k^9 Spectrum

(1) For linear acoustic case, Mark analytical estimates suggest a k^9 spectrum for GW, given that the kinetic spectrum is k^4

(2) We also had a verification of that by using unequal time correlation and numerical integration. However, we do not have a k^9 spectrum with expansion.

(3) Also verified with Pencil code but there are a few differences. One is oscillations at large k and second is that the spectrum is broader around the peak.

(4) To check: what is GW spectrum for other kinetic spectrum, for example k^2 or k^6. Also pay attention to the depth around the peak.




Date 5 June 2023

Title- Steepness of the GW spectrum from PTs

Intro- Mark 9, Isak, Not in 3D- synthetic, linear sound waves.
Boldyryv idea, 

Our approaches- 3D simulation from pencil code, numerical integration of Mark equation,

Results:
plot without expansion (Jani approach) (Fig11)
Discussion about the background with finite time integration in contrast to Mark results.
Discussion about the location of the peak of the GW spectrum in terms of the peak fo the kinetic spectum
plot with a comparison with Pencil code results (Fig 12),
Comparison of the synthetic sound waves and full numerical simulation with fluid equations
(Explain the difference if there is)
plot with expansion (Jani approach)

Conclusion

Run names with the NS equation
P1024_k01_kf10e
P1024_k1_kf10b