The influence of rotation on the spectral energy transfer of homogeneous
turbulence
is investigated in this paper. Given the fact that linear dynamics, e.g.
the inertial
waves regime found in an RDT (rapid distortion theory) analysis, cannot
affect
a homogeneous isotropic turbulent flow, the study of nonlinear dynamics
is of
prime importance in the case of rotating flows. Previous theoretical (including
both
weakly nonlinear and EDQNM theories), experimental and DNS (direct numerical
simulation) results are collected here and compared in order to give a
self-consistent picture of the nonlinear effects of rotation on turbulence.
The inhibition of the energy cascade, which is linked to a reduction
of
the dissipation
rate, is shown to be related to a damping of the energy transfer due to
rotation. A
model for this effect is quantified by a model equation for the derivative-skewness
factor, which only involves a micro-Rossby number
Roω=ω′/(2Ω) – ratio
of r.m.s.
vorticity and background vorticity – as the relevant rotation parameter,
in accordance with DNS and EDQNM results.
In addition, anisotropy is shown also to develop through nonlinear interactions
modified by rotation, in an intermediate range of Rossby numbers
(RoL<1 and
Roω>1), which is characterized by a
macro-Rossby number RoL based on
an integral
lengthscale L and the micro-Rossby number previously defined.
This anisotropy is
mainly an angular drain of spectral energy which tends to concentrate energy
in
the wave-plane normal to the rotation axis, which is exactly both the slow
and the
two-dimensional manifold. In addition, a polarization of the energy distribution
in
this slow two-dimensional manifold enhances horizontal (normal to the rotation
axis)
velocity components, and underlies the anisotropic structure of the integral
length-scales. Finally a generalized EDQNM (eddy damped quasi-normal Markovian)
model is used to predict the underlying spectral transfer structure and
all
the subsequent
developments of classic anisotropy indicators in physical space. The results
from the
model are compared to recent LES results and are shown to agree well. While
the
EDQNM2 model was developed to simulate ‘strong’ turbulence,
it is
shown that it has a strong formal analogy with recent weakly nonlinear
approaches to wave turbulence.