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The evolution of a linearly-polarized, long-wavelength Alfv\'en wave--propagating in a collisionless magnetized plasma with a shearedparallel-directed velocity flow-- is here studied by means of two-dimensionalhybrid Vlasov-Maxwell (HVM) simulations. The unperturbed sheared flow has beenrepresented by an exact solution of the HVM set of equations (Malara {\it etal.}, Phys. Rev. E 97, 053212), this avoiding spurious oscillations that wouldarise from the non-stationary initial state and inevitably affect the dynamicsof the system. We have considered the evolution of both a small and a moderateamplitude Alfv\'en wave, in order to separate linear wave-shear flow couplingsfrom kinetic effects, the latter being more relevant for larger waveamplitudes. The phase-mixing generated by the shear flow modifies the initialperturbation, leading to the formation of small-scale transverse fluctuationsat scales comparable with the proton inertial length. By analyzing both thepolarization and group velocity of perturbations in the shear regions, weidentify them as Kinetic Alfv\'en Waves (KAWs). In the moderate amplitude run,kinetic effects distort the proton distribution function in the shear region.This leads to the formation of a proton beam, at the Alfv\'en speed andparallel to the magnetic field. Such a feature, due to the parallel electricfield associated with KAWs, positively compares with solar-wind observations ofsuprathermal ions' populations, suggesting that it may be related to thepresence of ion-scales KAW-like fluctuations.

Kinetic Alfv\'en wave generation by velocity shear in collisionless plasmas