  Origin of hydrodynamic turbulence in rotating shear flow, e.g. plane Couette
flow including the Coriolis force, is a big puzzle. While the flow often
exhibits turbulence in laboratory experiments, according to the linear
perturbation theory it should always be stable. We demonstrate that the
secondary disturbance to the primarily perturbed flow triggers the elliptical
instability in such a system and hence an exponential growing eigenmode. This
result has an immediate application to astrophysics and geophysics which often
exhibit a turbulent flow with the Keplerian angular momentum profile. We
address the origin of turbulence in such a Keplerian flow which is similar to
rotating Couette flow.
