Characters of Surface Deformation and Surface Wave in Thermal Capillary Convection

In the field of fluid mechanics, free surface phenomena is one of the most important physical processes. In the present research work, the surface deformation and surface wave caused by temperature difference of sidewalls in a rectangular cavity have been investigated. The horizontal cross-section of the container is 52 mmx42 mm, and there is a silicon oil layer of height 3.5 mm in the experimental cavity. Temperature difference between the two side walls of the cavity is increased gradually, and the flow on the liquid layer will develop from stable convection to un-stable convection. An optical diagnostic system consisting of a modified Michelson interferometer and image processor has been developed for study of the surface deformation and surface wave of thermal capillary convection. The Fourier transformation method is used to interferometer fringe analysis. The quantitative results of surface deformation and surface wave have been calculated from a serial of the interference fringe patterns.The characters of surface deformation and surface wave have been obtained. They are related with temperature gradient and surface tension. Surface deformation is fluctuant with time, which shows the character of surface wave. The cycle period of the wave is 4.8 s, and the amplitudes are from 0 to 0.55 mu m. The phase of the wave near the cool side of the cavity is opposite and correlative to that near the hot side. The present experiment proves that the surface wave of thermal capillary convection exists on liquid free surface, and it is wrapped in surface deformation.

Study on current-random wave forces acting on a framework

The forces of random wave plus current acting on a simplified offshore platform (jacket) model have been studied numerically and experimentally. The numerical results are in good agreement with experiments. The mean force can be approximated as a function of equivalent velocity parameter and the root-mean-square force as a function of equivalent significant wave height parameter.

Dust-Cloud Structures behind a Shock Wave Moving Over a Deposited Layer of Fine Particles

The present paper investigates dispersed-phase flow structures of a dust cloud induced by a normal shock wave moving at a constant speed over a flat surface deposited with fine particles. In the shock-fitted coordinates, the general equations of dusty-gas

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.

Simulations of oil spread on a water surface

Numerical simulation of an oil slick spreading on still and wavy surfaces is described in this paper. The so-called sigma transformation is used to transform the time-varying physical domain into a fixed calculation domain for the water wave motions and, at the same time, the continuity equation is changed into an advection equation of wave elevation. This evolution equation is discretized by the forward time and central space scheme, and the momentum equations by the projection method. A damping zone is set up in front of the outlet boundary coupled with a Sommerfeld-Orlanski condition at that boundary to minimize the wave reflection. The equations for the oil slick are depth-averaged and coupled with the water motions when solving numerically. As examples, sinusoidal and solitary water waves, the oil spread on a smooth plane and on still and wavy water surfaces are calculated to examine the accuracy of simulating water waves by Navier-Stokes equations, the effect of damping zone on wave reflection and the precise structures of oil spread on waves.

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.

Variational Approach to the Lane-Emden Equation

By the semi-inverse method, a variational principle is obtained for the Lane-Emden equation, which gives much numerical convenience when applying finite element methods or Ritz method.

A Variational Approach to the Burridge-Knopoff Equation

A variational principle is obtained for the Burridge-Knopoff model for earthquake faults, and this paper considers an analytic approach that does not require linearization or perturbation.

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.