Root mean square of velocity fluctuations

Hello,

I am trying to calculate root mean square of velocity fluctuations in a 2D plane (x,y) coordinates with (U, V) velocity values.

Total number of points I have are 4489.

What am looking for is something like this:

Image reference: Lin, L. M., & Wu, Y. X. (2018). New interpretation of specific sign of Reynolds stress in the boundary layer on a flat plate. Theoretical and Applied Mechanics Letters, 8(6), 372-377.

I have tried the rms function:

clear all; clc; %close all;


path = pwd;
R = dir(fullfile(path,'data_2.txt')); 
S = natsortfiles(R);
if iscell(S) == 0;
    S = (S);
end

for k = 1:numel(S) 
    
    folder = S(k).folder; 
    filename = S(k).name; 
    F = fullfile(S(k).folder,S(k).name); 
    data = dlmread(F); 
    x = data(:,1); % x coordinate
    y = data(:,2); % y coordinate
    U(:,k) = data(:,4); % u velocity
    V(:,k) = data(:,5); % v velocity
    M_data = mean(V);
    RMS_data = rms(V);
    VrmsC = sqrt(mean(V.^2,2))/C;                    % RMS Velocity/C
    figure
    plot(y, V)
    plot(xlim, [1 1]*M_data, 'LineWidth',1.5) plot(xlim, [1 1]*RMS_data, 'LineWidth',1.5)
    plot(VrmsC, y, 'LineWidth',1.5)
    plot (y, RMS_data)
    
end

But with no luck getting something similar to the figure above.

The data file is attached if needed.

Any thoughts how to do so?

Thank you

Answer 1

[Star Strider]

The data are gridded, and actually for surfaces.

How do you want to calculate the RMS value of a surface?

data = readmatrix('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1245882/data_2.txt')

data = 4489×6

-0.0260 -0.1080 0.1000 0.3603 -0.2634 -0.0000 -0.0260 -0.1070 0.1000 0.4157 -0.2396 -0.0000 -0.0260 -0.1060 0.1000 0.4301 -0.2578 -0.0000 -0.0260 -0.1050 0.1000 0.4183 -0.2700 -0.0000 -0.0260 -0.1040 0.1000 0.3944 -0.2723 -0.0000 -0.0260 -0.1030 0.1000 0.3726 -0.2774 -0.0000 -0.0260 -0.1020 0.1000 0.3565 -0.2884 -0.0000 -0.0260 -0.1010 0.1000 0.3432 -0.3020 -0.0000 -0.0260 -0.1000 0.1000 0.3291 -0.3149 -0.0000 -0.0260 -0.0990 0.1000 0.3124 -0.3263 -0.0000

x = data(:,1); % x coordinate
y = data(:,2); % y coordinate
U = data(:,4); % u velocity
V = data(:,5); % v velocity
[Ux,ix] = unique(x);
Uix = unique(diff(ix))

Uix = 67

[Uy,iy] = unique(y);

N = Uix;
xv = linspace(min(x), max(x), N);
yv = linspace(min(y), max(y), N);
[X,Y] = ndgrid(xv,yv);
Um = reshape(U,Uix,[]);
Vm = reshape(V,Uix,[]);

RMS_U = sqrt(mean(Um.^2))

RMS_U = 1×67

0.2156 0.2281 0.2392 0.2515 0.2668 0.2857 0.3077 0.3329 0.3597 0.3886 0.4186 0.4489 0.4796 0.5088 0.5377 0.5653 0.5913 0.6162 0.6384 0.6596 0.6788 0.6961 0.7118 0.7248 0.7357 0.7442 0.7504 0.7547 0.7572 0.7583

RMS_V = sqrt(mean(Vm.^2))

RMS_V = 1×67

0.3592 0.3714 0.3846 0.4000 0.4175 0.4363 0.4547 0.4709 0.4832 0.4900 0.4903 0.4829 0.4676 0.4446 0.4149 0.3798 0.3405 0.2987 0.2565 0.2169 0.1850 0.1687 0.1751 0.2037 0.2472 0.2988 0.3537 0.4087 0.4624 0.5114

figure
plot(RMS_U, 'DisplayName','RMS(U)')
hold on
plot(RMS_V, 'DisplayName','RMS(V)')
hold off
grid
legend('Location','best')

figure
surfc(X,Y,Um)
grid on
colormap(turbo)
xlabel('X')
ylabel('Y')
zlabel('U')

figure
surfc(X,Y,Vm)
grid on
colormap(turbo)
xlabel('X')
ylabel('Y')
zlabel('V')

This calculates the RMS values by using the square root of the square of the column mean for each surface.

Experiment to get the result you want. See the documentation on mean to take the unweighted mean across the rows instead.

.

[Hussein Kokash]

Hello Star Strider, thank you for the informative comment, I have tested it out and I was able to plot:

plot(RMS_U, yv, 'DisplayName','RMS(U)')

This is the results:

Exactly what I was looking for!

Thank you for your non-stop support, appreciate it.

[Star Strider]

As always, my pleasure!