Proceedings of the 9th International Conference
on Hydrodynamics (ICHD 2010)
October 11 – 15, 2010，Shanghai, China
Editors: Y. S. Wu, S. Q. Dai, H. Liu, L. D. Zhou, X. C. Yang 
Theoretical Hydrodynamics (21) 
A11. Energy gradient method for turbulent transition with consideration of effect of disturbance frequency
Huashu Dou, Boo Cheong Khoo.
Maritime Research Centre, Nanyang Technological University, Nanyang Avenue 639798, Singapore
Abstract :
The energy gradient theory for flow instability and turbulent transition was proposed in our previous work. It was shown that the disturbance amplitude required for turbulent transition is inversely proportional to Re, which is in agreement with the experiments. In present study, the energy gradient theory is extended to include the effect of disturbance frequency on turbulent transition. The theoretical result obtained accords well with the experimental data in literature.

A12. Capturing the process of wave to runup.
K. M. Mok , Jielin Lu, K. I. Hoi.
Department of Civil and Environmental Engineering, University of Macau Av. Padre Tomás Pereira, Taipa, Macau SAR, China
Abstract :
Four types of wave to runup transition processes were examined by using a high speed video camera capable of capturing 490 frames per second. The present investigation was set out to capture the missing details reported in previous study using only 30 frames per second recording rate. Through examining the wave to runup transition processes of different incoming waves with offshore Froude number ranging from 1.08 to 1.49, it was found that the main features of the four types of transition process were consistent to those described in [1]. The nonoverturning process of the upper part of the wave front occurring in the collapsing type was confirmed. The water indeed shot out from the bottom to initiate the runup process on the dry beach. However, observations in the present study also suggested that there could be an inbetween transition mode existing between the plunging type and collapsing type; i.e. the upper part of the wave front may overturn onto the shotout wave toe before touching the dry beach. Further research is recommended.

A13. Generation of long waves in icecovered lakes by moving disturbances of atmospheric pressure.
Izolda V. Sturova.
Lavrentyev Institute of Hydrodynamics of SB RAS Novosibirsk, Russia.
Abstract :
The effect of ice cover on the oscillations of water in a twodimensional constantdepth basin within the linear theory of long waves is considered. The ice cover is treated as thin elastic plate in the presence of compressive force. The ice is fastened hardly to a shore. The eigenfrequencies and eigenfunctions of free oscillations (seishes) are obtained. The forced oscillations of fluid and ice cover under the action of a moving disturbance of atmospheric pressure are investigated. The input data are taken to have values typical of Lake Baikal. The time dependence of total mechanical energy of the fluid is calculated for different velocities of pressure motion. The variations in icebending stresses are determined and the causes of shoreice breaking are explained.

A14. Surface and interfacial gravity waves due to a disturbance steadily moving in a twolayer inviscid fluid.
Dongqiang Lu, Shiqiang Dai.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, China.
Abstract :
The generation and interaction of surface and interfacial gravity waves due to an submerged source moving in a twolayer fluid are investigated analytically for two dimensional cases. The fluid is assumed to be inviscid and incompressible. The density of each of the two layers is constant. Two different boundary conditions are considered for the upper surface. The upper fluid of finite depth is bounded above by a rigid lid or a free surface. Based on the assumption of smallamplitude waves, a linear system is established. The integral solutions for the freesurface and interfacial elevations are obtained by means of the Fourier transform. Then the corresponding asymptotic representations are derived for farfield waves by the residue theorem. The critical Froude numbers for the existence of farfield waves are derived for the twolayer system bounded above by a rigid lid or a free surface. The effect of different upper boundary conditions on the wave generation are discussed.

A15. Coherent vortical structures and methods of their control for drag reduction of bodies.
V. V. Babenko , H. H. Chun , Inwon Lee.
Institute of Hydromechanics National Academy of Sciences of Ukraine, Ukraine.
Abstract :
Now the increasing attention is given researches to effective methods of drag reduction. It is revealed, that, in particular, in a boundary layer all power exchanges are caused by features of separate kinds of coherent vortical structures. The analysis is carried out and ordering of the basic types of the coherent vortical structures arising at movement of bodies in real conditions is executed. Classification of coherent vortical structures and methods of their control in a boundary layer are developed depending on their intensity. The method of susceptibility is developed by a boundary layer of various disturbances. Some kinds of the combined method of drag reduction are resulted. The executed researches of physical features of resistance of friction control are checked up at an experimental research of integrated characteristics on various models axis symmetric bodies.

A21. On stability of MHD flows located on the surface of axisymmetric torus.
Boris A. Lugovtsov, Maria S. Kotelnikova.
Lavrentyev Institute of Hydrodynamics, Novosibirsk State University, Novosibirsk, Russia.
Abstract :
We consider the problem of the evolution of azimuthal perturbations (spontaneous swirling) in axisymmetric magnetohydrodynamic flows of an ideally conducting fluid with circular streamlines. The fluid is in a toroidal gap between two surfaces with constant values of the stream function. The equations of fluid motion are derived in the approximation of narrow gap. The parameters at which spontaneous swirling is possible are determined numerically, and the properties of secondary swirling flows resulting from instability of the initial steadystate poloidal flow are established. It is shown that for certain parameters of the initial poloidal flow, the energy of the initial flow is almost completely converted to the energy of the azimuthal (rotational) velocity field and magnetic field that arise. In this case, over a wide range of parameters of the initial flow, the timeaveraged energies of the rotational motion and magnetic field take identical values for large t. We note that even for a small degree of magnetization, instability can give rise to a considerable magnetic field, which can be treated as the spontaneous occurrence of a magnetic field due to extension of the force lines of the initial weak poloidal magnetic field. The numerical studies of spontaneous swirling revealed some properties of the secondary flow, which is irregular (chaotic) in time and its spatial structure is rather complex with the presence of differential rotation, which is a consequence of the conservation laws for the angular momentum and azimuthal magnetic flux.

A22. A new perturbation solution of groundwater table fluctuations in tidal beaches.
Yuqiang Xia, Hailong Li, Michel C Boufadel.
School of Environmental Studies & (MOE) Biogeology and Environmental Geology Lab, China University of Geosciences, Wuhan, China.
Abstract :
This paper modeled tideinduced groundwater flow in a vertical beach with a thin submarine outletcapping. By implementing a perturbation method based on the Boussinesq’s equation, a new approximate solution was derived for the model. Then the solution was compared with previous analytical solutions derived from the linearized Boussinesq’s equation. The results showed that the error between the present and previoussolutions increases with the value of the ratio of tidal amplitude to the aquifer’s depth below the mean sea level and the leakage of the submarine outletcapping.

A23. Bifurcation behavior of laminar flows of a boundary layer problem.
Chunqing Lu.
Department of Mathematics and Statistics, Southern Illinois University Edwardsville Edwardsville, IL 62026, USA
Abstract :
This paper presents a theoretical analysis on the bifurcation behavior of solutions to a nonlinear equation f '''f '' = 0 with boundary conditions: f(0) = C f ' (0)= ξand f '(∞) = 1 where ξ and C are parameters. It shows that if ξ ≥ 0 including the case ξ≥1, then for any C the boundary value problem has at most one solution. However, for any ξ < 0, there exist some C < 0 such that the boundary value problem admits at least two solutions.
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A24. On transmission of pressure across thermocline to ocean bottom.
Jiachun Le.
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University，Shanghai, China.
Abstract :
A direct route for pressure transmission from free surface to ocean bottom is discussed. The ocean is of infinite horizontal extent, the vertical sound profile is composed of three layers: in the upper (mixing) layer the sound velocity is constant, in the intermediate (thermocline) layer the sound velocity decreases exponentially with the depth, and in the lower layer the sound velocity increases linearly with the depth. Equations with easily found closed form solutions are obtained, and the pressure at the bottom depends upon the sound profile rather than the depth, therefore the effect of free surface may not die out.

A25. Flexuralgravity waves due to unsteady motion of point source under a floating plate in fluid of finite depth.
Alexandra V. Pogorelova, Victor M. Kozin.
Institute of Machining and Metallurgy Far Eastern Branch of the Russian Academy of Sciences，Komsomol’skonAmur, Russia.
Abstract :
The paper deals with the theoretical investigation of the straight unsteady motion of a point source submerged into the liquid of finite depth below the floating ice plate. The formulae describing the plate deflection and obtained with the help of integral and asymptotic methods are numerically analyzed with respect to velocity and submergence depth of point source, basin depth, ice plate thickness and Young’s modulus.

A31. Interaction of a submerged elliptic plate with waves.
Weiguang Bao, Kazuki Fujihashi,Takeshi Kinoshita.
Institute of Industrial Science, University of Tokyo,Tokyo, Japan.
Abstract :
With potential applications as a breakwater, an elliptic plate horizontally submerged in waves is investigated within the scope of linear wave theory. An elliptical coordinate system is adopted, which has anadvantage to represent the solution in an analytical form, i.e. an expansion of eigen functions. By means of separation of variables, it turns out that the eigen functions in the elliptical coordinates consist of the Mathieu functions and the modified Mathieu functions. The interaction of the elliptic plate with the waves is studied. The wave loads, as well as the scattered wave field, are evaluated.

A32. Modeling of fully nonlinear waveevolution over a submerged bar.
Binzhen Zhou, Bin Teng, Lifen Chen, DeZhi Ning.
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology,
Dalian , China
Abstract :
A threedimensional fully nonlinear numerical wave tank (NWT) is developed by using a timedomain higher order boundary element method (HOBEM). The source generation of waves is adopted to generate input waves. The mixed EulerianLagrangian (MEL) method is utilized to track and refresh the free surface. The model is applied to three examples of wave evolution and harmonic decomposition during propogation over a submerged bar and numerical results are compared with the experimental data and the solutions of Boussinesq model. It shows that the present model agrees better with the measurements than the Boussinesq model and more adaptable for stronger nonlinear waves.

A33. Wave interaction with a floating rectangular box near a vertical wall with step type bottom topography.
Joydip Bhattacharjee, C. Guedes Soares.
Centre for Marine Technology and Engineering (CENTEC), Technical University of Lisbon Instituto Superior Técnico, Av. Rovisco Pais, 1, 1049001 Lisboa, Portugal.
Abstract :
Diffraction of water waves by a floating structure near a wall with step type bottom topography is investigated under the twodimensional small amplitude wave theory. Full solution of the problem under the potential flow approach is obtained by using the matched eigenfunction expansion method. The waveinduced forces on the structure and on the wall are studied for different water depth ratios, dimension of the structure and the distance of the wall from the structure.

A34. Study of wave induced radiation stress and vertical mixing in the Yellow River runoff diffusion.
Bingchen Liang, Huajun Li, Jing Zhang.
College of Engineering, Ocean University of China，Qingdao, China.
Abstract :
The purpose of this paper is to study the role of wave induced radiation stress and vertical mixing in the Yellow river runoff diffusion in vertical profile. Firstly, only using a hydrodynamical model to simulate river runoff at yellow river estuary area, and then using a coupled model also to simulate yellow river runoff by introducing vertically varied radiation stress or wave induced vertical mixing. Under condition of only tide existing, river runoff diffused far away from coastal near water surface. When considering vertically varied wave radiation stress, the velocity increased and river runoff flowed near estuary not go into the sea. When considering wave induced vertical mixing, the surface velocity decreased and the value of velocity became to be uniformed. So the function of radiation stress and verticalmixing induced by wave is different.

A35. A shape identification problem in estimating the unknown interfacial surface for a multiple region domain.
Chenghung Huang , Hsimei Chen , Chiaying Liu.
Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University Tainan, China.
Abstract :
A thermal tomography problem, i.e. the shape identification problem or inverse geometry problem, in estimating the interfacial geometry for a threedimensional multiple region domains is examined in this study based on the Conjugate Gradient Method (CGM). The accuracy of this thermal tomography analysis is examined using the simulated temperatures measured by an imaginary infrared scanner. Different temperature measurement positions and errors are considered in the numerical experiments to justify the validity of the present algorithm in solving the threedimensional thermal tomography problem. Finally it is concluded that the reliable interfacial configurations can be estimated by the CGM.

A41. Lifting of a large object from a rigid porous seabed.
Hsuehmei Huang, Mengyu Lin, Lianghsiung Huang.
Department of Civil Engineering, National Taiwan University, Taipei, China.
Abstract :
This study investigates the flow field induced by the tilting lift of a large object from a rigid porous seabed and the induced force acting on the object using an analytical approach. In the corners between the object and the seabed, we assume the flow is a corner flow with a low Reynolds number, and the porous media flow in the seabed obeys Brinkman equations. The complete boundary conditions for viscous flow, including the continuity of velocities and stresses, are utilized at the seabedwater interface. The Helmholtz decomposition theorem, which decomposes the flow field into irrotational and rotational parts, and a perturbation expansion are employed to solve the boundaryvalue problem. Leadingorder analytical solutions for the flow in the water and in the porous seabed are presented, indicating that the flow inside the corners is not a parallel flow, and the porous media flow inside the seabed is a Stokes boundary layer flow that does not obey Darcy’s law

A42. Large transient waves generated through modulational instability in deep water.
Wenson Chiang, Hwenghwung Hwung.
Tainan Hydraulics Laboratory, NCKU, Tainan, China
Abstract :
The longterm evolution of nonlinear wave train in deep water with varied initial wave steepness is investigated experimentally in a super waveflume (300 m long, 5 m wide, 5.2 m deep). The initial wave train is the combination of one carrier wave and a pair of imposed sideband components. Increasing modulation of wave train is observed due to sideband instability until a critical value which either initiates wave breaking or reaches the maximum modulation. The observed maximum local wave steepness increases rapidly with the increase of the initial wave steepness, and levels off at initial wave steepness roughly equal to 0.15 despites that the data exhibits a little scattering. The normalized crest elevation at peak modulation increases rapidly with initial wave steepness and approached a maximum value almost equal to 3.5 which corresponds to initial wave steepness around kc ac = 0.15. The results reveal that the large transient wave such as freak wave could be generated during the propagation of nonlinear wave trains in deep water through sideband instability.

A43 Deepwater Engineering, DalianUniversity of Technology, Dalian,China.
Abstract :
Numerical simulation results of fluid oscillation in narrow gaps subjected to incident water waves are presented in this paper. Both viscous fluid model and potential flow model with artificial viscous damping are employed to investigate wave motions in a single narrow gap separated by twin bodies and double narrow gaps formed by three identical bodies. Variation of wave heights in the narrow gaps with incident wave frequency is compared with experimental data available in literatures. The numerical results demonstrate that both the viscous fluid model and the potential flow model are able to predict the resonant frequency reasonably well. However the conventional potential flow model (without introducing the artificial viscous damping) significantly overpredicts the wave height in narrow gaps around the resonant frequency. The potential flow model with artificial damping predicts resonant wave heights well with a properly tuned (or calibrated) damping coefficient. The horizontal wave force on the individual body is also examined in this work. It is found that a properly calibrated damping coefficient is also very important for estimating the horizontal wave forces onthe structures. A damping coefficient of 0.4 in the potential flow model is found to result in satisfactory predictions of wave heights in the narrow gaps and the horizontal hydrodynamic force for the cases considered in this work..

A44. An integrated model of waveseabedstructure interactions.
Jisheng Zhang, Bo Wang, Dongsheng Jeng, Philip L. –F. Liu , Ping Dong.
Division of Civil Engineering, University of Dundee, Dundee DD1 4HN, UK.
Abstract :
The phenomenon of waveseabedstructure interactions have occurred in the marine environment with a coastal permeable (or partially permeable) structure, which has attracted great attention from coastal engineers involved in the design of marine structures. In this study, a porous seabed model based on Biot’s consolidation equation and poreelastic theory is integrated into the COBRAS wavestructure model. This integrated model is verified by the laboratory experiments. Some dominant factors affecting the wave motion and its induced seabed response are examined by using this model, including wave parameters and structure properties.

A45. Studies on the oscillation behavior of a flexible plate in the wake of a Dcylinder.
Dingyi Pan, Hua Liu, Xueming Shao.
Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, China
Abstract :
This paper studies the oscillation behavior of a flexible plate in the wake of a Dsection cylinder. The interaction between the flexible body and its surrounding vortices is investigated. A modified immersed boundary method is used to solve the motion of fluid, integrated with a linearized EulerBernoulli beam model to govern the motion of the flexible plate. Results show that, when the distance between cylinder and plate is small, the surface of the plate is surrounded by vortices layers and the plate oscillates periodically, with amplitude similar to the cylinder movement. However, if the distance becomes large, we find that the vortices are shed from the Dcylinder in front of the plate, and the incoming vortices make the plate oscillate with large amplitude at the beginning and then slant laterally. Also, the amplitude becomes smaller compared to the case of the small distance.

A46. Lagrangian transport by peristalsis in a closed cavity.
Chiuon Ng, Ye Ma.
Department of Mechanical Engineering, The University of Hong Kong，Pokfulam Road, Hong Kong, China
Abstract :
In the context of fluid mixing in microelectromechanical systems, Lagrangian mass transport induced by peristaltic waves traveling on the boundaries of a twodimensional rectangular closed channel is studied analytically. Based on the Lagrangian description, an asymptotic analysis is performed to generate explicit expressions for the leadingorder oscillatory as well as the higherorder timemean mass transport velocities as functions of the wave properties. For small steadystreaming Reynolds number, we have revisited the problem studied previously in the literature, but with all the results fully presented in the Lagrangian sense.
