A unified intrinsic functional expansion theory for solitary waves

A new theory is developed here for evaluating solitary waves on water, with results of high accuracy uniformly valid for waves of all heights, from the highest wave with a corner crest of 120 down to very low ones of diminishing height. Solutions are sought for the Euler model by employing a unified expansion of the logarithmic hodograph in terms of a set of intrinsic component functions analytically determined to represent all the intrinsic properties of the wave entity from the wave crest to its outskirts. The unknown coefficients in the expansion are determined by minimization of the mean-square error of the solution, with the minimization optimized so as to take as few terms as needed to attain results as high in accuracy as attainable. In this regard, Stokess formula, F2= tan , relating the wave speed (the Froude number F) and the logarithmic decrement of its wave field in the outskirt, is generalized to establish a new criterion requiring (for minimizing solution error) the functional expansion to contain a finite power series in M terms of Stokess basic term (singular in ), such that 2M is just somewhat beyond unity, i.e. 2M1. This fundamental criterion is fully validated by solutions for waves of various amplitude-to-water depth ratio =a/h, especially about 0.01, at which M=10 by the criterion. In this pursuit, the class of dwarf solitary waves, defined for waves with 0.01, is discovered as a group of problems more challenging than even the highest wave. For the highest wave, a new solution is determined here to give the maximum height hst=0.8331990, and speed Fhst=1.290890, accurate to the last significant figure, which seems to be a new record.

Theoretical solution for wave diffraction by wedge or corner with arbitrary reflection characteristics

An exact analytic solution for wave diffraction by wedge or corner with arbitrary angle (rπ) and reflection coefficients (R0 and Rr) is presented in this paper. It is expressed in two forms-series and integral representations, corresponding recurrence relation and asymptotic expressions are also derived. The solution is simplified for some special cases of rπ. For Rr= R0,r= 1/N and Rr≠R0,r = 1/2N, the solution can be reduced to linear superpositions of incident and partially reflected waves, hence a nonlinear solution of forth order for this problem can be obtained by using the author's theory of nonlinear interaction among gravity surface waves. The given solution is related to inhomogeneous Robin boundary conditions, which include the Neumann boundary conditions usually accepted in wave diffraction theory.

A Practical Speed Loss Prediction Model at Arbitrary Wave Heading for Ship Voyage Optimization

This paper proposes a semi-empirical model to predict a ship’s speed loss at arbitrary wave heading.In the model,the formulas that estimate a ship’s added resistance due to waves attacking from different heading angles have been further developed.A correction factor is proposed to consider the nonlinear effect due to large waves in power estimation.The formulas are developed and verified by model tests of 5 ships in regular waves with various heading angles.The full-scale measurements from three different types of ships,i.e.,a PCTC,a container ship,and a chemical tanker,are used to validate the proposed model for speed loss prediction in irregular waves.The effect of the improved model for speed loss prediction on a ship’s voyage optimization is also investigated.The results indicate that a ship’s voyage optimization solutions can be significantly affected by the prediction accuracy of speed loss caused by waves.

NUMERICAL ANALYSIS OF NONLINEAR WAVE FORCE ON LARGE BODY WITH ARBITRARY SHAPE

In this paper a nonlinear diffraction theory due to Stoke's 2nd-order wave for computing the wave force on the large body is presented. The radiation condition as r-∞ for 2nd-order scattered potential has been studied in connection with asymptotic solutions. A numerical procedure has been developed for the purpose of calculating the nonlinear wave force on the large body with arbitrary shape.

Scattering of steady cross-plane shear waves by surfaces of arbitrary shape in homogeneous and transversely isotropic media

Two-dimensional scalar equation for the displacement of steady cross-plane shear (SH) waves in homogeneous and transversely isotropic media like unidirectional fibrous com-posites is given. Then, thrbugh a simple coordinate system transform, the scalar equation is standardized into a Helmholtz equation. Corresponding integral equations are derived for the scattering problems and boundary element method (BEM) is used to calculate the scattered fields of arbitrarily shaped obstacles with both soft and rigid boudary conditions numerically.A discussion is given on the numerical results which is mainly focused on the influence of the a-nisotropy of the media to the directivity of the scattered fields by circular cylindrical voids.

WAVE PROPAGATION IN A TRANSVERSELY ISOTROPIC THERMOELASTIC SOLID CYLINDER OF ARBITRARY CROSS-SECTION

The wave propagation in an infinite, homogeneous, transversely isotropic solid cylin- der of arbitrary cross-section is studied using Fourier expansion collocation method, within the frame work of linearized, three-dimensional theory of thermoelasticity. Three displacement po- tential functions are introduced, to uncouple the equations of motion and the heat conduction. The frequency equations are obtained for longitudinal and flexural （symmetric and antisymmet- ric） modes of vibration and are studied numerically for elliptic and parabolic cross-sectional zinc cylinders. The computed non-dimensional wave numbers are presented in the form of dispersion curves.