142 Computational Modelling in Hydraulic and Coastal Engineering
Computer code 6.1
% Example 6.1 One Dimensional Linear Long Wave Over a
Sloping Plane Bed
% ho = Water depth [m];
% ev = Eddy viscosity [m^2/s];
% ec = Coefficient for the eddy viscosity relation
[dimensionless];
% fb = Bed friction [s^(-1)];
% a = Incident wave amplitude [m];
% T = Wave period [seconds];
% Dx = Spatial step [m];
% Dt = Time step [s];
% nx = Number of computational steps;
% nt = Number of time steps;
clc; clear all; close all;
% Input data;
g=9.81;
ho=5;
fbo=0.001;
a=1;
T=8;
ec=0.4;
10
9
8
7
6
5
4
3
2
1
0 0
2 0
40
60
80
100
120
140
160
180
200
Number of spatial steps × 2 (m)
(m), (m 2
), (m 2
/s)
Bed
Time = nt*Dt (s)
Wave height (m)
Wave-breaking location
(h-rms) 2 (m 2 )
Eddy viscosity (m 2 /s)
Figure 6.2 Wave shoaling over a sloping plane seafloor.