Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

How to compute multidimensional inverse Fourier transform

  1. Nov 15, 2014 #1
    Hello, everybody. I am currently working on deriving solutions for Stokes flows. I encounter a multidimensional inverse Fourier transform. I already known the Fourier transform of the pressure field:
    [itex]\tilde{p}=-\frac{i}{{{k}^{2}}}\mathbf{F}\centerdot \mathbf{k}[/itex]
    where [itex]i[/itex] is the imaginary unit, [itex]\mathbf{k}[/itex] is the frequency vector, [itex]k[/itex] is the length of [itex]\mathbf{k}[/itex] (That is, [itex]k=\left\| \mathbf{k} \right\|[/itex]), and [itex]\mathbf{F}[/itex] is a constant vector. I don't know how to perform the inverse transform, although I have found the final answer in some references, which reads
    [itex]p=\frac{\mathbf{F}\centerdot \mathbf{x}}{4\pi {{r}^{3}}}[/itex]
    where [itex]r=\left\| \mathbf{x} \right\|[/itex]
    Does anybody has an idea? Thanks a lot.
     
  2. jcsd
  3. Nov 15, 2014 #2

    Evo

    User Avatar

    Staff: Mentor

    If you could show what you fear is the problem you have in solving these problems, it could help us understand where you need help.
     
  4. Nov 16, 2014 #3
    Oh, I have found the answer. It is presented in the following link:
    http://www.fuw.edu.pl/~mklis/publications/Hydro/oseen.pdf
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook