Laboratory Study on the Interaction Between Regular Obliquely Incident Waves and Vertical Walls

The characteristics of wave forces are studied based on physical model tests with regular waves. The ratio of obliquely incident wave forces to normally incident wave forces on unit length of a vertical wall is related with various factors. A linear reduction of the mean force of obliquely incident waves is confirmed with an increase in the relative caisson length. Also the characteristics of reflection coefficient of diagonal waves are discussed.

The theoretical study on diagonal wave interaction with perforated-wall breakwater with rock fill

The interaction of diagonal waves with perforated-wall breakwater partially filled with rock fill is studied using the linear potential theory. By means of the matched eigenfunction expansion method, an analytical method is presented to calculate the reflection coefficient and the wave force coefficient of the breakwater. The calculated results of the reflection coefficient for limiting cases are the same to the existing results. The main effect factors of the reflection coefficient and the wave force coefficient are analyzed by numerical examples. With the increasing of thickness of rock fill, the wave force coefficient on the perforated wall generally decreases, while the reflection coefficient increases. With the increasing of the incident angle of the wave, the reflection coefficient of the breakwater first decreases, reaches its minimum, and then increases monotonously.

Quantization of the Kinetic Energy of Deterministic Chaos

In previous works, the theoretical and experimental deterministic scalar kinematic structures, the theoretical and experimental deterministic vector kinematic structures, the theoretical and experimental deterministic scalar dynamic structures, and the theoretical and experimental deterministic vector dynamic structures have been developed to compute the exact solution for deterministic chaos of the exponential pulsons and oscillons that is governed by the nonstationary three-dimensional Navier-Stokes equations. To explore properties of the kinetic energy, rectangular, diagonal, and triangular summations of a matrix of the kinetic energy and general terms of various sums have been used in the current paper to develop quantization of the kinetic energy of deterministic chaos. Nested structures of a cumulative energy pulson, an energy pulson of propagation, an internal energy oscillon, a diagonal energy oscillon, and an external energy oscillon have been established. In turn, the energy pulsons and oscillons include group pulsons of propagation, internal group oscillons, diagonal group oscillons, and external group oscillons. Sequentially, the group pulsons and oscillons contain wave pulsons of propagation, internal wave oscillons, diagonal wave oscillons, and external wave oscillons. Consecutively, the wave pulsons and oscillons are composed of elementary pulsons of propagation, internal elementary oscillons, diagonal elementary oscillons, and external elementary oscillons. Topology, periodicity, and integral properties of the exponential pulsons and oscillons have been studied using the novel method of the inhomogeneous Fourier expansions via eigenfunctions in coordinates and time. Symbolic computations of the exact expansions have been performed using the experimental and theoretical programming in Maple. Results of the symbolic computations have been justified by probe visualizations.

Stochastic Chaos of Exponential Oscillons and Pulsons

An exact three-dimensional solution for stochastic chaos of I wave groups of M random internal waves governed by the Navier-Stokes equations is developed. The Helmholtz decomposition is used to expand the Dirichlet problem for the Navier-Stokes equations into the Archimedean, Stokes, and Navier problems. The exact solution is obtained with the help of the method of decomposition in invariant structures. Differential algebra is constructed for six families of random invariant structures: random scalar kinematic structures, time-complementary random scalar kinematic structures, random vector kinematic structures, time-complementary random vector kinematic structures, random scalar dynamic structures, and random vector dynamic structures. Tedious computations are performed using the experimental and theoretical programming in Maple. The random scalar and vector kinematic structures and the time-complementary random scalar and vector kinematic structures are applied to solve the Stokes problem. The random scalar and vector dynamic structures are employed to expand scalar and vector variables of the Navier problem. Potentialization of the Navier field becomes available since vortex forces, which are expressed via the vector potentials of the Helmholtz decomposition, counterbalance each other. On the contrary, potential forces, which are described by the scalar potentials of the Helmholtz decomposition, superimpose to generate the gradient of a dynamic random pressure. Various constituents of the kinetic energy are ascribed to diverse interactions of random, three-dimensional, nonlinear, internal waves with a two-fold topology, which are termed random exponential oscillons and pulsons. Quantization of the kinetic energy of stochastic chaos is developed in terms of wave structures of random elementary oscillons, random elementary pulsons, random internal, diagonal, and external elementary oscillons, random wave pulsons, random internal, diagonal, and external wave oscillons, random group pulsons, random internal, diagonal, and external group oscillons, a random energy pulson, random internal, diagonal, and external energy oscillons, and a random cumulative energy pulson.