This paper presents a fifth-order analytical solution for the threedimensional fully reflected short-crested waves through a perturbation technique. The present solution derived for short-crested waves can be reduced to both standing waves and progressive waves (with zero and ninety degree of incident waves). Three variables for short-crested waves, the velocity potential (A, wave frequency (w) and wave profile (7) are derived. Numerical results demonstrate the influences of the higher-order components on the kinematics properties of short-crested waves are greater especially in shallow water.
It has been discussed for a long time that standing waves, which arrives transversely to the wall, create great scouring capacity on a sedimentary bed in front of marine structures. As to be more realistic, when water waves arrive obliquely to breakwater faces, a short-crested wave system is formed in front of the breakwater. lnstead of having a transverse wave profile, the intersecting wave crests of short-crested waves forms a complex double-periodic diamond-shaped profile (Fig. 1). Previously, the two-dimensional wave systems (standing and progressive waves) have been the popular topic for researchers and little attention was available for short-crested waves due to the complex properties short-crested waves inherent. In fact the consideration of short-crested waves in the failure of marine structure should not be ignored. The state of excess pore pressure and stresses within sediments due to the short-crested waves vary from that result from the twodimensional wave systems. This is because the energy components within short-crested wave fluctuate in three directions (x-, y- and zdirections), whereas for two dimensional wave systems, the effective components are only in X- and z-directions. As reported in the literature, the theory for short-crested wave was firstly developed by Fuchs (1952) who successfully derived the solution for short-crested wave up to the second order.
