Need Help Understanding the 'oceanwave()' Function

Hello, I found this code for creation of ocean waves but i am not able to understand the function oceanwave in the code. Please do help me with this. Code:

%% wave propagation

% initialize matlab
clc;
clear all;
close all;

% time division
Td = 0.1;           % second

% total propagation time
Tp = 20;            % second

%
figure;

% maximize window to screen size
set(gcf,'units','normalized','outerposition',[0 0 1 0.7])

% loop
for t=0:Td:Tp %
    % calculate wave field
    [surfaceX,surfaceY,surfaceZ1] = function_oceanwave(5,0.5,-10,200,300,1,t);
    [surfaceX,surfaceY,surfaceZ2] = function_oceanwave(8,0.2,30,200,300,1,t);
    
    % superposition
    surfaceZ=surfaceZ1+surfaceZ2;
    %
    tic
    
    % left figure of wavefield
    s1 = subplot(1,2,1);
    surf(surfaceX,surfaceY,surfaceZ);
    axis([0 200 0 300 -1.5 1.5]);
    xlabel('west-east distance (m)');
    ylabel('south-north distance (m)');    
    shading interp;    
    colorbar
    colormap(jet)
    view(3);
    
    % right figure of wavefield
    s2 = subplot(1,2,2);
    surf(surfaceX,surfaceY,surfaceZ);
    axis([0 200 0 300 -1.5 1.5]);
    xlabel('west-east distance (m)');
    ylabel('south-north distance (m)');    
    shading interp;    
    colorbar
    colormap(jet)
    view(2)    
    axis equal;    
    toc
    
    % update plots
    drawnow;
end

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% ------ function file: function_oceanwave ----
function [surfaceX,surfaceY,surfaceZ] = function_oceanwave(period,height,direction,waterWidth,waterLength,gridSize,time)
    % acceleration of gravity
    g = 9.8; % m/s/s
    
    % wave length
    waveLength = g*period*period/(2*pi);
    
    % wave phase
    wavePhase =(2*pi/period)*time;
    
    % surface grid
    x = [0:gridSize/waveLength*2*pi:waterWidth/waveLength*2*pi];
    y = [0:gridSize/waveLength*2*pi:waterLength/waveLength*2*pi];
    [gridX,gridY] = meshgrid(x,y);
    
    % directional factors
    dirX=cos(deg2rad(direction+270));
    dirY=sin(deg2rad(direction+270));
    
    % water particle positions
    [surfaceX,surfaceY] = meshgrid(0:1:length(x)-1,0:1:length(y)-1);
    surfaceZ = (height/2)*cos(dirX*gridX +dirY*gridY - wavePhase);
end

[Dyuman Joshi]

Please format your code properly.

[Sam Chak]

@Vaishnavi P, I tried helping, but your original code is copied/pasted as a one-line code in the forum. Due to the source comes from you, we need your intervention to help us move forward.

[Vaishnavi P]

Please do check now

[Sam Chak]

@Vaishnavi P, The propagation time is reduced from 100 s to 20 s because your original code took longer than 55 seconds to run.

[Vaishnavi P]

@Sam Chak Yes My doubt is surface z is defined in function ocean wave right, I am not getting on what basis it's written

[Vaishnavi P]

@Sam Chak Hey,I just wanted to understand the physics behind surfaceZ = (height/2)*cos(dirX*gridX +dirY*gridY - wavePhase);

Thank You

Answer 1

[Sam Chak]

HI @Vaishnavi P

I regret to inform you that I am not an oceanographer. From the context, it appears that you are most likely a student specializing in the study of the physical properties and processes of the ocean, encompassing aspects such as ocean currents, tides, waves, and the circulation of water masses.

However, in your provided MATLAB code, the positions of water particles in the Z-direction of the Cartesian coordinate system are defined as follows:

surfaceZ = (height/2)*cos(dirX*gridX + dirY*gridY - wavePhase);

This expression can be mathematically interpreted as follows:

, where the phase is ,

with surfaceZ (z) represents the vertical position of water particles, height (h) is a parameter that influences the wave's amplitude, dirX () and dirY () are directional coefficients affecting the wave's orientation, gridX (x) and gridY (y) denote spatial coordinates, and lastly, wavePhase () is a phase term contributing to wave oscillation.

It is evident that the function defines a sinusoidal plane wave. While sine and cosine functions are commonly employed to describe the shape of an "idealized" ocean wave, it is important to note that the actual motion can be more precisely characterized as a "trochoid." Nevertheless, the MATLAB-generated topographical representation of the ocean wave appears to be quite impressive.

For a more comprehensive understanding of the physics underlying ocean waves, I recommend exploring the following resources:

1. Mathematics of Ocean Waves and Surfing
2. HyperPhysics - Water Waves
3. Lumen Learning - Mathematics of Waves
4. Celer Network - Mathematics of Ocean Waves

Additionally, you may find valuable insights in the book titled "Introduction to Ocean Waves" authored by Prof. Emeritus Rick Salmon. You can access this book at the following link: http://www-pord.ucsd.edu/rsalmon/111.textbook.pdf.

I hope these resources provide you with the necessary information to delve deeper into the field of oceanography and the mathematics behind ocean waves.

[Vaishnavi]

@Sam Chak Thank You for the valuable info. Also one more question regarding the same

dirX = cos(deg2rad(direction + 270));

dirY = sin(deg2rad(direction + 270));

What these equations are based on?

[Sam Chak]

You're welcome, @Vaishnavi P. If you find the resourses helpful, please consider clicking 'Accept' ✔ on the answer and voting 👍 for it. Thanks a bunch!

Returning to the directional equations, I speculate that they are related to the direction of wave propagation resulting from wind interacting with the surface water. When I conducted a keyword search on Google, it led me to the Wikipedia page on Wind Waves:

https://en.wikipedia.org/wiki/Wind_wave

Scrolling down to the section on Spectral Models, you will notice that the function describing wave elevation, denoted by the symbol zeta (ζ), exhibits similarities to your surfaceZ function. In science & engineering, the term "elevation" is frequently employed to denote the height or vertical position of a physical object or an molecular particle concerning a reference point or surface.

[Vaishnavi]

@Sam Chak Thanks you for the help