how to azimuthally average a N*N data ?

I have a 291*291 velocity data from LES . I want to azimuthally average the data so that for any angle from the origin at a particular radial distance i get the same value of velocity.

please suggest the way to do it.

Following figure shows the pictorial reperesentation of velocity data in yz plane

here is the attached file for the data

Answer 1

[Star Strider]

I seriously doubt that what you want to do is possible, simply because your data do not work that way,

Likely the best you can do is to use the scatteredInterpolant function to interpolate one value as a function of the other two.

That would go something like this —

files = dir('*.txt');

for k = 1:numel(files)
    filename = files(k).name
    A{k} = readmatrix(filename);
end

filename = 'u11.txt'

filename = 'y1.txt'

filename = 'z1.txt'

V = A{1};
X = A{2};
Y = A{3};

[Vmin,Vmax] = bounds(V,'all')

Vmin = -0.0094

Vmax = 0.3075

[Xmin,Xmax] = bounds(X,'all')

Xmin = -6.4631

Xmax = 5.5760

[Ymin,Ymax] = bounds(Y,'all')

Ymin = -6.4583

Ymax = 5.5812

[A,R,Z] = cart2pol(X, Y, V);

[Amin,Amax] = bounds(A,'all')

Amin = -3.1389

Amax = 3.1411

[Rmin,Rmax] = bounds(R,'all')

Rmin = 0.0056

Rmax = 9.1315

[Vmin,Vmax] = bounds(Z,'all')

Vmin = -0.0094

Vmax = 0.3075

Farv = scatteredInterpolant(A(:),R(:),Z(:));                    % Velocity As A Function Of Angle & Radius
Favr = scatteredInterpolant(A(:),Z(:),R(:));                    % Radius As A Function Of Angle & Velocuty
Frva = scatteredInterpolant(R(:),Z(:),A(:));                    % Angle As A Function Of Radius & Velocity

N = 10;
Aq = linspace(Amin, Amax, N).';
Rq = linspace(Rmin, Rmax, N).';
Vi = Farv(Aq, Rq);

ARV_Interpolations = table(Aq, Rq, Vi, 'VariableNames',{'Angle (radians)','Radius','Velocity'})

ARV_Interpolations = 10x3 table
    Angle (radians)     Radius       Velocity 
    _______________    _________    __________

        -3.1389        0.0056004       0.30167
        -2.4411           1.0196       0.23859
        -1.7433           2.0336       0.12867
        -1.0456           3.0476      0.072741
       -0.34777           4.0616      0.024575
           0.35           5.0755    -0.0064853
         1.0478           6.0895    -0.0058249
         1.7456           7.1035    -0.0059815
         2.4433           8.1175    -0.0057644
         3.1411           9.1315    -0.0058383

N = 10;
Aq = linspace(Amin, Amax, N).';
Vq = linspace(Vmin, Vmax, N).';
Ri = Favr(Aq, Vq);

AVR_Interpolations = table(Aq, Vq, Ri, 'VariableNames',{'Angle (radians)','Velocity','Radius'})

AVR_Interpolations = 10x3 table
    Angle (radians)     Velocity     Radius 
    _______________    __________    _______

        -3.1389        -0.0093831     9.4498
        -2.4411          0.025822     3.8114
        -1.7433          0.061027     2.6731
        -1.0456          0.096232     2.5875
       -0.34777           0.13144     2.5345
           0.35           0.16664     1.6565
         1.0478           0.20185     1.0082
         1.7456           0.23705    0.77004
         2.4433           0.27226    0.52475
         3.1411           0.30746    0.43572

N = 10;
Rq = linspace(Rmin, Rmax, N).';
Vq = linspace(Vmin, Vmax, N).';
Ai = Frva(Rq, Vq);

RVA_Interpolations = table(Rq, Vq, Ai, 'VariableNames',{'Radius','Velocity','Angle (radians)'})

RVA_Interpolations = 10x3 table
     Radius       Velocity     Angle (radians)
    _________    __________    _______________

    0.0056004    -0.0093831          -873.3   
       1.0196      0.025822         -176.62   
       2.0336      0.061027         0.53339   
       3.0476      0.096232         0.73956   
       4.0616       0.13144          2.5574   
       5.0755       0.16664        -0.52377   
       6.0895       0.20185         0.68435   
       7.1035       0.23705         0.83499   
       8.1175       0.27226       -0.071844   
       9.1315       0.30746         -2.0362   

figure
hs = surfc(X, Y, V, 'EdgeColor','interp');
colormap(turbo)
xlabel('X')
ylabel('Y')
zlabel('Velocity')
daspect([1 1 0.05])

figure
[c,hc] = contour(X, Y, V, 'ShowText',1);
colormap(turbo)
axis('equal')

This gives an example of thte interpolation approach. The various funcitons created by scatteredInterpolant will return appropriate values for any of the first two arguments that are within their limits, as calculated using the bounds calls.

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