Dark matter flow data and manuscript: On the statistical theory of self-gravitating collisionless dark matter flow: High order kinematic and dynamic relations

Manuscript and CSV data behind the figures and tables of Xu (2024), On the statistical theory of self-gravitating collisionless dark matter flow: High order kinematic and dynamic relations, Physics of Fluids 36, 075146, doi:10.1063/5.0215026, arXiv:2202.02991. Contents: the revised manuscript (PDF) and the CSV files of every plotted series and table, in the format of the author's dark matter flow datasets. Pair statistics from the Virgo SCDM N-body simulation at redshifts z = 10 to 0. Companion datasets: Part I (halo-based) doi:10.5281/zenodo.6541231, Part II (correlation-based) doi:10.5281/zenodo.6757654. Major findings (Virgo SCDM N-body simulation, redshifts z = 10 to 0): Kinematic relations of any order are derived for incompressible, constant-divergence and irrotational flow, and validated by the simulation. On large scales, third-order velocity correlations can be related to the density correlation or the pairwise velocity. The p-th order velocity correlations follow a^((p+2)/2) for odd p and a^(p/2) for even p (a = scale factor). The fitted exponents for odd p are smaller than these predictions. The overdensity is proportional to the density correlation on the same scale, <delta> ∝ <delta delta'>; the velocity dispersion on a scale r is proportional to the overdensity on that scale. The effective viscosity of the adhesion model originates from velocity fluctuations; the negative viscosity is due to the inverse energy cascade. On small scales, a self-closed velocity evolution is obtained by splitting velocity into motion within haloes and motion of haloes. Vorticity, enstrophy and energy evolution follow from it. The mean pairwise velocity follows <Δu_L> = −H a r. The third moment follows <(Δu_L)^3> ∝ ε_u a r, with a constant energy-cascade rate ε_u ≈ −4.6×10⁻⁷ m²/s³. The combined kinematic and dynamic relations give exponential velocity correlations on large scales and one-fourth power-law correlations on small scales; the p-th order correlations follow a^((3p−5)/4) for odd p and a^(3p/4) for even p.