Guohai Dong

Generalizing homotopy analysis method to solve Lotka-Volterra equation

In the paper, we generalized the homotopy analysis method to solve Lotka-Volterra equation. As a simple but typical example, it illustrates the validity and the great potential of the homotopy analysis method to solve differential difference equations. Comparisons are made between the results of the proposed method and exact solutions. The results reveal that the proposed method is valid for the Lotka-Volterra equation.

Laboratory Study of Unidirectional Focusing Waves in Intermediate Depth Water

The results of laboratory measurements of large focusing wave groups, which were generated using the New Wave theory, are presented. The influences of both the steepness and frequency bandwidth on focused wave characteristics were examined. The influence of frequency bandwidth on focused wave groups with small and moderate steepness was very small. However, for cases with the large steepness, the nonlinearity increased with increasing bandwidth frequency and widened free-wave regimes are identified for those cases with large steepness at the focal location. The underlying nonlinear phase coupling of focused waves was examined using wavelet-based bicoherence and biphase, which can detect nonlinear phase coupling in a short time series. For wave groups with large initial steepness, as wave groups approached the focal location, the values of bicoherence between primary waves and its higher harmonics progressively increased to 1 and the corresponding biphase was gradually close to zero, suggesting that an extreme wave event can be produced by considering Stokes-like nonlinearity to very high-order. Furthermore, the fast change of bicoherence of focused wave groups indicates that the nonlinear energy transfer within focusing waves is faster than that of nonfocusing wave trains.

Laboratory observations of wave evolution, modulation and blocking due to spatially varying opposing currents

The nonlinear evolution of waves propagating on a spatially varying opposing current has been observed in a wave-current flume. Regular waves with different initial periods and different initial steepness, s (0.05 < s < 0.19), were generated and observed. Frequency downshift, even with very small initial steepness, was identified. As expected, it was found that opposing currents can have significant interactions with wavetrains. The ultimate frequency downshift increases with the increase in initial steepness. The evolution of frequency modulation was observed via the instantaneous frequency extracted by the Morlet-wavelet transform. The instantaneous frequency showed that often the process of frequency downshift can be local in time and gradual, but abrupt changes of local frequency were also detected. The presence of an opposing current can gradually block the primary wave energy and destroy the conservation of the wave action at downwave locations, thus increasing the asymmetric modulation and accelerating the effective frequency downshift.

Extreme waves generated by modulational instability on adverse currents

Physical experiments focusing on the propagation of gravity waves of finite depth on adverse currents were implemented to examine their effect on the development of the modulational instability and to study the geometric characteristics of extreme waves. A series of wave trains with varying initial steepness, perturbation frequency, and initial perturbed strength were mechanically generated in a wave-current flume. The present results show that opposing currents can speed the growth of the modulational instability, verifying the previous theory qualitatively. A current-modified nonlinear Schrodinger equation can predict the measured sideband growth rates well for wave trains with lower perturbation frequencies, but overestimated those with higher perturbation frequencies. On the other hand, the limiting steepness of extreme waves measured in the presence of opposing currents was smaller than that measured in quiescent water. Additionally, current strength was found to have limited influence on the geometr...

Numerical simulation of a submerged gravity cage with the frame anchor system in irregular waves

When typhoon or extreme wave conditions occur, submergence under water may be an effective way for the net cage to avoid the attack. In this paper, a numerical method is developed to simulate the hydrodynamic behavior of net cage, which has been verified in our previous paper. Herein, by the numerical model the mooring line force and cage motion are calculated when the net cage is both in floating and submerging conditions. According to the simulated results, it can be found that the decrease of the mooring line force and cage motion is obvious when the net cage is submerged. The results of this study will give a good reference for better knowledge of dynamic behavior of submersible net cage.

Numerical simulation of the effects of weight system on the hydrodynamic behavior of 3-D net of gravity cage in current

In this article, a model of 3-D net is set up by using lumped mass method. Model test results made by Lader and Enerhaug are cited to verify the numerical model. The aim of this paper is to investigate the effects of weight system on the hydrodynamic behavior of 3-D net of gravity cage in current. Using the 3-D net model, with different styles and masses of weight system, hydrodynamic behavior of gravity cage net in current is simulated. In this article, two styles of common weight system are used, which include: (1) sinker system, (2) bottom collar-sinker system. Under each style, three different masses of weight system are adopted. The numerical results indicate that the bottom collar-sinker system is practically feasible in improving the cage net volume deformation. Results of this study will give references for better knowledge of hydrodynamic behavior of gravity cage.

Numerical study of transient harbor resonance induced by solitary waves

The main purpose of this article is to decompose the response amplitudes of different resonant modes and to further study the wave energy distributions systematically inside long and narrow rectangular harbors with different bottom slopes when harbor oscillations are induced by normal-incident solitary waves. A series of numerical experiments are carried out using the FUNWAVE 2.0 model. The analysis procedure is mainly based on the improved normal mode decomposition method. Results show that when the incident wave height is small, the resonant wave energy inside harbors is dominated by the lowest few modes, and the higher modes only possess a very small proportion of the resonant energy; when the incident wave height increases, the relative energy distribution becomes uniform, and the proportion of energy in the higher modes increases. In addition, for the same incident wave height, the change of the bottom slope inside the harbor has a negligible effect on the relative energy distribution within the ranges of the variation in bottom slopes and the incident wave heights studied in this article.

Numerical Simulation and PIV Study of Unsteady Flow Around Hollow Cube Artificial Reef with Free Water Surface

Abstract There are studies of the flow fields of artificial reefs by comprehensive 3D numerical investigations in the literature. In this paper, the flow fields within and around a hollow cube artificial reef are investigated. The complicated three-dimensional unsteady turbulent flow simulation is carried out on the basis of Navier-Stokes solver. A one-phase model is embedded with a renormalization group (RNG) k-ε turbulence model and sloved using the method of SIMPLEC algorithm. Free water surface is modeled as a wall boundary condition with zero shear force. The flow fields are solved by employing fmite volume method (FVM) simulation. In order to validate the simulated results, non-invasive particle image velocimetry (PIV) measurements are conducted to measure the flow patterns. The comparisons shows a good agreement between the numerical and experimental results concerning the scales and characteristics of the major current arising from the artificial reef. Based on the experimental verification, the effects of variation in reef height on the flow field are simulated and analyzed. Unit artificial reef effect is also calculated and analyzed. According to the numerical results, a better unit artificial reef effect is obtained when the ratio of reef height to water-depth is in the vicinity of 0.2.

Improvements on the normal mode decomposition method used in harbor resonance

In the article by Sobey (Rodney J. Sobey, 2006. Normal mode decomposition for identification of storm tide and tsunami hazard. Coastal Engineering 53, 289–301), the author proposed a normal mode decomposition method to calculate the eigenfrequencies, the eigenmodes and the response amplitudes of different resonant modes in natural harbors that are subjected to storm tides and tsunamis. However, the numerical method to address the no-flow boundary condition in that article is imprecise, which would lead to inexact eigenfrequencies and eigenmodes. In this article, the mirror-image method was proposed to improve this handling process. The accuracy of the improved normal mode decomposition method was verified using three verification tests. With a set of numerical experiments, it was determined that during the process of decomposing the response amplitudes of different resonant modes, the numerical fitting error between the simulated free surfaces and the corresponding fitted ones gradually increases with the wave nonlinearity inside the harbor. This article sought to identify the critical wave condition under which the normal mode decomposition method can accurately decompose the response amplitudes of different modes.

Numerical simulation of the oscillatory flow around two cylinders in tandem

A numerical study on oscillatory flow past two cylinders in tandem is carried out. The Reynolds-averaged Navier-Stokes equations are solved using a finite element method (FEM) with a k-ω turbulence closure. The numerical model is validated against oscillatory flows past a single circular cylinder where the experimental data are available in literature. Then the numerical model is employed to simulate the flow around cylinders in a tandem arrangement. It is found that the distance between the cylinders affects the flow characteristics. Two parallel transverse vortex streets are observed for large distances and two oblique vortex streets for moderate distances. For small distances, only one vortex street can be found. The two cylinders behave like a single bluff body when the distance between the two cylinders is small. The effect of the distance on the force coefficients are investigated in this paper.