fluctuations with specified mean velocity and amplitude

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

[Image Analyst]

Not sure I understand. It looks like you ARE plotting velocity versus time, so what's the problem?

[Alina Abdikadyr]

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

Answer 1

[VBBV]

plot(t,v+V,'-*')
hold on
plot(t,V)

Do you mean the above ?

Answer 2

[Walter Roberson]

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.

[Alina Abdikadyr]

thank you! how would you plot?

[Walter Roberson]

   plot3(time, x, y)

Or you might want to use quiver

[Alina Abdikadyr]

sorry, where did you get time?

[Walter Roberson]

In your context, time is t .

However, you have

t=(1:1:N);

and that should probably instead be

t = (0:N-1) / SamplingFrequency;

for some appropriate Sampling Frequency (which might be < 1 if you are sampling less than once per second).

[Alina Abdikadyr]

sorry, the error appeared:

Error using plot3
Vectors must be the same length.

Error in untitled (line 10)
plot3(t, x, y)

[Walter Roberson]

t = (0:N) / SamplingFrequency;

for the case where you generate N points after the starting point.