  We propose a one-fluid analytical model for a turbulently flowing dilute
suspension, based on modified Navier-Stokes equation with a $k$-dependent
effective density of suspension, $\rho_ {eff}(k)$, and an additional damping
term $\propto \gamma_ p(k)$, representing the fluid-particle friction
(described by Stokes law). The statistical description of turbulence within the
model is simplified by a modification of the usual closure procedure based on
the Richardson-Kolmogorov picture of turbulence with a differential
approximation for the energy transfer term. The resulting ordinary differential
equation for the energy budget is solved analytically for various important
limiting cases and numerically in the general case. In the inertial interval of
scales we describe analytically two competing effects: the energy suppression
due to the fluid particle friction and the energy enhancement during the
cascade process due to decrease of the effective density of the small scale
motions. An additional suppression or enhancement of the energy density may
occur in the viscous subrange, caused by the variation of the extent of the
inertial interval due to the combined effect of the fluid-particle friction and
the decrease of the kinematic viscosity of the suspensions. The analytical
description of the complicated interplay of these effects supported by
numerical calculations is presented. Our findings allow one to rationalize the
qualitative picture of the isotropic homogeneous turbulence of dilute
suspensions as observed in direct numerical simulations.
