Calculating the circulation given specific parameters

I am trying to calculate the circulation using the following code. Although the code works, the calculated data doesn't make sense as I get a linear plot. I would also like to create a image plot, if possible. Any help would be greatful!

close all;
clear all;
clc;

h = 200; % height of stack in meters
z = (0:10); % average wind in the vertical
mr = 2.5; % mean mixing ratio
sigmaz = z*mr; %vertical mixing 
dt = (24:72)*60*60; %change in time

for i = 1:length(z)
    for j = 1:length(dt)
        
        c = exp(-(z+h).^2.)/((2*sigmaz.^2))./dt;
        
    end
end

plot((1:numel(dt)),(1:numel(c)))

[Torsten]

What's the definition of "circulation" in this context ?

And your plot command

plot((1:numel(dt)),(1:numel(c)))

means that you plot (1:49) against (1:49) without using the values calculated for c. This doesn't make sense.

[madhan ravi]

are you sure of the c formula? exp(- larger number) is closer to zero

[Jonathon Klepatzki]

You were correct, I made an error.

However, perhaps you can help me. I changed the equation to include either:

C = (2./pi).^1/2.*(Q./sigmaz.*meanu.*W.*dt) or C = Q./meanu.*h.*W.*sigmaz.*dt

and the surf plot provided by Matt J doesn't work. Any ideas?

[Jonathon Klepatzki]

Never mind, I figured out what I did wrong.

Answer 1

[Matt J]

Perhaps this is what you meant. The expression for c looks like it's supposed to be Gaussian, and the double for-loop suggests this is supposed to be a surface plot.

h = 200; % height of stack in meters
z = (0:10); % average wind in the vertical
mr = 2.5; % mean mixing ratio
sigmaz = z*mr; %vertical mixing 
dt = (24:72)'*60*60; %change in time

c = exp(   -0.5 * ( (z+h)./sigmaz).^2 )./dt;

surf(z,dt,c)

[madhan ravi]

+1 like always, awesome interpration and like the way you used vector expansion without the use of meshgrid()

[Jonathon Klepatzki]

@Matt J it is indeed Gaussian. I narrowed down the equation that spoke of dispersion to only account for the upper-levels insteand of the surface. This is an attempt for me to conduct a study of aerosols in the upper-levels at a given depth in the arctic (Master's degree) when significant snow fall events are taking place.

I like your plots btw! And thank you.

[Jonathon Klepatzki]

@Matt J, quick question. I had to change the equation to include the full dispersion (mathematicl error) and noticed that when I changed the variable "mr" to either 1 or 3, it gives me a linear plot once again. Could this be an issue with the dimensions?