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deepWaterWaves.m
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deepWaterWaves.m
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clear
close all
% constants
inc=0.5;
H=0.8;
g=9.81;
% variables
T=1:inc:5;
D=[4:inc:60];
% D=[4,6,8,16,21,29,31];
for j=1:length(T);
% 3 equations from Xu, D. et al. (1999)
% Xu, D. et al (1999)
lambda(j,2)=0.86*(g/(2*pi))*(T(j)^2);
% common inverse method
lambda(j,1)=(g/(2*pi))*(T(j)^2);
% Neumann-spectrum derived relationship
lambda(j,3)=(2/3)*(g/(2*pi))*(T(j)^2);
% Ursell number from mike documentation, I think
for i=1:length(D);
Us(i,j)=(H*(lambda(j,2)^2))/D(i);
end
% from Soulsby (pages 70-72) - with fine increments of T, same as
% common inverse method; coarsen the T interval, and they differ...
omega(j)=(2*pi)/T(j);
xi(j)=(omega(j)^2*D(j))/g;
if xi(j)<=1
nu(j)=xi(j)^0.5*(1+(0.2*xi(j)));
else
nu(j)=xi(j)*(1+(0.2*exp(2-(2*xi(j)))));
end
k(j)=nu(j)/D(j);
lambda(j,4)=(2*pi)/k(j);
end
threshold=ones(size(D))*25;
figure(1)
scrsz=get(0,'ScreenSize');
set(gcf,'Position',[scrsz(3)/4 scrsz(4)/4 scrsz(3)/2 scrsz(4)/2])
plot(D,Us,'-x')
hold on
plot(D,threshold,'r:')
xlabel('Depth (m)')
ylabel('Ursell number (U_{s})')
items_period=cell(size(T));
for i=1:length(T)
items_period{i}=['Period = ',num2str(T(i)),'s'];
end
% items={['Period = ',num2str(T)]};
% legend('Period 2s','Period 3s','Period 4s','Period 5s','Period 6s','Period 7s','Period 8s')
legend(items_period)
figure(2)
scrsz=get(0,'ScreenSize');
set(gcf,'Position',[scrsz(3)/4 scrsz(4)/4 scrsz(3)/2 scrsz(4)/2])
plot(T,lambda,'-x');
xlabel('Period (s)')
ylabel('Wavelength (m)')
legend('Common inverse relationshsip','Xu et al. (1999)','Neumann-spectrum derived relationship','Soulsby method')