  We present the extension of a modeling technique for Lagrangian tracer
particles [B. Viggiano et al., J. Fluid Mech.(2020), vol. 900, A27] which
accounts for the effects of particle inertia. Thereby, the particle velocity
for several Stokes numbers is modeled directly by a multi-layered
Ornstein-Uhlenbeck process and a comparison of key statistical quantities
(second-order velocity structure function, acceleration correlation function,
and root mean square acceleration) to expressions derived from Batchelor's
model as well as to direct numerical simulations (DNS) is performed. In both
approaches, Stokes' drag is treated by an approximate ``linear filter'' which
replaces the particle position entering the fluid velocity field by the
corresponding ideal tracer position. Effects of preferential concentration of
inertial particles are taken into account in terms of an effective Stokes
number that is determined from the zero crossing of the acceleration
correlation function from DNS. This approximation thus allows the modeling of
inertial particle statistics through stochastic methods and models for the
Lagrangian velocity; the particle velocity is effectively decoupled from the
particle position. In contrast to the ordinary filtering technique [Cencini et
al., J. Turbul. (2006), 7, N36], our method captures the effects of
preferential concentration of particles at low Stokes numbers which manifest
themselves for instance by a sharp decrease of the acceleration variance for
increasing Stokes numbers.
