Route of hydrodynamic turbulence in rotating shear flow: Secondary perturbation triggers growing eigenmodes through the elliptical instability

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.