Simulation of subcritical flow pattern in 180° uniform and convergent open-channel bends using SSIIM 3-D model

In meandering rivers, the flow pattern is highly complex, with specific characteristics at bends that are not observed along straight paths. A numerical model can be effectively used to predict such flow fields. Since river bends are not uniform-some are divergent and others convergent-in this study, after the SSIIM 3-D model was calibrated using the result of measurements along a uniform 180° bend with a width of 0.6 m, a similar but convergent 180v bend, 0.6 m to 0.45 m wide, was simulated using the SSI1M 3-D numerical model. Flow characteristics of the convergent 180° bend, including lengthwise and vertical velocity profiles, primary and secondary flows, lengthwise and widtbwise slopes of the water surface, and the helical flow strength, were compared with those of the uniform 180° bend. The verification results of the model show that the numerical model can effectively simulate the flow field in the uniform bend. In addition, this research indicates that, in a convergent channel, the maximum velocity path at a plane near the water surface crosses the channel＇s centerline at about a 30° to 40° cross-section, while in the uniform bend, this occurs at about the 50° cross-section. The varying range of the water surface elevation is wider in the convergent channel than in the uniform one, and the strength of the helical flow is generally greater in the uniform channel than in the convergent one. Also, unlike the uniform bend, the convergent bend exhibits no rotational cell against the main direction of secondary flow rotation at the 135° cross-section.

Numerical study on residual current and its impact on mass transport in the Hangzhou Bay and the Changjiang Estuary I. A3-D joint model of the Hangzhou Bay and the Changjiang Estuary

A 3-D numerical model is set up in a large domain covering the Hangzhou Bay and the Changjiang Estuary based on the ECOM model in orthogonal curvilinear coordinates.The numerical schemes for baroclinic pressure gradient (BPG)terms and convective terms are improved in the paper according to the characteristics of velocity field and mass transport in the area.The model is validated by the simulations of residual current and salinity transport in the Hangzhou Bay and the Changjiang Estuary.

A Higher-Efficient Non-Hydrostatic Finite Volume Model for Strong Three-Dimensional Free Surface Flows and Sediment Transport

In order to accurately simulate strong three-dimensional （3-D） free surface flows and sediment transport, the fully 3- D non-hydrostatic pressure models are developed based on the incompressible Navier-Stokes equations and convection-diffusion equation of sediment concentration with the mixing triangle and quadrilateral grids. The governing equations are discretized with the unstructured finite volume method in order to provide conservation properties of mass and momentum, and flexibility with practical application. It is shown that it is first-order accurate on nonuniform plane two-dimensional （2-D） grids and second-order accurate on uniform plane grids. A third-order approximation of the vertical velocity at the top-layer is applied. In such a way, free surface zero stress boundary condition is satisfied maturely, and very few vertical layers are needed to give an accurate solution even for complex discontinuous flow and short wave simulation. The model is applied to four examples to simulate strong 3-D free surface flows and sediment transport where non-hydrostatic pressures have a considerable effect on the velocity field. The newly developed model is verified against analytical solutions with an excellent agreement.

Formation of the Tibetan Plateau during the India-Eurasia Convergence:Insight from 3-D Multi-Terrane Thermomechanical Modeling

Various models exist to explain the formation of the Tibetan Plateau,including“tectonic escape”,“pure shear thickening”,“convective removal of the lithospheric mantle”,and“lower crustal flow”model.The first two models are primarily constructed on pure mechanical models but are unable to reasonably explain the tension and shear phenomena inside the plateau.The latter two are rheological dynamic models based on deep geophysical observations.However,the spatial range of the lower crustal flow and its role in the plateau formation/uplift remain controversial.Five multi-terrane viscoplastic thermomechanical models were constructed to simulate the uplift and lithospheric structure change of the Tibetan Plateau during the post-collision stage(since 35 Ma)under the convergence of the Indian Plate.Results show that the plateau's formation begins with crustal thickening,blocked by strong terranes at the northern plateau,and expanded laterally to the east.The lithosphere thickens gradually and experiences delamination at its base,elevating temperature within the crust and forming partial melting layers in the central plateau.As convergence persists on the southern side,the northern plateau's lithosphere bends downward and undergoes delamination,further heating the crust and promoting the northward and eastward flow of partial melting layers,leading to secondary uplift around the plateau.

A New Efficient Finite Volume Modeling of Small Amplitude Free Surface Flows with Unstructured Grid

A staggered finite-volume technique for non-hydrostatic, small amplitude free surface flow governed by the incompressible Navier-Stokes equations is presented there is a proper balance between accuracy and computing time. The advection and horizontal diffusion terms in the momentum equation are discretized by an integral interpolation method on the orthogonal unstructured staggered mesh and, while it has the attractive property of being conservative. The pressure-correction algorithm is employed for the non-hydrostatic pressure in order to achieve second-order temporal accuracy. A conservative scalar transport algorithm is also applied to discretize k - c equations in this model. The eddy viscosity is calculated from the k-c turbulent model. The resulting model is mass and momentum conservative. The model is verified by two examples to simulate unsteady small amplitude free surface flows where non-hydrostatic pressures have a considerable effect on the velocity field, and then applied to simulate the tidal flow in the Bohai Sea.

A NUMERICAL MODEL FOR 3-D FLOW IN OPEN CHANNELS

A 3-D model based on the Reynolds equations with closed k-ε turbulence model is presented in this paper,which can be used to predict surface water flow in open channels.In- stead of the“rigid lid”approximation,the solution of the free surface equation is implemented in the velocity-pressure iterative procedure on the basis of the conventional SIMPLE method.This model was used to compute the flow in rectangular channels with trenches dredged across the bot- tom.The velocity,eddy viscosity coefficient,turbulent shear stress,turbulent kinetic energy and elevation of the free surface over the trenches dredged in the main channel,can be obtained. The computed results are in good agreement with existing experimentaing data.

THREE-DIMENSIONAL NUMERICAL MODELING OF SECONDARY FLOWS IN A WIDE CURVED CHANNEL

Most natural rivers are curved channels, where the turbulent flows have a complex helical pattern, as has been extensively studied both numerically and experimentally. The helical flow structure in curved channels has an important bearing on sediment transport, riverbed evolution, and pollutant transport study. In this article, different turbulence closure schemes i.e., the mixing-length model and the k-ε model with different pressure solution techniques i. e., hydrostatic assumptions and dynamic pressure treatments are applied to study the helical secondary flows in an experiment curved channel. The agreements of vertically-averaged velocities between the simulated results obtained by using different turbulence models with different pressure solution techniques and the measured data are satisfactory. Their discrepancies with respect to surface elevations, superelevations and secondary flow patterns are discussed.

EXPERIMENTAL STUDY OF 3-D TURBULENT BEND FLOWS IN OPEN CHANNEL

A generalized hend flow model, treating a 90° single bend and 60° continuous hends, was designed to quantitatively describe 3-D turhulenee mechanism of circulating notfully-developed flow in open channels with hends. The 3-D fluctuating veloeities of turbulent flow were measured and analyzed with a 3 D acoustic-Doppler velocimeter. Formula for 3 D turbulent intensity was derived using the dimension analysis approaeh. Expressions of vertical turbulent intensity distributions were obtained with the multivariant-rcgression theo ry, whieh agree with experiment data. Distrihutions of turbulent intensity and turbulent stress were characterized, and their relationships were concluded. In the bend-turbulent flow core region, longitudinal and lateral turbulent-intensity distri hutions are coincident with linear distribution, hut in nearwall region are coincident with the Gamma distribution. Verotical turbulent intensity distributions are coincident with the Rayleigh distribution. Herein, it is concluded that the bend turbulence is anisotropic.

河口海岸三维双σ坐标斜压水流数值模型研究

在海底地形陡变、垂向密度分层明显的水域,三维σ坐标模式中会出现一种"伪"水平斜压梯度力,并会引起"伪"密度流,以至于影响模拟的精度。垂向上引入双σ坐标变换,建立河口海岸水域三维斜压水流数值模型。数值试验结果表明,在海底地形陡变水域,双σ坐标模式可以减小水平斜压梯度力处理引起的误差。