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 ) \times 10 ^ { -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 .