Phase shifting graphs and limit range of x-axis

Hi there, I'm currently making my dissitation on free-stream velocity fluctuation in tides. Spring tides (highest velocity) occur twice in a lunar cycle and neap tides (lowest velocity) occur also twice in a lunar cycle. Lunar cycles occur every 29.53 approximately with Spring tides and neap tides a quarter of a cycle apart. I'm trying to simulate the the fluctuation, however I've come across a couple of problems. There is phase shift which I haven't included because shifting the initial graph would also mean changing the initial amplitude. I've tried doing It this way but I just get further problems later on. I've also chosen to further the range by adding an additional quarter forward of time and before x = 0 in case of phase shift. What I want to do is first of all eliminate the problem of the reflected wave before x=0 and the wave after x=0 not being joined together, secondly shift the wave by E(k)/24, and thirdly limit the x-axis between 0 and 29.53 so that the wave can only be seen between 0 and 29.53. I've attached the Excel file that's imported.

[data, titles, r]=xlsread('Tidal Sites.xlsx');
A=data(:,4); %Amplitude
B=data(:,10); %Exponential decrease
C=data(:,11); %Frequency 
E=data(:,6); %Number of hours difference spring tide is relative to dover
F=titles(:,2); %Site name
for k=1:length(E)
    if ~isnan(E(k))
        x1=linspace(0, 7.3826475, 10000); 
        y1=det(A(k))*((exp(1).^(det(-B(k)).*x1))).*cos((det(C(k)).*x1));
        figure, plot(x1,y1), hold on
        x2 = x1(end) + cumsum(fliplr(diff(x1))); 
        y2 = fliplr(y1(1:end-1)); %Reflection after the first quarter of lunar cycle
        x3 = x2(end) + cumsum(fliplr(diff(x2)));
        y3 = fliplr(y2(1:end-1)); 
        x4 = x3(end) + cumsum(fliplr(diff(x3)));
        y4 = fliplr(y3(1:end-1)); %2 more reflections to give lunar cycle
        x5 = x4(end) + cumsum(fliplr(diff(x4)));
        y5 = fliplr(y4(1:end-1)); % an additional quarter of cycle to make up for phase difference FORWARD
        x6 = 0 - cumsum(fliplr(diff(x1)));
        y6 = y1(1:end-1); %an additional quarter of cycle to make up for phase difference BEHIND
        x = horzcat(x1, x2, x3, x4, NaN, x5, NaN, x6);
        y = horzcat(y1, y2, y3, y4, NaN, y5, NaN, y6);
        plot(x, y), hold on
        title(F(k+1))
        xlabel('Time (days)')
        ylabel('Free-stream velocity (m/s)')%Problem arises at x = 0 where the reflected curve lines don't join
    end
end

Answer 1

[Geoff Hayes]

M - you mention the problem of the reflected wave before x=0 and the wave after x=0 not being joined together. If I iterate through the above code, the x6 is an array of negative elements in decreasing order from -0.12 to -7.5. Why have you appended this to the end of x and not to the beginning like

 x = horzcat(flip(x6), x1, x2, x3, x4, NaN, x5, NaN);
 y = horzcat(flip(y6), y1, y2, y3, y4, NaN, y5, NaN);

That will "bridge the gap" around x=0.

As for shifting the wave by E(k)/24, what do you mean by that? Your code does

 x6 = E(1)/24 - cumsum(fliplr(diff(x1)));

for every k, so that seems not to be correct. And you are only applying the above to x1. Why not x2, x3, etc.?

And, to limit the x-axis to a fixed interval, just use xlim as

 xlim([0 29.53]);

Though by doing this, you will no longer observe the problem of the wave not being joined together around 0.

I think that you may want to revisit your application of the "shift" and the values in E.

[Ellis]

Hi Geoff, thanks for responding, I need to shift the entire wave by E(k)/24, that was a typo from what I attempted previously, I've updated the x6 function now.

[Ellis]

how would I go about shifting?

[Geoff Hayes]

Wouldn't you just add E(k)/24 to your x that has been created without the x6?

[Ellis]

I tried that but the last 4 graphs show 2 graphs for values of x < 0.

[Geoff Hayes]

Probably because E(k)/24 is less than zero. What does this value represent? Does it make sense if it is negative?

[Ellis]

Hi Geoff, i sorted that problem out. i only put the phase on one of the plot functions. That was the first part. If you look at the second one the graphs actually differ significantly. I'm asking for something else now :)