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On the analogy between gravitationally driven turbulence and classical turbulence

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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-
1. Introduction
A recent paper [1] includes power spectra of simulated density fluctuations
generated by gravitational fragmentation. We have used [2] 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:
ratio ,(1)
where Eis energy.
For large wavenumbers, energy is dissipated and becomes an exponential
Email address: (Nils T. Basse)
P(kratio)dissipation exp(n×kratio),(2)
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.
P(k) [a.u.]
PRL 124, 061301 (2020)
3D Kolgomorov cascade
Exponential fit
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
are used.
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 [5]. This departure from isotropy might be
related to the anisotropy of cosmic acceleration [6].
4. Conclusions
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.
[1] Musoke N, Hotchkiss S and Easther R. Lighting the dark: Evolution of
the postinflationary universe. Phys. Rev. Lett. 2020;124:061301.
[2] Plot Digitizer 2020.
[3] Basse NP. Density fluctuations on mm and Mpc scales. Physics Letters
A 2005;340:456-460.
[4] Basse NP. A study of multiscale density fluctuation measurements. IEEE
Transactions on Plasma Science 2008;36:458-461.
[5] Dickau JJ. Fractal cosmology. Chaos, Solitons and Fractals
[6] Colin J, Mohayaee R, Rameez M and Sarkar S. Evidence for anisotropy
of cosmic acceleration. Astronomy & Astrophysics 2019;631:L13.
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Full-text available
We will in this Letter report on suggestive similarities between density fluctuation power versus wavenumber on small (mm) and large (Mpc) scales. The small scale measurements were made in fusion plasmas and compared to predictions from classical fluid turbulence theory. The data is consistent with the dissipative range of 2D turbulence. Alternatively, the results can be fitted to a functional form that cannot be explained by turbulence theory. The large scale measurements were part of the Sloan Digital Sky Survey galaxy redshift examination. We found that the equations describing fusion plasmas also hold for the galaxy data. The comparable dependency of density fluctuation power on wavenumber in fusion plasmas and galaxies might indicate a common origin of these fluctuations.
Full-text available
Intriguing parallels between density fluctuation power versus wavenumber on small (in millimeter) and large (in megaparsec) scales are presented. The comparative study is carried out between fusion plasma measurements and cosmological data. Based on predictions from classical fluid turbulence theory, we argue that our observations are consistent with 2-D turbulence. The similar dependencies of density fluctuations on these disparate scales might indicate that primordial turbulence has been expanded to cosmological proportions.
In simple inflationary cosmological scenarios, the near-exponential growth can be followed by a long period in which the Universe is dominated by the oscillating inflaton condensate. The condensate is initially almost homogeneous, but perturbations grow gravitationally, eventually fragmenting the condensate if it is not disrupted more quickly by resonance or prompt reheating. We show that the gravitational fragmentation of the condensate is well-described by the Schrödinger-Poisson equations and use numerical solutions to show that large overdensities form quickly after the onset of nonlinearity. This is the first exploration of this phase of nonlinear dynamics in the very early Universe, which can affect the detailed form of the inflationary power spectrum and the dark matter fraction when the dark sector is directly coupled to the inflaton.
Observations reveal a “bulk flow” in the local Universe which is faster and extends to much larger scales than are expected around a typical observer in the standard ΛCDM cosmology. This is expected to result in a scale-dependent dipolar modulation of the acceleration of the expansion rate inferred from observations of objects within the bulk flow. From a maximum-likelihood analysis of the Joint Light-curve Analysis catalogue of Type Ia supernovae, we find that the deceleration parameter, in addition to a small monopole, indeed has a much bigger dipole component aligned with the cosmic microwave background dipole, which falls exponentially with redshift z : q0 = qm + qd . n̂ exp(- z / S ) . The best fit to data yields qd = −8.03 and S = 0.0262 (⇒ d ∼ 100 Mpc), rejecting isotropy ( qd = 0) with 3.9 σ statistical significance, while qm = −0.157 and consistent with no acceleration ( qm = 0) at 1.4 σ . Thus the cosmic acceleration deduced from supernovae may be an artefact of our being non-Copernican observers, rather than evidence for a dominant component of “dark energy” in the Universe.
  • J J Dickau
Dickau JJ. Fractal cosmology. Chaos, Solitons and Fractals 2009;41:2103-2105.