COMPENSATORY REVERSE FLOW OF PROGRESSIVE WAVES WITH FINITE AMPLITUDE

The various aspects of the propagation of long waves onto a shelf (i.e., reflection, transmission and propagation on the shelf) are examined experimentally and theoretically. The results are applied to tsunamis propagating onto the continental shelf. A numerical method of solving the one-dimensional Boussinesq equations for constant depth using finite element techniques is presented. The method is extended to the case of an arbitrary variation in depth (i.e., gradually to abruptly varying depth) in the direction of wave propagation. The scheme is applied to the propagation of solitary waves over a slope onto a shelf and is confirmed by experiments. A theory is developed for the generation in the laboratory of long waves of permanent form, i.e., solitary and cnoidal waves. The theory, which incorporates the nonlinear aspects of the problem, applies to wave generators which consist of a vertical plate which moves horizontally. Experiments have been conducted and the results agree well with the generation theory. In addition, these results are used to compare the shape, celerity and damping characteristics of the generated waves with the long wave theories. The solution of the linear nondispersive theory for harmonic waves of a single frequency propagating over a slope onto a shelf is extended to the case of solitary waves. Comparisons of this analysis with the nonlinear dispersive theory and experiments are presented. Comparisons of experiments with solitary and cnoidal waves with the predictions of the various theories indicate that, apart from propagation, the reflection of waves from a change in depth is a linear process except in extreme cases. However, the transmission and the propagation of both the transmitted and the reflected waves in general are nonlinear processes. Exceptions are waves with heights which are very small compared to the depth. For these waves, the entire process of propagation onto a shelf in the vicinity of the shelf is linear . Tsunamis propagating from the deep ocean onto the continental shelf probably fall in this class.

Limiting conditions for cnoidal and Stokes waves : Laitone E. V., 1962. J. Geophys. Res., 67 (4): 1555–1564

ABSTRACTResearch on the response of random wave on offshore structures has received great deal of attention of many researchers and engineers in the design of marine structures. Most previous investigations have been limited to the regular waves. In this paper, based on Longuet–Higgins random wave theory and finite element method, a numerical model for random wave-induced seabed response is established. The seabed is treated as poroelastic medium and characterized by Biot’s partly dynamic equations (u–p model). The JONSWAP spectrum is adopted in Longuet–Higgins model, which is based on the cumulative superposition of linear diffraction solution. Based on the numerical results, the effects of random wave on seabed response are investigated by comparing with the corresponding Stokes wave and cnoidal wave. Then, a parametric study is conducted to examine the effect of wave and soil characteristic on the seabed.

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean’s stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

We report a simple yet highly efficient chemical motor that can be controlled with visible light. The motor made from a noble metal and doped silicon acts as a pump, which is driven through a light-activated catalytic reaction process. We show that the actuation is based on electro-osmosis with the electric field generated by chemical reactions at the metal and silicon surfaces, whereas the contribution of diffusio-osmosis to the actuation is negligible. Surprisingly, the pump can be operated using water as fuel. This is possible because of the large ζ-potential of silicon, which makes the electro-osmotic fluid motion sizable even though the electric field generated by the reaction is weak. The electro-hydrodynamic process is greatly amplified with the addition of reactive species, such as hydrogen peroxide, which generates higher electric fields. Another remarkable finding is the tunability of silicon-based pumps. That is, it is possible to control the speed of the fluid with light. We take advantage of this property to manipulate the spatial distribution of colloidal microparticles in the liquid and to pattern colloidal microparticle structures at specific locations on a wafer surface. Silicon-based pumps hold great promise for controlled mass transport in fluids.

Wave-induced steady streaming, mass transport and net sediment transport in rough turbulent ocean bottom boundary layers

The work presents new expressions related to wave energy density and flux based on Stokes and cnoidal waves theories. It shows that as progressive waves of finite amplitude propagate a compensatory reverse flow is formed within the bottom fluid layers. The existence of such flow was experimentally confirmed. Modified mathematical models for surface waves over a non-uniform bottom and of a free plane configuration are suggested. A method of calculating the wave transformation and the currents in the surf zone is proposed. Computations made over a wide range of variations in wave parameters are presented.

We have considered the effect due to the presence of two-temperature electrons on the formation and propagation of cnoidal waves in a weak relativistic plasma. Since the cnoidal wave is equivalent to an infinite series of solitary waves, it is worthy of study for the situation where more than one solitary wave is important. The phase velocity of the modulated periodic wave is plotted as a function of the amplitude. The form of the wave for small values of ellipticity of the cnoidal wave shows up as a series of harmonics. Such cnoidal excitations are important in determining the anomalous transport coefficients of a plasma.

Hydrodynamic interactions of cnoidal waves with a vertical cylinder

A three-dimensional numerical flume is developed to study cnoidal wave interaction with multiple arranged perforated quasi-ellipse caissons. The continuity equation and the Navier-Stokes equations are used as the governing equation, and the VOF method is adopted to capture the free surface elevation. The equations are discretized on staggered cells and then solved using a finite difference method. The generation and propagation of cnoidal waves in the numerical flume are tested first. And the ability of the present model to simulate interactions between waves and structures is verified by known experimental results. Then cnoidal waves with varying incident wave height and period are generated and interact with multiple quasi-ellipse caissons with and without perforation. It is found that the perforation plays an effective role in reducing wave runup/rundown and wave forces on the caissons. The wave forces on caissons reduce with the decreasing incident wave period. The influence of the transverse distance of multiple caissons on wave forces is also investigated. A closer transverse distance between caissons can produce larger wave forces. But when relative adjacent distanceL/D(Lis the transverse distance andDis the width of the quasi-ellipse caisson) is larger than 3, the effect of adjacent distance is limited.

The definition of mass transport in gravity waves is recalled. The arbitrariness in the calculation of mass transport due to the arbitrariness of the basic assumption for nonlinear wave theories is analyzed. A review of cnoidal wave theories is presented, and the mass transport in a second order cnoidal wave theory is calculated. The mass transport is shown to have a constant value along a vertical, whereas the amplitude of particle orbit increases from bottom to surface.

In this paper, the rate equations describing the operation of intracavity-pumped Q-switched terahertz parametric oscillators based on stimulated polariton scattering are given for the first time. The rate equations are obtained under the plane-wave approximation, the oscillating fundamental and Stokes waves are supposed to be round uniform beam spots. Considering the fact that the terahertz wave nearly traverses the pump and Stokes beams and using the coupled wave equations, the terahertz wave intensity is expressed as the function of the fundamental and Stokes intensities. Thus, the rate equations describing the evolution processes of the fundamental and Stokes waves are obtained in the first step. The THz wave properties are then obtained. Several curves based on the rate equations are generated to illustrate the effects of the nonlinear coefficient, the THz wave absorption coefficient, and pulse repetition rate on the THz laser characteristics. Taking the intracavity-pumped Mg:LiNbO3 TPO as an example, the THz frequency tuning characteristic and the dependences of the fundamental, Stokes, and THz wave powers on the incident diode pump power are calculated. The theoretical results are in agreement with the experimental results on the whole.

Hydrodynamics of offshore structures with specific focus on wind energy applications

The propagation of long waves of finite amplitude in water with depth to wavelength ratios less than about one-tenth and greater than about one-fiftieth can be described by cnoidal wave theory. To date little use has been made of the theory because of the difficulties involved in practical application. This paper presents the theory necessary for predicting the transforming characteristics of long waves based on cnoidal theory. Basically the method involves calculating the power transmission for a wave train m shallow water from cnoidal theory and equating this to the deep water power transmission assuming no reflections or loss of energy as the waves move into shoaling water. The equations for wave power have been programmed for the range of cnoidal waves, and the results are plotted in non-dimensional form.

Propagating waves are observed in the olfactory or procerebral (PC) lobe of the terrestrial mollusk, Limax maximus. Wave propagation is altered by cutting through the various layers of the PC lobe both parallel and transverse to the direction of wave propagation. We present a model for the PC lobe based on two layers of coupled cells. The top layer represents the cell layer of the PC lobe, and the bottom layer corresponds to the neuropil of the PC lobe. To get wave propagation, we induce a coupling gradient so that the most apical cells receive a greater input from neighbors than the basal cells. The top layer in the model is composed of oscillators coupled locally, whereas the bottom layer is comprised of oscillators with global coupling. Odor stimulation is represented by an increase in the strength of coupling between the two layers. This model allows us to explain a number of experimental observations: 1) the intact PC lobe exhibits regular propagating waves, which travel from the apical to the basal end; 2) there is a gradient in the local frequency of slices cut transverse to the axis of wave propagation, with apical slices oscillating faster than basal slices; 3) with partial cuts through the cell layer or the neuropil layer, the apical and basal ends remain tightly coupled; 4) removal of the neuropil layer does not prevent wave propagation in the cell layer; 5) odor stimulation causes the waves to collapse and the cells in the PC lobe oscillate synchronously; and 6) by allowing a single parameter to vary in the model, we capture the reversal of waves in low chloride medium.