TABLE OF CONTENTS 6.1. Applying the Dean stream function coefficients from the Dean Stream Function Tables (1974), compute the dimensionless water surface elevation ? ? and horizontal water particle velocity u ? for the following conditions and compare with the tabulated values from the Dean Stream Function Tables (1974):
| Dean ? Tables (1974) | | ? (deg) | | |
|---|---|---|---|---|
| Case 10D | 0.9 | 130 | ?0.294 | ?0.625 |
| 0.9 | 140 | |||
| 0.9 | 130 |
in which
Case 10D: 3rd Order Stream Function Wave Theory
Definitions: ? 0=( g/2 ?) T 2 is the deep-water wavelength calculated from linear wave theory, H is the wave height, g is the gravitational constant, T is the wave period, X(n) is the nth stream function coefficient, ? is the nonlinear wavelength, ? ? is the value of stream function on the free surface ?( ?).
Dimensionless stream function coefficients:
6.2. Verify that Eqs. (6.82 and 6.83) satisfy exactly the kinematic free surface boundary condition given by Eq. (6.81c).
