing fluid by the interfacial velocity shear. The K-H instability becomes weaker with the slope distan...

Numerical simulations are carried out to investigate the spreading of two-dimensional plane turbulent aerated and nonaerated jets in a tank filled with finite water depth. A multiphase model is applied to simulate the problem under investigation. The governing equations, their numerical scheme, and the boundary conditions are presented. Aerated and nonaerated turbulent jets are simulated for a range of the jet velocity and width at exit, the initial air content at exit, and the water depth in tank. The simulated results show that a self-similar Gaussian velocity distribution exists from the distance downstream being larger than five jet slot width for both the aerated and nonaerated jets. Good agreement between the simulated velocity profiles and available laboratory experiments is obtained. The simulated slope of the jet velocity decay along the jet center line is in good agreement with the experimental measurements. The effect of air content on pressure distribution and the maximum impinging hyd...

Results are presented from a series of laboratory model studies of the flushing of saline water from a partially- or fully-closed estuary. Experiments have been carried out to determine quantitatively the response of the trapped saline volume to fresh water Hushing discharges Q for different values of the estuary bed slope a and the density difference (Δρ)0 between the saline and fresh water. The trapped saline water forms a wedge within the estuary and for maintained steady discharges, flow visualisation and density profile data confirm that its response to the imposition of the freshwater purging flow occurs in two stages, namely (i) an initial phase characterised by intense shear-induced mixing at the nose of the wedge and (ii) a relatively quiescent second phase where the mixing is significantly reduced and the wedge is forced relatively slowly down and along the bed slope. Scalings based upon simple energy balance considerations are shown to be successful in (i) describing the time-dependent wedge be...

Results are presented from two sets of laboratory model experiments on the effects of an isolated seamount upon the flow of an intermediate-water slope current along a continental shelf. The experimental results for initial ambient conditions of respectively two-layer and linearly stratified fluids show that the structure of such a boundary current depends primarily on the values of the appropriate set of dimensionless dynamical parameters (namely the Burger (Bu), Ekman (Ek) and Rossby (Ro) numbers), as well as the dimensionless lateral separation of the seamount and shelf and the proportional height of the seamount relative to the distance from the bottom at which the intermediate-water flows. Comparisons of the present results with those from a previous two-layer fluid study with no obstacle present reveals that the presence of the obstacle does not alter significantly the stability of the current even when situated close to the shelf. However, for such configurations, the density, velocity and vorticity fields in the local zone of interaction between the current and the obstacle are distorted significantly by the presence of the obstacle, provided that the summit of the obstacle penetrates the level of current flow. Measurements of density, velocity and vorticity fields show no significant dependence of the flow interaction upon the detailed bathymetry of the shelf-slope. For stable intermediate-water slope currents, the nature of the interaction with the obstacle is determined primarily by (i) the lateral separation of the obstacle and the shelf edge and (ii) the Ro of the flow. For sufficiently low values of the former and high values of the latter, the interaction results in a splitting of the incident flow around the obstacle, with cyclonic and anticyclonic eddy pairs being generated in the lee. Geostrophic equilibrium is seen to be maintained in the current, even in the near wake of the obstacle. For cases in which the summit of the seamount is below the initially-undisturbed intermediate water level, no Taylor column-like division of the slope current occurs and no significant distortion of the current structure (velocity and density) occurs for the parameter ranges investigated. For linearly stratified cases, measurements show that no significant local elevation or depression of the density interfaces is observed in the interaction zone. The distributions of the local buoyancy frequencies calculated from the density profiles reveal that the minimum value of the frequency upstream of the obstacle is smaller than that downstream, indicating that the flow interactions generate local mixing downstream, with consequent erosion of the density interfaces.

Laboratory experiments are presented from a modelling investigation into the influence of shelf and slope topography on f-plane surface and intermediate flows along ocean boundaries. The surface flows are formed from an upstream source by the release of fresh water into a rotating tank containing salt water, while for the intermediate-water counterpart flows, neutrally-buoyant fluid was released from a submerged source into stably-stratified (two-layer) and quiescent receiving waters in solid body rotation. It is shown that the stability of these buoyancy-driven currents can be described satisfactorily by a combination of the dimensionless parameters Bu=N2/f2, Ek=2ν/fD02 and Ro=U0/fL0, where N and f are the buoyancy and Coriolis frequencies respectively, D0, L0 and U0 are the initial depth, width and velocity of the currents, respectively, and ν is the kinematic viscosity of the fluid. Furthermore, comparison with physical models of surface and intermediate flows along a vertical wall and over a flat bottom reveals that the stability regimes are not significantly altered by the presence of shelf topography. Variation of the depth of the surface flows with respect to the total fluid depth above the underlying shelf is shown to have a significant effect on the velocity and density structure of these flows. When the depth and width ratios are small, the surface flow is not affected by the varying topography. However, when the current occupies a considerable height above the shelf and is at least as wide as the shelf, upper layer fluid is transported offshore through the bottom Ekman layer, where it is arrested above the sloping bottom. At this location, a deepening of the upper layer develops due to potential vorticity conservation of the lower layer, accompanied by a local alongshore velocity maximum. This shelf break front prevents significant offshore transport of upper layer fluid far beyond the shelf break, even in cases where the flow is unstable. Comparison of the intermediate currents with dynamically-similar currents above a flat bottom does not reveal a stabilising effect of the slope. For unstable intermediate currents, offshore transport is not prohibited (as it is shown to be for surface currents over narrow shelves, due to the presence of the slope), and large scale instability patterns can extend over great distances from the slope. It is shown that the geostrophic nature of these currents is destroyed close to the sloping bottom. Here, the upper and lower density interfaces, denoting the vertical extents of the intermediate current, tilt sharply downwards.

An experimental investigation is presented on the large-scale motion field and associated mixing of an initially two-layer, equal depth stratified fluid driven by an impulsively-started, rotating disk at the base of the (cylindrical) fluid container. For sufficiently large Reynolds numbers and fixed geometry, the flow is shown to depend on a single parameter, the Richardson number Ri = g'H/(ωRT)2, where g' is the reduced gravity, H is the depth of each of the fluid layers, and ω and RT are the disk rotation rate and radius, respectively. For Ri < 1.5 the primary mixing mechanism is found to be shear-induced billowing along the primary density interface, with the mixed fluid along this interface being advected into the lower fluid interior by secondary motions. An analysis is advanced to show that the elevation of the interface separating the upper (almost quiescent) layer of constant density from the lower mixed region grows as [Ri−1(H/RT)−1]ωt, where t is the time. The experimental observations are in good agreement with this scaling. The studies reveal that the large-scale secondary motion fields characteristic of this physical system force secondary interfaces, or fronts, to be formed periodically in the lower mixed layer region. These secondary fronts are shown to be relatively weak, with the velocity and density jumps across them being small compared with those across the primary interface.

The problem of gravity-driven free-surface flows is difficult to solve due to the nonlinear character of the boundary condition. Using methods based on complex analysis, only flows past simple geometrical boundaries have been investigated. The fluid flow from a reservoir, through a slit with an arbitrarily curved boundary, into downstream in the pattern of a free jet has both characters of free jet and flow from a sluice gate. The solution of the problem is more difficult to obtain than either free jet or flow under a sluice gate. When the total energy head, namely, the depth of water in reservoir is given, not only the velocity on the solid boundary and the profiles of the free surfaces need to be calculated, but also the discharge needs to be determined. In the present paper, by using the theory of the boundary-value problem of analytical function and the substitution of variables, the boundary-integral equations in the physical plane are derived. According to the consistency between the discharge and the uniform velocity at far upstream, the writers present a synchronous iterative method for the discharge and flow pattern. The profile of the free surfaces, the velocity and pressure distributions on the walls, and the discharge are calculated. The computed results agree well with the measured results.

Results are presented from a series of laboratory experiments in which a flow has been generated in a linearly-stratified fluid (initially at rest in a cylindrical container of radius RT) by the impulsive steady azimuthal rotation of a flat, smooth, horizontal circular disk of radius Rd. Experiments have been conducted for a range of disk sizes Rd, disk rotation rates ω and buoyancy frequencies N0, and the spatial and temporal development of the motion and density fields (and mixing associated therewith) have been shown to be critically dependent on the ratio Rd/RT. For cases in which this ratio is close to unity, the principal mixing mechanisms affecting the flow development are shown to be (i) the localised overturning of fluid forced by the disk Ekman layers and confining sidewalls and (ii) shear-induced billow entrainment along the outer edge of the so-called primary interface between the upper, unmixed fluid and the lower, partially-mixed fluid regions adjacent to the disk. For the large disk case, for sufficiently high values of ω/N0, density gradients develop sequentially with time within the partially-mixed region and the forms of the associated density interfaces also change with time as the primary interface migrates vertically. At the other extreme, for small values of the ratio Rd/RT but otherwise identical external conditions, the container walls play a negligible role in the flow development and the initial mixing is achieved primarily by shear-induced billow overturning at the primary interface. A scaling analysis is advanced to predict the growth rate of the primary interface and the experimental data are shown to be in good agreement with the analysis.

The Hangzhou Bay, located at the East of China, is widely known for having one of the world’s largest tidal bores. It is connected with the Qiantang River and the Eastern China Sea, and contains lots of small islands collectively referred as Zhoushan Islands (see Figure 1). The estuary mouth of the Hangzhou Bay is about 100 km wide; however, the head of bay (Ganpu) which is 86 km away from estuary mouth is significantly narrowed to only 21 km wide. The tide in the Hangzhou Bay is an anomalistic semidiurnal tide due to the irregular geometrical shape and shallow depth and is mainly controlled by the M2 harmonic constituent. The M2 tidal constituent has a period about 12 hours and 25.2 minutes, exactly half a tidal lunar day. The Hangzhou Bay faces frequent threats from tropical cyclones and suffers a massive damage from its resulting strong wind, storm surge and inland flooding. According to the 1949-2008 statistics, about 3.5 typhoons occur in this area every year. When typhoon generated in tropic open sea moves towards the estuary mouth, lower atmospheric pressure in the typhoon center causes a relatively high water elevation in adjacent area and strong surface wind pushes huge volume of seawater into the estuary, making water elevation in the Hangzhou Bay significantly increase. As a result, the typhoon-induced external forces (wind stress and pressure deficit) above sea surface make the tidal hydrodynamics in the Hangzhou Bay further complicated. In the recent years, some researches have been done to study the tidal hydrodynamics in the Hangzhou Bay and its adjacent areas. For example, Hu et al. (2000) simulated the current field in the Hangzhou Bay based on a 2D model, and their simulated surface elevation and current field preferably compared with the field observations. Su et al. (2001), Pan et al. (2007) and Wang (2009) numerically investigate the formulation, propagation and dissipation of the tidal bore at the head of Hangzhou Bay. Also, Cao & Zhu (2000), Xie et al. (2007), Hu et al. (2007) and Guo et al. (2009) performed numerical simulation to study the typhoon-induced 9

In this paper, a three-dimensional numerical model is developed to analyze the ocean wave-induced seabed response. The pipeline is assumed to be rigid and anchored within a trench. Quasi-static soil consolidation equations are solved with the aid of the proposed Finite Element (FE) model within COMSOL Multiphysics. The influence of wave obliquity on seabed responses, the pore pressure and soil stresses, are studied. A comprehensive tests of FE meshes is performed to determine appropriate meshes for numerical calculations. The present model is verified with the previous analytical solutions without a pipeline and two-dimensional experimental data with a pipeline. Numerical results suggest that the effect of wave obliquity on soil responses can be explained through the following two mechanisms: (i) geometry-based three-dimensional influences, and (ii) the formation of inversion nodes. However, the influences of wave obliquity on the wave-induced pore pressure are insignificant.

An innovative computational model is presented for the large eddy simulation of multi-dimensional unsteady turbulent flow problems in complex geometries. The main objectives of this research are (i) to better understand the structure of turbulent flows in complex geometry and (ii) to investigate the 3D characteristics of such complex fluid flow. The filtered Navier-Stokes equations are used to simulate large scales of the turbulence, while the energy transfer from large scales to subgrid-scales (SGS) is simulated using dynamical mixed one-equation subgrid models. In the proposed SGS model, the SGS kinetic energy, k s g s , is used for scaling the velocity for the eddy-viscosity part of the model. The proposed SGS model contains not only some information on the small scales as described in traditional Smagorinsky model or Germano dynamical model but also includes additional scale-similarity as that in the models of Ghosal et al. (J. Comput. Phys. 1995; 118:24-37) or Davidson (11th International Symposium on Turbulent Shear Flow, Grenoble, vol. 3, 1997; 26.1-26.6). The Navier-Stokes equations and the derived k sgs equation are solved using implicit finite-volume method. The models have been applied to simulate the 3D flows over a backward-facing step and in a strong 3D skew runner blade passage of a Francis hydro turbine, respectively. Good agreement between simulated results and experimental results as well as other numerical results was obtained.

In this study, a numerical model for wave-induced horizontal non-homogeneous seabed response is developed. Two new coefficients are proposed to describe the influence degrees of horizontal non-homogeneous soil property. The effects of wave condition and adjacent soil properties on the local soil response are investigated. Numerical results show that the influence range of the horizontal non-homogeneous soil property increases with the increase of wave period, wave height and soil permeability, and increases with the decrease of soil air content.

The response of a stratified fluid to the imposition of a surface stress has long been a topic of interest in geophysical fluid dynamics because of the relevance of the problem to mixing and overturning in large lakes, reservoirs and ocean basins. In the first definitive laboratory investigations (e.g Kato and Phillips, 1969; Kantha et al., 1977; Scranton and Lindberg, 1983) in this area, a linearly-stratified fluid contained in an annular tank was subjected to a constant surface stress imposed by the motion of a rotating screen and the process of entrainment was thereby initiated. As a result, a so-called mixed layer was generated, the thickness of which grew with time at a rate dependent upon the appropriate Richardson number of the established flow. In the annular geometry, the presence of secondary flows ensured that the development of the mixed layer was three-dimensional. Further experiments have been carried out by many authors since the above investigations and the reader is referred specifically to the recent article by Fernando (1991) for a comprehensive record and review of the resulting data

In the present study, the subgrid-scale (SGS) eddy-viscosity model developed by Vreman [Phys. Fluids 16 (2004) 3670] and its dynamic version [Phys. Fluids 19 (2007) 065110] are tested in large-eddy simulations (LES) of the inhomogeneous turbulent flow in a full passage of Francis turbine. Distributions of pressure, velocity and vortices as well as some flow structure are gained, which is helpful to examine the performance of SGS model for complex turbulent flow and understand the flow characters in full passage of Francis turbine.

The wave–seabed interaction issue is of great importance for the design of foundation around marine infrastructures. Most previous investigations for such a problem have been limited to uncoupled or one-way coupled methods connecting two separated wave and seabed sub models with the continuity of pressures at the seabed surface. In this study, a strongly coupled model was proposed to realize both wave and seabed processes in a same program and to calculate the wave fields and seabed response simultaneously. The information between wave fields and seabed fields were strongly shared and thus results in a more profound investigation of the mechanism of the wave–seabed interaction. In this letter, the wave and seabed models were validated with previous experimental tests. Then, a set of application of present model were discussed in prediction of the wave-induced seabed response. Numerical results show the wave-induced liquefaction area of coupled model is smaller than that of uncoupled model.

This paper investigates the dynamic angle of repose underneath the submarine pipeline. A series of tests are carried out to explore the bottom velocity in the scour hole for the case of with spoiler, and gap-ratio in unidirectional current. On that basis, the formulas of dynamic angle of repose in the scour hole are proposed using a sand deposition model. The formulas consider the bottom velocity (which is mainly influenced by the spoiler height and gap-ratio) that dominates the angle of repose. The calculation results are verified by the test data and a good agreement is obtained.