We present results of time-dependent numerical modeling of the internal structure of the collisionless shock terminating the pulsar wind in Crab Nebula. We treat the equatorial relativistic wind as composed of ions and electron-positron plasma with an embedded toroidal magnetic field. Relativistic cyclotron instability of the ion ring downstream from the shock is found to launch outward propagating magnetosonic waves. Due to the fresh supply of ions crossing the shock, the time-dependent process achieves a limit-cycle pattern, in which the waves are launched with periodicity on the order of the ion Larmor time. Compressions in magnetic field and pair density associated with these waves as well as their propagation speed qualitatively reproduce the features observed in the wisps.