Calculating the Line Spatial Fourier Transform

Use the values in this range to create a line spatial Fourier transform. The velocity of propagation is calculated from this transform.

  1. Right-click the Tools > Data Set Functionsnode and select New > Line Spatial Fourier Transform (F[G[h[l]]]).
  2. Rename the newly created F(G(l)) 1 node to Fxx(l).
  3. Select the Data Set Functions > Fxx(l) node and set Start Signal to 0.0 m.
  4. Set End Signal to 0.2 m.

  5. Right-click Fxx(l) > Derived and select New derived data from derived data.
  6. Rename the newly created Line Derived node to PSD.
  7. Select Fxx(l) > Derived > PSD and set Input Derived Data to [Power Spectra].
  8. Activate Update Active.

With the Update Active property activated, the line spatial Fourier transform is automatically calculated. This process takes a few minutes, depending on the processor speed of your computer.

When the Fourier transform has been computed, visualize the spectra:

  1. Select PSD > Output control and activate Log data.
Create a new scalar scene and rename it to PSD.
  1. Select PSD > Outline 1 and deactivate Outline.
  2. Select PSD > Scalar 1 > Parts and select Derived Data > PSD.
  3. Click OK.
The power spectral density plot appears in the Graphics window. Use the mouse to adjust the view.
  1. To color the plot, select PSD > Scalar 1 > Scalar Field and set Function to Derived Data > PSD.
  2. To visualize the Power Spectral Density as a two-dimensional contour, click (Save-Restore-Select views) in the toolbar and select Projection Mode > Parallel.
  3. To align with the X-Y plane, press the <T> key.

The slope of the distinctive line in the wavenumber-frequency plot is used to calculate the group velocity of the disturbances traveling along the domain. For this case, the group velocity is estimated as

2π10,0001560 m/s = 40.3 m/s

which is, as expected, roughly 80% of the inlet velocity.