Damping of Vertically Excited Surface Wave in Weakly Viscous Fluid

In a vertically oscillating circular cylindrical container, singular perturbation theory of two-time scale expansions is developed in weakly viscous fluids to investigate the motion of single free surface standing wave by linearizing the Navier-Stokes equation. The fluid field is divided into an outer potential flow region and an inner boundary layer region. The solutions of both two regions are obtained and a linear amplitude equation incorporating damping term and external excitation is derived. The condition to appear stable surface wave is obtained and the critical curve is determined. In addition, an analytical expression of damping coefficient is determined. Finally, the dispersion relation, which has been derived from the inviscid fluid approximation, is modified by adding linear damping. It is found that the modified results are reasonably closer to experimental results than former theory. Result shows that when forcing frequency is low, the viscosity of the fluid is prominent for the mode selection. However, when forcing frequency is high, the surface tension of the fluid is prominent.

Non-Linear Wave-Induced Transient Response of Soil Around a Trenched Pipeline

Submarine pipelines are always trenched within a seabed for reducing wave loads and thereby enhancing their stability. Based on Biot’s poroelastic theory, a two-dimensional finite element model is developed to investigate non-linear wave-induced responses of soil around a trenched pipeline, which is verified with the flume test results by Sudhan et al. [Sudhan, C.M., Sundar, V., Rao, S.N., 2002. Wave induced forces around buried pipeline. Ocean Engineering, 29, 533–544] and Turcotte et al. [Turcotte, B.R., Liu, P.L.F., Kulhawy, F.H., 1984. Laboratory evaluation of wave tank parameters for wave-sediment interaction. Joseph H. Defree Hydraulic Laboratory Report 84-1, School of Civil and Environmental Engineering, Cornell University]. Non-linear wave-induced transient pore pressure around pipeline at various phases of wave loading is examined firstly. Unlike most previous investigations, in which only a single sediment layer and linear wave loading were concerned, in this study, the influences of the non-linearity of wave loading, the physical properties of backfill materials and the geometry profile of trenches on the excess pore pressures within the soil around pipeline, respectively, were explored, taking into account the in situ conditions of buried pipeline in the shallow ocean zones. Based on the parametric study, it is concluded that the shear modulus and permeability of backfill soils significantly affect the wave-induced excess pore pressures around trenched pipeline, and that the effect of wave non-linearity becomes more pronounced and comparable with that of trench depth, especially at high wave steepness in shallow water.

Wave Dynamic Processes in Cellular Detonation Reflection from Wedges

When the cell width of the incident detonation wave (IDW) is comparable to or larger than the Mach stem height, self-similarity will fail during IDW reflection from a wedge surface. In this paper, the detonation reflection from wedges is investigated for the wave dynamic processes occurring in the wave front, including transverse shock motion and detonation cell variations behind the Mach stem. A detailed reaction model is implemented to simulate two-dimensional cellular detonations in stoichiometric mixtures of H (2)/O (2) diluted by Argon. The numerical results show that the transverse waves, which cross the triple point trajectory of Mach reflection, travel along the Mach stem and reflect back from the wedge surface, control the size of the cells in the region swept by the Mach stem. It is the energy carried by these transverse waves that sustains the triple-wave-collision with a higher frequency within the over-driven Mach stem. In some cases, local wave dynamic processes and wave structures play a dominant role in determining the pattern of cellular record, leading to the fact that the cellular patterns after the Mach stem exhibit some peculiar modes.

Diffusive Wave Solutions for Open Channel Flows with Uniform and Concentrated Lateral Inflow

The diffusive wave equation with inhomogeneous terms representing hydraulics with uniform or concentrated lateral inflow intoa river is theoretically investigated in the current paper. All the solutions have been systematically expressed in a unified form interms of response function or so called K-function. The integration of K-function obtained by using Laplace transform becomesS-function, which is examined in detail to improve the understanding of flood routing characters. The backwater effects usuallyresulting in the discharge reductions and water surface elevations upstream due to both the downstream boundary and lateral infloware analyzed. With a pulse discharge in upstream boundary inflow, downstream boundary outflow and lateral inflow respectively,hydrographs of a channel are routed by using the S-functions. Moreover, the comparisons of hydrographs in infinite, semi-infiniteand finite channels are pursued to exhibit the different backwater effects due to a concentrated lateral inflow for various channeltypes.

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress,intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.

Propagation Properties of Electromagnetic Wave in a Plasma Slab

In this paper, the calculated results about the propagation properties of electromagnetic wave in a plasma slab are described. The relationship of the propagation properties with frequencies of electromagnetic wave, and parameters of plasma (electron temperature, electron density, dimensionless collision frequency and the size of the plasma slab) is analyzed.

Hydrothermal Wave in a Shallow Liquid Layer

The oscillatory thermocapillary convection and hydrothermal wave in a shallow liquid layer, where a temperature difference is applied between two parallel sidewalls, have been numerically investigated in a two-dimensional model. The oscillatory thermocapillary convection and hydrothermal wave appear if the Marangoni number is larger than a critical value. The critical phase speed and critical wave number of the hydrothermal wave agree with the ones given analytically by Smith and Davis in the microgravity environment, and it travels in the direction opposed to the surface flow. Another wave traveled downstream in addition to the hydrothermal wave traveled upstream was observed in the case of earth gravity condition.

A New Version of Smoothed Point Method to Simulate Linear Elastic Wave Propagation

By using the kernel function of the smoothed particle hydrodynamics (SPH) and modification of statistical volumes of the boundary points and their kernel functions, a new version of smoothed point method is established for simulating elastic waves in solid. With the simplicity of SPH kept, the method is easy to handle stress boundary conditions, especially for the transmitting boundary condition. A result improving by de-convolution is also proposed to achieve high accuracy under a relatively large smooth length. A numerical example is given and compared favorably with the analytical solution.

The Optical Methods on Measuring Surface Deformation and Surface Wave in The Thermal Capillary Convection

An optical diagnostic system consisting of the Michelson interferometer with the image processor has been developed for the study of the kinetics of the thermal capillary convection. The capillary convection, surface deformation, surface wave and the velocity field in a rectangular cavity with different temperature's sidewalls have been investigated by optical interference method and PIV technique. In order to calculate the surface deformation from the interference fringe, Fourier transformation is used to grating analysis. The quantitative results of the surface deformation and surface wave have been calculated from the interference fringe pattern.

Shock wave diffraction and reflection around a dusty square cavity

The diffraction and reflection of planar shock wave around a dusty square cavity is investigated numerically, which is embedded in the net bottom surface of a two-dimensional channel, and the induced gas-particle two-phase now. The wave patterns at different times are obtained for three different values of the particle diameter. The computational results show that the existence of particles affects appreciably the shock wave diffraction and cavity flow.

Variation of drag coefficient with wind wave development

Turbulent air flows over developing wind waves in the air-sea boundary layer are numerically simulated without considering wave breaking. Influences of wind waves on air flows are considered using a model of significant wave and surface roughness, with a formula proposed for calculating the surface roughness, k - epsilon model is adopted to simulate turbulent flows. The results of the drag coefficient and turbulence characteristics agree well with the observations.

Numerical Investigation of Toroidal Shock Wave Focusing in a Cylindrical Chamber

In this paper, focusing of a toroidal shock wave propagating from an annular shock tube into a cylindrical chamber was investigated numerically with the dispersion controlled dissipation (DCD) scheme. The first case for an incident Mach number of 1.5 was conducted and compared with experiments for validation. Then, several cases were calculated for higher incident Mach numbers varying from 2.0 to 5.0, and complicated flow structures were observed. The numerical study was mainly focused on two aspects: focusing process and flow structures. The process, including diffraction, focusing, and reflection, is displayed to reveal the focusing mechanism, and the flow structures at different incident. Mach numbers are used to demonstrate shock reflection styles and focusing characteristics.

Improved Analysis Method for Wave-Induced Pipeline Stability on Sandy Seabed

The existing Det Norske Veritas DNV Recommended Practice RP E305 for pipeline on-bottom stability is mainly based on the pipe–soil interaction model reported by Wagner et al. in 1987, and the wake model reported by Lambrakos et al. in 1987, to calculate the soil resistance and the hydrodynamic forces upon pipeline, respectively. Unlike the methods in the DNV Practice, in this paper, an improved analysis method is proposed for the on-bottom stability of a submarine pipeline, which is based on the relationships between Um/ gD 0.5 and Ws / D2 for various restraint conditions obtained by the hydrodynamic loading experiments, taking into account the coupling effects between wave, pipeline, and sandy seabed. The analysis procedure is illustrated with a detailed flow chart. A comparison is made between the submerged weights of pipeline predicted with the DNV Practice and those with the new method. The proposed analysis method may provide a helpful tool for the engineering practice of pipeline on-bottom stability design.

Heating characteristics of blunt swept fin-induced shock wave turbulent boundary layer interaction

An experimental study was conducted on shock wave turbulent boundary layer interactions caused by a blunt swept fin-plate configuration at Mach numbers of 5.0, 7.8, 9.9 for a Reynolds number range of (1.0.similar to 4.7) x 10(7)/m. Detailed heat transfer and pressure distributions were measured at fin deflection angles of up to 30 degrees for a sweepback angle of 67.6 degrees. Surface oil flow patterns and liquid crystal thermograms as well as schlieren pictures of fin shock shape were taken. The study shows that the flow was separated at deflection of 10 degrees and secondary separation were detected at deflection of theta greater than or equal to 20 degrees. The heat transfer and pressure distributions on flat plate showed an extensive plateau region followed by a distinct dip and local peak close to the fin foot. Measurements of the plateau pressure and heat transfer were in good agreement with existing prediction methods, but pressure and heating peak measurements at M greater than or equal to 6 were significantly lower than predicted by the simple prediction techniques at lower Mach numbers.

Two-Dimensional Kinematic Wave Model of Overland-Flow

A two-dimensional kinematic wave model was developed for simulating runoff generation and flow concentration on an experimental infiltrating hillslope receiving artificial rainfall. Experimental observations on runoff generation and flow concentration on irregular hillslopes showed that the topography of the slope surface controlled the direction and flow lines of overland flow. The model-simulated results satisfactorily compared with experimental observations. The erosive ability of the concentrated flow was found to mainly depend on the ratio of the width and depth of confluent grooves.