  In this paper, we consider the physical mechanism for the clustering of
inertial particles in the inertial range of isotropic turbulence. We analyze
the exact, but unclosed, equation governing the radial distribution function
(RDF) and compare the mechanisms it describes for clustering in the dissipation
and inertial ranges. We demonstrate that in the limit ${St_r\ll1}$, where
$St_r$ is the Stokes number based on the eddy turnover timescale at separation
$r$, the clustering in the inertial range can be understood to be due to the
preferential sampling of the coarse-grained fluid velocity gradient tensor at
that scale. When ${St_r\gtrsim\mathcal{O}(1)}$ this mechanism gives way to a
non-local clustering mechanism. These findings reveal that the clustering
mechanisms in the inertial range are analogous to the mechanisms that we
identified for the dissipation regime (see \emph{New J. Phys.}
\textbf{16}:055013, 2014). Further, we discuss the similarities and differences
between the clustering mechanisms we identify in the inertial range and the
"sweep-stick" mechanism developed by Coleman \& Vassilicos (Phys. Fluids
21:113301, 2009). We argue that when ${St_r\ll1}$ the sweep-stick mechanism is
equivalent to our mechanism in the inertial range if the particles are
suspended in Navier-Stokes turbulence, but that the sweep-stick mechanism
breaks down for ${St_r\gtrsim\mathcal{O}(1)}$. The argument also explains why
the sweep-stick mechanism is unable to predict particle clustering in kinematic
simulations. We then consider the closed, model equation for the RDF given in
Zaichik \& Alipchenkov (Phys. Fluids. 19:113308, 2007) and use this, together
with the results from our analysis, to predict the analytic form of the RDF in
the inertial range for ${St_r\ll1}$, which, unlike that in the dissipation
range, is not scale-invariant. The results are in good agreement with direct...
