Spectra Properties:

Variable	Value
Prolongation method	Spectral
Shape of spectra region	Rectangle
Window function	Cosine

Everything else is default, see: ​page

Spectra Region

Following the wiki page on spectra objects, to calculate the spectra region in the simulation domain, you should compute the region in coarse cells first.

I took this to be a constant 40 pc (the diameter of the cylinder) in y & z, and adjusted the length in x to accommodate the shear angle + 10 pc on either side at its widest point:

Computing the number of coarse zones in this rectangular region gives,

Theta	Coarse Zones (Nx,Ny,Nz)
0	(13, 26, 26)
15	(20, 26, 26)
30	(28, 26, 26)
60	(58, 26, 26)

Power Spectrum

To get a power spectrum, one takes a fourier transform of the data, and then takes the complex conjugate of the resultant fourier transform. This gives the power in each of the component frequencies of the signal.

Kinetic Energy

There seems then to be 2 different ways of computing the power spectrum of the kinetic energy. First, we can take the fourier transform of \sqrt{\rho (v_x + v_y + v_z)^2} and then square this to get the power spectrum. Or, we can take \sqrt{\rho v_x^2} and then sum up the squares of the various fourier transforms for each dimension. That is, does

(F(\sqrt{v_x^2 + v_y^2 + v_z^2} ~))^2 = (F(v_x))^2 + (F(v_y))^2 + (F(v_z))^2 ~?

Further, which do we want,

(F(\sqrt{\rho(v^2)} ~))^2 ~or~ (F(\sqrt{\rho}))^2*(F(v))^2

as it seems both give the same units..