# fluctuations with specified mean velocity and amplitude

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Alina Abdikadyr on 26 Feb 2023
Commented: Walter Roberson on 27 Feb 2023
Hello everyone!
Could you please help me with a code. How could I plot the random fluctuation plots with specified mean velocity and amplitude of fluctiations
My code is:
clc
clear
N=100;
t=(1:1:N);
for i=1:N;
v(i)=randn(1,1);
end
V(1:N)=mean(v)
plot(t,v,'-*')
hold on
plot(t,V)
title('Reynolds Decomposition of Velocity')
xlabel('Time')
ylabel('Mean+Fluctuating Velocity v')
grid on
##### 2 CommentsShow 1 older commentHide 1 older comment
Alina Abdikadyr on 26 Feb 2023
so, if in the begining i would have as the inpute the fluctuatuins and specific amplitude, how to generate the random velocities with specified fluctuations and amplitude

VBBV on 26 Feb 2023
plot(t,v+V,'-*')
hold on
plot(t,V)
Do you mean the above ?

Walter Roberson on 26 Feb 2023
You say working with velocity, which is a vector, but you only have a single coordinate.
If you want your velocity functuations to have a specified amplitude then that means that you need to use at least two dimensions for your points, and you need to generate a vector at each location, with random angle(s) but particular amplitude. For example,
ang = rand(1,N) * 2 * pi;
amp = AppropriateConstant
deltax = sin(ang) .* amp;
deltay = cos(ang) .* amp;
x = cumsum([x0, deltax]);
y = cumsum([y0, deltay]);
If you needed a particular mean velocity then instead of using rand() you would have to use a beta distribution over 0 to 2*pi, which had been tuned so that the mean of the distribution was the desired mean.
Walter Roberson on 27 Feb 2023
t = (0:N) / SamplingFrequency;
for the case where you generate N points after the starting point.

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