We investigate the hydrodynamics of a variant of classical Bondi-Hoyle-Lyttleton accretion: a totally absorbing sphere moves at various Mach numbers (3 and 10) relative to a medium, which is taken to be an ideal gas having a velocity gradient (of 3% or 20% over one accretion radius) perpendicular to the relative motion. We examine the influence of the Mach number of the flow and the strength of the gradient upon the physical behaviour of the flow and the accretion rates of the angular momentum in particular. The hydrodynamics is modeled by the ``Piecewise Parabolic Method (PPM). The resolution in the vicinity of the accretor is increased by multiply nesting several grids around the sphere. Similarly to the 3D models without gradients published previously, models exhibit non-stationary flow patterns, although the Mach cone remains fairly stable. The accretion rates of mass, linear and angular momenta do not fluctuate as strongly as published previously for 2D models, but similarly to the 2D models, transient disks form around the accretor that alternate their direction of rotation with time. The average specific angular momentum accreted is roughly between 7% and 70% of the total angular momentum available in the accretion cylinder and is always smaller than the value of a vortex with Kepler velocity around the surface of the accretor. The fluctuations of the mass accretion rate in the models with small gradients (2%) are similar to the values of the models without gradients, while the models with large gradients (20%) exhibit larger fluctuations. The mass accretion rate is maximal when the specific angular momentum is zero, while the specific entropy tends to be smaller when the disks are prograde.
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