  In this paper we propose and examine a physical mechanism which can lead to
the generation of noise in the mass accretion rate of low mass X-ray binaries
on time-scales comparable to the orbital period of the system. We consider
modulations of mass captured by the compact object from the companion star's
stellar wind in binaries with late type giants, systems which usually have long
orbital periods. We show that a hydrodynamical interaction of the wind matter
within a binary system even without eccentricity results in variability of the
mass accretion rate with characteristic time-scales close to the orbital
period. The cause of the variability is an undeveloped turbulent motion
(perturbed motion without significant vorticity) of wind matter near the
compact object. Our conclusions are supported by 3D simulations with two
different hydrodynamic codes based on Lagrangian and Eulerian approaches -- the
SPH code GADGET and the Eulerian code PLUTO. In this work we assume that the
wind mass loss rate of the secondary is at the level of $(0.5-1)\times10^{-7}
M_\odot$/year, required to produce observable variations of the mass accretion
rate on the primary. This value is higher than that, estimated for single giant
stars of this type, but examples of even higher mass loss rate of late type
giants in binaries do exist. Our simulations show that the stellar wind matter
intercepted by the compact object might create observational appearances
similar to that of an accretion disc corona/wind and could be detected via high
energy resolution observations of X-ray absorption lines, in particular, highly
ionized ions of heavy elements.
