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Velocityfield and stream function

  1. Mar 4, 2009 #1
    1. The problem statement, all variables and given/known data
    A velocity field is given by v = ui + vj
    where:
    u = cos(x)sin(y)
    v = -sin(x)cos(y)
    x = y = [-pi/2,pi/2]


    the stream function psi is:

    psi = cos(x)cos(y)

    Matlab function:
    --------------------------------------
    function[X,Y,psi] = streamfun(n)

    if nargin < 1;
    n=20;
    end

    x=linspace(-0.5*pi,0.5*pi,n);
    [X,Y] = meshgrid(x,x);
    psi=cos(X).*cos(Y);

    ------------------------------------------
    2. Relevant equations


    calculate the velocity numerically with [tex]\nabla[/tex]psi


    3. The attempt at a solution
    I am starting with the assumption, the velocity is [tex]\nabla[/tex]psi, is this correct?

    --------------------------------------

    [x,y,psi] = streamfun(20)
    [u,v] = gratient(20)

    quiver(x,y,u,v)

    and I get numfield.jpg, see attachment, but this is not the same as my velocityfield.jpg

    which I got from:

    -----------------------------------------------
    x = linspace(-0.5*pi,0.5*pi,n);
    [x,y] = meshgrid(x,x);

    u = cos(x).*sin(y);
    v = -sin(x).*cos(y);

    quiver(x,y,u,v)
    ----------------------------------------------------------
    Can someone please help me and tell me what I am doing wronge.

    Edit:
    nabla*psi = -sin(x)cos(y)i - cos(x)*sin(y)j
     

    Attached Files:

    Last edited: Mar 4, 2009
  2. jcsd
  3. Mar 4, 2009 #2
    One more question:

    A velocity field is given by v = ui + vj
    where:
    u = cos(x)sin(y)
    v = -sin(x)cos(y)

    Draw stream vectors along the x and y axes.

    What is a stream vector?
    Is it just like arrows with magnitude and direction v?
     
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