Js. Bagla et T. Padmanabhan, TRANSFER OF POWER IN NONLINEAR GRAVITATIONAL CLUSTERING, Monthly Notices of the Royal Astronomical Society, 286(4), 1997, pp. 1023-1031
We investigate the transfer of power between different scales and the
coupling of modes during the non-linear evolution of gravitational clu
stering in an expanding universe. We start with a power spectrum of de
nsity fluctuations that is exponentially damped outside a narrow range
of scales, and use numerical simulations to study the evolution of th
is power spectrum. Non-linear effects generate power at other scales,
with most power flowing from larger to smaller scales. The 'cascade' o
f power leads to equipartition of energy at smaller scales, implying a
power spectrum with index n approximate to -1. We find that such a sp
ectrum is produced in the range 1 < delta < 200 for density contrast d
elta. This result continues to hold even when small-scale power is add
ed to the initial power spectrum. Semi-analytic models for gravitation
al clustering suggest a tendency for the effective index to move towar
ds a critical index n(c) approximate to -1 in this range. For n < n(c)
, power in this range grows faster than linear rate, while if n > n(c)
, it grows at a slower rate - thereby changing the index closer to n(c
). At scales larger than the narrow range of scales with initial power
, a k(4) tail is produced. We demonstrate that non-linear small scales
do not affect the growth of perturbations at larger scales.