On the analogy between gravitationally driven
turbulence and classical turbulence
Nils T. Bassea
aElsas v¨ag 23, 423 38 Torslanda, Sweden
April 17, 2020
Power spectra of simulated density ﬂuctuations generated by gravitational
fragmentation are compared to corresponding expressions from classical tur-
A recent paper  includes power spectra of simulated density ﬂuctuations
generated by gravitational fragmentation. We have used  to extract the
power spectrum for the scale factor a= 200, so there are inaccuracies in our
Previously, we have studied large-scale cosmological power spectra and
attempted to place them in the context of classical turbulence using the
example of turbulence measured in fusion plasmas [3, 4].
2. Power spectra
We treat power spectra Pas a function of wavenumber ratio kratio ≡
k/khorizon. For classical turbulence, the 3D Kolmogorov scaling is:
where Eis energy.
For large wavenumbers, energy is dissipated and becomes an exponential
Email address: firstname.lastname@example.org (Nils T. Basse)
where nis a constant.
Results are summarized in Fig. 1:
The Kolmogorov scaling agrees with the simulated power spectrum over
roughly an order of magnitude of intermediate wavenumber ratios.
The exponential ﬁt is applied for wavenumber ratios larger than 10;
here, n= 1.14.
PRL 124, 061301 (2020)
3D Kolgomorov cascade
Threshold for exponential fit
Figure 1: Simulated power spectrum (blue) with Kolmogorov scaling (black) and exponen-
tial ﬁt (red) versus wavenumber ratio. The vertical magenta line indicates the wavenumber
ratio used for the exponential ﬁt: Only wavenumber ratios larger than the threshold value
3. Dimensionality of cosmological turbulence
Findings in this work indicate that density ﬂuctuations based on gravita-
tional fragmentation appear to be 3D. However, our previous work has shown
that large-scale cosmological power spectra are most likely closer related to
Thus, we speculate that early cosmological turbulence was 3D and during
expansion transitioned to 2D . This departure from isotropy might be
related to the anisotropy of cosmic acceleration .
We have shown that the simulations of density ﬂuctuations based on
gravitational fragmentation can be analysed as classical turbulence. Based
on this, we argue that an analogy exists between ﬂuctuations observed in
cosmology and classical turbulence.
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 Dickau JJ. Fractal cosmology. Chaos, Solitons and Fractals
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