The instability of viscous incompressible fluid flows caused in a thin spherical layer by torsional oscillations of the inner sphere in a thin spherical layer with respect to the sate of rest is studied numerically. It has been established that an increase in the frequency of torsional oscillations leads to a change in the mode of the instability, with a transition from secondary flows in the form of Taylor vortices to structures not observed earlier. The revealed instability is observed in the frequency range from 0.61 to 2.45 Hz or, if the wavelengths are taken relative to the layer thickness, from 0.67 to 1.33.