Propagation of surface waves on irregular bed topography

This paper deals with the exact solution of surface gravity waves in an ocean with irregular bed topography. In order to obtain water surface elevation and run-up of infra-gravity waves when the bed is either wavy or exponential, closed form solutions are obtained. Numerical computations indicate that when solitary wave or sinusoidal wave conditions are applied at the boundary, water surface elevation attains near Gaussian profile.     

Stokes flow of an assemblage of porous particles: stress jump condition

The present article investigates the overall bed permeability of an assemblage of porous particles. For the bed of porous particles, the fluid-particle system is represented as an assemblage of uniform porous spheres fixed in space. Each sphere, with a surrounding envelope of fluid, is uncoupled from the system and considered separately. This model is popularly known as cell model. Stokes equations are employed inside the fluid envelope and Brinkman equations are used inside the porous region. The stress jump boundary condition is used at the porous-liquid interface together with the continuity of normal stress and continuity of velocity components. On the surface of the fluid envelope, three different possible boundary conditions are tested. The obtained expression for the drag force is used to estimate the overall bed permeability of the assemblage of porous particles and the behavior of overall bed permeability is analyzed with various parameters like modified Darcy number (Da*), stress jump coefficient (??), volume fraction (??), and effective viscosity.     

Study of storm surge due to Typhoon Linda (1997) in the Gulf of Thailand using a three dimensional ocean model

Numerical integrations using the three dimensional ocean model based on the princeton ocean model (POM) were applied for the study of both sea level elevation and ocean circulation patterns forced by the wind fields during typhoons that moved over the Gulf of Thailand (GoT). The simulation concerned a case of Typhoon Linda which occurred during November 1-4, 1997. Typhoon Linda was one of the worst storms that passed the Gulf of Thailand and hit the southern coastal provinces of Thailand on November 3, 1997. It caused flooding and a strong wind covering large areas of agriculture and fisheries, which destroyed households, utilities and even human lives. The model is the time-dependent, primitive equation, Cartesian coordinates in a horizontal and sigma coordinate in the vertical. The model grid has 37 × 97 orthogonal curvilinear grid points in the horizontal, with variable spacing from 2 km near the head of the GoT to 55 km at the eastern boundary, with 10 sigma levels in the vertical conforming to a realistic bottom topography. Open boundary conditions are determined by using radiation conditions, and the sea surface elevation is prescribed from the archiving, validation and interpretation of satellite oceanographic data (AVISO). The initial condition is determined from the spin up phase of the first model run, which was executed by using wind stress calculated from climatological monthly mean wind, restoring-type surface heat and salt and climatological monthly mean freshwater flux. The model was run in spin up phase until an ocean model reached an equilibrium state under the applied force. A spatially variable wind field taken from the European Centre for Medium-Range Weather Forecasts (ECMWF) is used to compute the wind stress directly from the velocity fluctuations. Comparison of tendency between the sea surface elevations from model and the observed significant wave heights of moored buoys in the Gulf of Thailand under Seawatch project is investigated. The model predicts the sea level elevation up to 68.5 cm at the Cha-Am area located in the north of where the typhoon strands to the shore. Results of sea level elevation show that there is an area of peak set-up in the upper gulf, particularly in the western coast, and the effects of the storm surge are small at the lower gulf. During the entire period of this study, the surge in the gulf was induced by the northeasterly wind blowing over it.     

A mapping technique for numerical computations of bed evolutions

Free surface flow is one of the most difficult problems in engineering to be solved, since velocity and pressure fields depend on the free surface. On the other hand, the position of the free surface is unknown previously. Furthermore, the boundary condition on the free surface is expressed by a complicated equation. In an alluvial stream, where the boundaries of the domain are not fixed, addition of free surface at the bed will increase this difficulty. A domain mapping technique is developed in this paper to study the bed evolutions. The flow is considered 2D, choosing two coordinates in streamwise and upward directions. With a proper transformation, the hydrodynamics and sediment transport governing equations in irregular domain will be mapped into a simple rectangular one. The new domain can be discretize by finite elements. The transformed governing equations are solved to obtain desired variables in the mapped domain. With a proper transformation, there is no need of inverse mapping to obtain the free water surface profile and bedform evolution and migration in the actual domain. The model has been applied to streams with movable bed and the results show a good agreement with the experimental experiences.     

The effect of variable viscosity on MHD viscoelastic fluid flow and heat transfer over a stretching sheet

An analysis has been carried out to study the momentum and heat transfer characteristics in an incompressible electrically conducting non-Newtonian boundary layer flow of a viscoelastic fluid over a stretching sheet. The partial differential equations governing the flow and heat transfer characteristics are converted into highly non-linear coupled ordinary differential equations by similarity transformations. The effect of variable fluid viscosity, Magnetic parameter, Prandtl number, variable thermal conductivity, heat source/sink parameter and thermal radiation parameter are analyzed for velocity, temperature fields, and wall temperature gradient. The resultant coupled highly non-linear ordinary differential equations are solved numerically by employing a shooting technique with fourth order Runge–Kutta integration scheme. The fluid viscosity and thermal conductivity, respectively, assumed to vary as an inverse and linear function of temperature. The analysis reveals that the wall temperature profile decreases significantly due to increase in magnetic field parameter. Further, it is noticed that the skin friction of the sheet decreases due to increase in the Magnetic parameter of the flow characteristics.     

Numerical modeling of hydrodynamic and hydrothermal characteristics in subtropical alpine lake

A three-dimensional, time-dependent hydrodynamic and hydrothermal model was performed and applied to the subtropical alpine Yuan-Yang Lake (YYL) in northeastern region of Taiwan. The model was driven with discharge inflow, heat, and wind stress to simulate the hydrodynamic and hydrothermal in the lake. The model was validated with measured water surface elevation, current, and temperature in 2008. The overall model simulation results are in quantitative agreement with the available field data. The validated model was then used to investigate wind-driven current, mean circulation, and residence time in the YYL. The modeling results reveal that the velocity field along the wind axis present the variations over depth with return current where the velocity at the surface layer is along the wind direction while it is opposite near 1 m below water surface. The simulated mean current indicates that the surface currents flow towards the southwest direction and form a clock-wise rotation. The calculated residence time is strongly dependent on the inflows and wind effects. Regression analysis of model results reveals that an exponential regression equation can be employed to correlate the residence time to change of discharge input. The residence time without wind stress is higher than that with wind effect, indicating that wind plays an important role in lake mixing. The calculated residence time is approximately 2-2.5 days under low inflow with wind effect.     

Numerical simulation of scour around a submarine pipeline using computational fluid dynamics and discrete element method

Scour under a submarine pipeline can lead to structural failure; hence, a good understanding of the scour mechanism is paramount. Various numerical methods have been proposed to simulate scour, such as potential flow theory and single-phase and two-phase turbulent models. However, these numerical methods have limitations such as their reliance on calibrated empirical parameters and inability to provide detailed information. This paper investigates the use of a coupled computational fluid dynamics-discrete element method (CFD-DEM) model to simulate scour around a pipeline. The novelty of this work is to use CFD-DEM to extract detailed information, leading to new findings that enhance the current understanding of the underlying mechanisms of the scour process. The simulated scour evolution and bed profile are found to be in good agreement with published experimental results. Detailed results include the contours of the fluid velocity and fluid pressure, particle motion and velocity, fluid forces on the particles, and inter-particle forces. The sediment transport rate is calculated using the velocity of each single particle. The quantitative analysis of the bed load layer is also presented. The numerical results reveal three scour stages: onset of scour, tunnel erosion, and lee-wake erosion. Particle velocity and force distributions show that during the tunnel erosion stage, the particle motion and particle–particle interactive forces are particularly intense, suggesting that single-phase models, which are unable to account for inter-particle interactions, may be inadequate. The fluid pressure contours show a distinct pressure gradient. The pressure gradient force is calculated and found to be comparable with the drag force for the onset of scour and the tunnel erosion. However, for the lee-wake erosion, the drag force is shown to be the dominant mechanism for particle movements.     

A STUDY ON GRADIENT BLOW UP FOR VISCOSITY SOLUTIONS OF FULLY NONLINEAR, UNIFORMLY ELLIPTIC EQUATIONS

We investigate sharp conditions for boundary and interior gradient estimates of continuous viscosity solutions to fully nonlinear,uniformly elliptic equations under Dirichlet boundary conditions. When ...     

微通道液体流动双电层阻力效应

采用数值方法求解双电层的Poisson-Boltzmann方程和液体运动的Navier-Stokes方程,研究微通道双电层对压强梯度液体流动的阻力效应． 量纲分析表明,双电层阻力大小可以用一个无量纲的电阻力数表示．它与液体的介电系数、固体表面的zeta电位平方成正比,与液体的动力粘性系数、电导率以及微通道的宽度平方成反比．在计算流动诱导的流动电位势和电阻力时,提出电流密度平衡条件,可以消除传统电流平衡条件导致的固壁附近产生局部回流的不合理物理现象．还给出不同电阻力数的微通道流量、流量损失率、速度剖面的数值结果,合理解释了双电层对微通道液体流动的阻力效应．     

Axisymmetric torsional fretting contact between a spherical punch and an FGPM coating

The axisymmetric torsional fretting contact between a rigid conducting spherical punch and a functionally graded piezoelectric material (FGPM) coating is studied in this paper. The exponential model is used to simulate the inhomogeneous electro-mechanical properties of the FGPMs coating. The conducting spherical punch with a constant surface electric potential is considered in the contact. A normal force and a cyclic torque are applied to the two contact bodies. The applied torque produces an outer annular slip area and an inner stick area. The torsion angle is produced within the inner stick area as a rigid body. With the aid of the Hankel integral transform technique, we can reduce the contact problem to the singular integral equations of the Cauchy type. Then the unknown electro-mechanical fields and stick/slip area can be obtained numerically. The effect of the gradient index on the surface electro-mechanical fields is discussed at loading and unloading phases. The Mises stress and principal stress at the contact surface are also discussed to predict the possible location of fretting damage and failure.     

Two layer transient water waves over a viscoelastic ocean bed

A two-layer analysis of the transient development of water waves over a viscoelastic ocean bed is presented here. This is a two-dimensional initial value investigation of the transient development of surface and internal wave motions governed by harmonic pressure distribution acting on the free surface in an inviscid liquid over a viscous and elastic ocean bed. The equations of motion and the equation of continuity are described in terms of velocity potential and stream functions. The solution of this problem is obtained by using Laplace and Fourier transform methods. Limiting case of the layers to obtain free surface elevation is also presented.     

Anomalous waves as an object of statistical topography: Problem statement

Based on ideas of statistical topography, we analyze the boundary-value problem of the appearance of anomalous large waves (rogue waves) on the sea surface. The boundary condition for the sea surface is regarded as a closed stochastic quasilinear equation in the kinematic approximation. We obtain the stochastic Liouville equation, which underlies the derivation of an equation describing the joint probability density of fields of sea surface displacement and its gradient. We formulate the statistical problem with the stochastic topographic inhomogeneities of the sea bottom taken into account. It describes diffusion in the phase space, and its solution must answer the question whether information about the existence of anomalous large waves is contained in the quasilinear equation under consideration.     

Effects of temperature dependent viscosity on peristaltic flow of a Jeffrey-six constant fluid in a non-uniform vertical tube

This paper deals with the influence of heat transfer and temperature dependent viscosity on peristaltic flow of a Jeffrey-six constant fluid. The two-dimensional equations of Jeffrey-six constant fluid are simplified by making the assumptions of long wave length and low Reynolds number. The arising equations are solved for temperature, velocity profile and axial pressure gradient using regular perturbation method and homotopy analysis method. The integration appeared in the pressure rise is treated numerically to find the solution. The expressions for pressure rise, temperature, pressure gradient and stream functions are sketched for various embedded parameters and interpreted. The graphical results are also presented for five different wave shapes.     

A numerical computation of the non-dimensional form of a non-linear hydrodynamic model in a uniform reservoir

A mathematical model is used to simulate the water current and the elevation in a uniform reservoir. A non-linear hydrodynamic model that provides the velocity field and elevation of the water flow is considered. In the simulating process, the Lax–Wendroff technique is used to approximate the solutions. The numerical solution can be the input data for a water-quality model that is applicable for the optimal control of water treatment in the system to achieve minimum cost.     

弹性动脉血管中血液流动特性的模拟和分析

研究了两个不同的非牛顿血液流动模型:低粘性剪切简单幂律模型和低粘性剪切及粘弹性振荡流的广义Maxwell模型．同时利用这两个非牛顿模型和牛顿模型,研究了磁场中刚性和弹性直血管中血液的正弦型脉动．在生理学条件下,大动脉中血液的弹性对其流动性态似乎并不产生影响,单纯低粘性剪切模型可以逼真地模拟这种血液流动．利用高剪切幂律模型模拟弹性血管中的正弦型脉动流,发现在同一压力梯度下,与牛顿流体相比较,幂律流体的平均流率和流率变化幅度都更小．控制方程用Crank-Niclson方法求解．弹性动脉中血液受磁场作用是产生此结果的直观原因．在主动脉生物流的模拟中,与牛顿流体模型比较,发现在匹配流率曲线上,幂律模型的平均壁面剪切应力增大,峰值壁面剪切应力减小．讨论了弹性血管横切磁场时的血液流动,评估了血管形状和表面不规则等因素的影响．     

Couple stress fluid flow with variable properties: A second law analysis

The present work examines the combined influence of variable thermal conductivity and viscosity on the irreversibility rate in couple stress fluid flow in between asymmetrically heated parallel plates. The dimensionless fluid equations are solved by using homotopy analysis method (HAM) and validated with Runge‐Kutta shooting method (RKSM). The convergent series solution is then used for the irreversibility analysis in the flow domain. The effects of thermal conductivity and viscosity variation parameters, couple stress parameter, Reynolds number, Grashof number, Hartmann number on the velocity profile, temperature distribution, entropy production, and heat irreversibility ratio are presented through graphs, and salient features of the solutions are discussed. The computations show that the entropy production rate decreases with increased magnetic field and thermal conductivity parameters, whereas it rises with increasing values of couple stress parameter, Brinkman number, viscosity variation parameter, and Grashof number. The study is relevant to lubrication theory.     

Hydrodynamic interaction in suspended sediment distribution of open channel turbulent flow

In the present study, a theoretical model is proposed to predict the vertical distribution of suspended sediment in open channel turbulent flow. We derive our mathematical model based on the six prominent hydrodynamic mechanisms, which are upward sediment flux due to the turbulent diffusion, downward gravitational settling of the sediment, hindered settling phenomenon, secondary current, fluid induced lift force on the suspended particles and the gradient of Reynolds normal stress of the suspended sediment. The importance of the hydrodynamics is described by the changes of suspended sediment concentration profile in terms of the particle-flow interaction caused by those mechanisms. We also address the significance of the co-existence of those mechanisms for estimating the suspended sediment concentration profile. The present model agrees satisfactorily with a wide spectrum of experimental data in available literature. Unlike the previous researchers, we select a broad range of previously published models of vertical sediment concentration distribution for comparison analysis, and the proposed model shows better prediction accuracy which is confirmed by error analysis.     

On determining current profiles in oscillatory flows

The time dependency of the linear three-dimensional hydrodynamic equations which describe oscillatory flow, is removed by expressing the horizontal components of current in terms of rotary components at a prescribed frequency. By this means two time independent equations (one for each rotary component) are derived, which can be readily solved using the Galerkin method, in a manner analogous to that developed by the author for steady-state wind-induced flow. The method is used to examine the influence of eddy viscosity on tidal current profiles. Two distinct flow regimes are identified. In one the water depth exceeds the thickness of the bottom stress layer, in the other, water depth is less than the thickness of this layer. The influence of these two depth regimes, and the magnitude and vertical variation of eddy viscosity on tidal current profiles is examined. The possibility of using the method to give tidal profiles from vertically integrated models is discussed.     

An augmented stress‐based mixed finite element method for the steady state Navier‐Stokes equations with nonlinear viscosity

A new stress‐based mixed variational formulation for the stationary Navier‐Stokes equations with constant density and variable viscosity depending on the magnitude of the strain tensor, is proposed and analyzed in this work. Our approach is a natural extension of a technique applied in a recent paper by some of the authors to the same boundary value problem but with a viscosity that depends nonlinearly on the gradient of velocity instead of the strain tensor. In this case, and besides remarking that the strain‐dependence for the viscosity yields a more physically relevant model, we notice that to handle this nonlinearity we now need to incorporate not only the strain itself but also the vorticity as auxiliary unknowns. Furthermore, similarly as in that previous work, and aiming to deal with a suitable space for the velocity, the variational formulation is augmented with Galerkin‐type terms arising from the constitutive and equilibrium equations, the relations defining the two additional unknowns, and the Dirichlet boundary condition. In this way, and as the resulting augmented scheme can be rewritten as a fixed‐point operator equation, the classical Schauder and Banach theorems together with monotone operators theory are applied to derive the well‐posedness of the continuous and associated discrete schemes. In particular, we show that arbitrary finite element subspaces can be utilized for the latter, and then we derive optimal a priori error estimates along with the corresponding rates of convergence. Next, a reliable and efficient residual‐based a posteriori error estimator on arbitrary polygonal and polyhedral regions is proposed. The main tools used include Raviart‐Thomas and Clément interpolation operators, inverse and discrete inequalities, and the localization technique based on triangle‐bubble and edge‐bubble functions. Finally, several numerical essays illustrating the good performance of the method, confirming the reliability and efficiency of the a posteriori error estimator, and showing the desired behavior of the adaptive algorithm, are reported. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1692–1725, 2017     

正交各向异性功能梯度材料Ⅲ型裂纹尖端动态应力场

研究了无限大正交各向异性功能梯度材料Griffith裂纹受反平面剪切冲击作用的问题.材料两个方向的剪切模量假定为成比例按特定梯度变化.通过采用积分变换-对偶积分方程方法,获得了裂纹尖端动态应力场.动态应力强度因子计算结果显示:增加剪切模量梯度或增加垂直于裂纹面方向的剪切模量可以抑制动态应力强度因子的幅值.