Application of artificial bee colony algorithm in Rayleigh wave inversion

In order to solve the problems of multi-parameter,multi-extreme and multi-solution in the nonlinear iterative optimization process of Rayleigh wave inversion,the artificial bee colony(ABC)algorithm is selected for global nonlinear inversion.The global nonlinear inversion method does not rely on a strict initial model and does not need to calculate the derivative of the objective function.The ABC algorithm uses the local optimization behavior of each individual artificial bee to finally highlight the global optimal value in the colony,and the convergence speed is faster.While searching for the global optimal solution,an effective local search can also be performed to ensure the reliability of the inversion results.This paper uses the ABC algorithm to perform Rayleigh wave dispersion inversion on the actual seismic data to obtain a clear undergrounding of shear wave velocity profile and accurately identify the location of the high-velocity interlayer.It is verified that the ABC algorithm used in the inversion of the Rayleigh wave dispersion curve is stable and converges quickly.     

ON THE NONLINEAR WAVES IN A DEVELOPING PROCESS PART 1. THE DERIVATION OF THE GOVERNING EQUATIONS

Until now most of the nonlinear wave theories are confined to expound the nonlinear properties relative to a stationary wave train and inclusive of three dimensional instabilities, bifurcation into a new steady solution, statistical properties of random wave field and so on. Under the wind blowing over the sea the atmosphere near the sea surface will continuously transmit energy into the sea waves due to the resonant and coupling mechanisms. Wind-generated waves are essentially a developing process associated with the rate of energy     

Wave interaction with a partially reflecting vertical wall protected by a submerged porous bar

This study gives an analytical solution for wave interaction with a partially reflecting vertical wall protected by a submerged porous bar based on linear potential theory. The whole study domain is divided into multiple sub-regions in relation to the structures. The velocity potential in each sub-region is written as a series solution by the separation of variables. A partially reflecting boundary condition is used to describe the partial reflection of a vertical wall. Unknown expansion coefficients in the series solutions are determined by matching velocity potentials among different sub-regions. The analytical solution is verified by an independently developed multi-domain boundary element method(BEM) solution and experimental data. The wave run-up and wave force on the partially reflecting vertical wall are estimated and examined, which can be effectively reduced by the submerged porous bar. The horizontal space between the vertical wall and the submerged porous bar is a key factor, which affects the sheltering function of the porous bar. The wave resonance between the porous bar and the vertical wall may disappear when the vertical wall has a low reflection coefficient. The present analytical solution may be used to determine the optimum parameters of structures at a preliminary engineering design stage.     

MODELLING THE HYDRODYNAMICS OF THE BOHAI SEA IN CHINA

The effects of tides, wind and river discharges on the flow patterns in Bohai Sea are investigated. The Finite Element Method is used to cast the vertically integrated, long wave equations into a system of nonlinear ordinary equations in time. For simplicity we adopted linear triangular elements which are easily integrated exactly and lead to matrices of relatively small bandwidth. The system of ordinary differential equations is solved using a simple finite difference scheme.Because of the small contribution from three partial tides S2, K1 and O1, we take only the M2 tide into account. In this study the computations show Liaodong Bay in the north to be the locale of both the maximum flood and ebb strengths; tidal currents in Laizhou Bay in the south are of less importance in the tidal circulation of Bohai Sea. The discharges of four major rivers and wind speed of 7.0 m/s blowing from the north are used for examining the change in the M2 tidal current field. The simulations show that the influence of wi     

INTERNAL WAVE EIGENMODES AND THEIR WEAK NONLINEAR RESONANT INTERACTION IN A NONLINEARLY STRATIFIED FLUID- A PRELIMINARY THEORETICAL AND EXPERIMENTAL STUDY

A preliminary theoretical and experimental study was conducted on internal wave modes and their weak nonlinear resonant interaction in a nonlinearly stratified fluid . An asymptotical solution of the modes and a dispersion relation of internal waves in a stratified fluid with density profile similar to that in our experiment were obtained theoretically . The resonant-interaction mechanism to 2nd order approximation is also discussed . The resonant interaction of the 3rd and 4th mode internal waves excited by the unstable 1st mode wave is analyzed on the basis of data obtained by conductivity probes. The resonant-interaction condition, , is examined . It is shown that the resonant instability increases with pycnocline thickness and wave maker driving frequency .     

Water wave solutions obtained by variational method

Abstract Variational problem for irrotational, incompressible inviscid fluid in finite water depth is considered. Based on the variational principle, a special solution of the problem is presented under the assumption that the dispersion /u and the nonlinearity ?satisfied e = O(fj2) as the Lagrange function is expanded up to O(//). It is shown that the elevation of the free surface should be expanded to // order to ensure the Lagrange function is in fj* order. Comparison the nonlinear free surface profiles obtained from the solution with the corresponding ones obtained from linear solutions showed that the wave crest of the nonlinear wave is steepened but the trough is flattened compared to the linear wave as expected.     

Experimental Investigation of Wave Load and Run-up on the Composite Bucket Foundation Influenced by Regular Waves

In the design of wind turbine foundations for offshore wind farms, the wave load and run-up slamming on the supporting structure are the quantities that need to be considered. Because of a special arc transition, the interaction between the wave field and the composite bucket foundation(CBF) becomes complicated. In this study, the hydrodynamic characteristics, including wave pressure, load, upwelling, and run-up, around the arc transition of a CBF influenced by regular waves are investigated through physical tests at Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China. The distributions of the wave pressures and upwelling ratios around the CBF are described, and the relationship between the wave load and the wave parameters is discussed. New formulae based on the velocity stagnation head theory with linear wave theory and the second-order Stokes wave theory for wave kinematics are proposed to estimate the wave run-up. Moreover, the multiple regression method with nonlinear technology is employed to deduce an empirical formula for predicting run-up heights. Results show that the non-dimensional wave load increases with the increase in the values of the wave scattering parameter and relative wave height. The wave upwelling height is high in front of the CBF and has the lowest value at an angle of 135? with the incoming wave direction. The performance of the new formulae proposed in this study is compared using statistical indices to demonstrate that a good fit is obtained by the multiple regression method and the analytical model based on the velocity stagnation head theory is underdeveloped.     

Statistical distribution of nonlinear random water wave surface elevation

This study deals with the development of statistical modeling for water wave surface elevation by using a method that combines a dynamic solution with random process statistics. Ocean wave data taken from four NOAA (National Oceanic and Atmospheric Administration) buoys moored in the northeast Pacific were used to validate the model. The results indicated that the nonlinear probability density distribution of ocean wave surface elevation derived from the model described the measurements much better than Gaussian distribution and Longuet-Higgins distribution.     

Fully coupled time-domain simulation of dynamic positioning semi-submersible platform using dynamic surface control

A fully coupled 6-degree-of-freedom nonlinear dynamic model is presented to analyze the dynamic response of a semi-submersible platform which is equipped with the dynamic positioning （DP） system. In the control force design, a dynamic model of reference linear drift frequency in the horizontal plane is introduced. The dynamic surface control （DSC） is used to design a control strategy for the DP. Compared with the traditional back-stepping methods, the dynamic surface control combined with radial basis function （RBF） neural networks （NNs） can avoid differentiating intermediate variables repeatedly in every design step due to the introduction of a first order filter. Low frequency motions obtained from total motions by a low pass filter are chosen to be the inputs for the RBF NNs which are used to approximate the low frequency wave force. Considering the propellers’ wear and tear, the effect of filtering frequencies for the control force is discussed. Based on power consumptions and positioning requirements, the NN cen-ters are determined. Moreover, the RBF NNs used to approximate the total wave force are built to monitor the disturbances. With the DP assistance, the results of fully coupled dynamic response simulations are given to illustrate the effectiveness of the proposed con-trol strategy.     

Estimation and Prediction of Typhoons and Wave Overtopping in Qingdao,China

This study aims to estimate and predict the impact of climate change on typhoons and wave overtopping during typhoon progresses in Qingdao, China. The SWAN wave model is used to simulate wave elements. The scale coefficients of wave overtopping are estimated using an empirical prediction formula. A total of 75 tropical cyclones affected Qingdao from 1949 to 2019. These tropical cyclones can be grouped into eight categories according to typhoon tracks. Typhoon wind speed during Track G is projected to decrease, and those of the other seven typhoon progresses will increase by 0.35% – 0.75% in 2025, 0.69% – 1.5% in 2035, and 1.38% – 3.0% in 2055. The significant wave height and wave overtopping outside the bay are greater than those inside the bay. Among the 506 typical points selected, the maximum values of the significant wave height and wave overtopping inside the bay are mainly distributed in the range of 0 – 2 m and 0 – 60 m~3 km~(-1) s~(-1), respectively. The increments of the significant wave height and wave overtopping of Track F are most obvious. The significant wave height of Track F will increase by 50.5% in 2025, 51.8% in 2035, and 53.4% in 2055. In the 2℃ scenario, the maximum value of wave overtopping of Track F will increase by 21.9% in 2025, 24.3% in 2035, and 29.5% in 2055. In the 4℃ scenario, the maximum value of wave overtopping of Track F will increase by 21.9% in 2025, 24.3% in 2035, and 29.5% in 2055.     

Dissipative Travelling Wave Solution for EI Ni(n)o Tropic Sea-air Coupled Oscillator

El Ni(n)o and Southern Oscillation(ENSO)is an interannual phenomenon involved in the tropical Pacific sea-air interactions.An asymptotic method of solving equations for the ENSO model is proposed.Based on a class of oscillator of ENSO model and by employing a simple and valid method of the variational iteration,the coupled system for a sea-air oscillator model of interdecadal climate fluctuations is studied.Firstly,by introducing a set of functionals and computing the variationals,the Lagrange multipliers are obtained.And then,the generalized variational iteration expressions are constructed.Finally,by selecting appropriate initial iteration,and from the iterations expressions,the approximations of solution for the sea-air oscillator ENSO model are solved successively.The approximate dissipative travelling wave solution of equations for corresponding ENSO model is studied.It is proved from the results that the method of the variational iteration can be used for analyzing the sea surface temperature anomaly in the equatorial Pa-cific of the sea-air oscillator for ENSO model.     

Dissipative travelling wave solution for El Niño tropic sea-air coupled oscillator

El Niño and Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific sea-air interactions. An asymptotic method of solving equations for the ENSO model is proposed. Based on a class of oscillator of ENSO model and by employing a simple and valid method of the variational iteration, the coupled system for a sea-air oscillator model of interdecadal climate fluctuations is studied. Firstly, by introducing a set of functionals and computing the variationals, the Lagrange multipliers are obtained. And then, the generalized variational iteration expressions are constructed. Finally, by selecting appropriate initial iteration, and from the iterations expressions, the approximations of solution for the sea-air oscillator ENSO model are solved successively. The approximate dissipative travelling wave solution of equations for corresponding ENSO model is studied. It is proved from the results that the method of the variational iteration can be used for analyzing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for ENSO model.     

A new method for the estimation of oceanic mixed-layer depth using shipboard X-band radar images

Shipboard X-band radar images acquired on 24 June 2009 are used to study nonlinear internal wave characteristics in the northeastern South China Sea. The studied images show three nonlinear internal waves in a packet. A method based on the Radon Transform technique is introduced to calculate internal wave parameters such as the direction of propagation and internal wave velocity from backscatter images. Assuming that the ocean is a two-layer finite depth system, we can derive the mixed-layer depth by applying the internal wave velocity to the mixed-layer depth formula. Results show reasonably good agreement with in-situ thermistor chain and conductivity-temperature-depth data sets.     

振荡型Rossby孤立波与大气阻塞

从正压涡度方程出发,在弱非线性和弱基流切变条件下,导得了描述非线性大气长波活动的推广的Ｋｄｖ方程,并得到了方程的孤立波解及其色散关系。取近似于实际大气运动的物理参数作数值计算,得到了振荡型Ｒｏｓｂｙ孤立波的水平结构和移动特征,其结果较之寻常的Ｋｄｖ孤立波更接近于实际大气中的阻塞流型。     

Numerical analysis of the nonlinear parameterization of waves in currents over a submerged sill with a non-hydrostatic model

An investigation of the effects of a uniform current strength direction (following or opposing wave propagation) on the nonlinear transformation of irregular waves over a submerged trapezoidal sill is carried out using SWASH, a non-hydrostatic numerical wave model. The nonlinear parameters (i.e., asymmetry, skewness, and kurtosis) are calculated, and the empirical formulas for these parameters are presented as a function of the local Ursell number based on the present numerical data measured. In the shoaling area of the submerged sill, the nonlinear characteristics of waves are more obvious when waves propagate in the same direction as the currents than when waves propagate in the opposite direction. Whereas nonlinear parameters grow with the strengthening of the following currents over the crest, they tend to decrease as the adverse current velocity increases over the crest area of the submerged sill.     

EQUAITON ON SPATIAL VARIATION OF SHALLOW WATER WAVES AMPLITUDE

mODUCTIONAsknowntoall,noulinearwavesaresomofthemostinterestingsubectsinthefieldofflnid~cs.ShallowwaterwavesarenotablefortheirirnPOrtanaPPlicationsinneaxshore,riveroudiow,lOngcanal,etc.AstheeqUaionsgovwhngwaterwavesarenonhnearitisveryallctilttoobtalntheirexatanalyticalsoluhons.SO,anuInberofaSyInPtOhcmethedshaVebousedinthePa8sevenddecades(JefferyandKawahara,1982;Debna,l994)tosohenoulinearwavs.AInOngthesemeththe,BoussineSq'stheorydescribingthebalanebetweenthenoallndtyanddispersion(Mei…     

Oblique wave motion over multiple submerged porous bars near a vertical wall

This study examines oblique wave motion over multiple submerged porous bars in front of a vertical wall. Based on linear potential theory, an analytical solution for the present problem is developed using matched eigenfunction expansions. A complex dispersion relation is adopted to describe the wave elevation and energy dissipation over submerged porous bars. In the analytical solution, no limitations on the bar number, bar size, and spacing between adjacent bars are set. The convergence of the analytical solution is satisfactory, and the correctness of the analytical solution is confirmed by an independently developed multi-domain BEM (boundary element method) solution. Numerical examples are presented to examine the reflection and transmission coefficients of porous bars, C _R and C _T , respectively, for engineering applications. The calculation results show that when the sum of widths for all the porous bars is fixed, increasing the bar number can significantly improve the sheltering function of the bars. Increasing the bar height can cause more wave energy dissipation and lower C _R and C _T . The spacing between adjacent bars and the spacing between the last bar and the vertical wall are the key parameters affecting C _R and C _T . The proposed analytical method may be used to analyze the hydrodynamic performance of submerged porous bars in preliminary engineering designs.