Stochastically driven instability in rotating shear flows
  Origin of hydrodynamic turbulence in rotating shear flows is investigated.
The particular emphasis is the flows whose angular velocity decreases but
specific angular momentum increases with increasing radial coordinate. Such
flows are Rayleigh stable, but must be turbulent in order to explain observed
data. Such a mismatch between the linear theory and observations/experiments is
more severe when any hydromagnetic/magnetohydrodynamic instability and then the
corresponding turbulence therein is ruled out. The present work explores the
effect of stochastic noise on such hydrodynamic flows. We essentially
concentrate on a small section of such a flow which is nothing but a plane
shear flow supplemented by the Coriolis effect. This also mimics a small
section of an astrophysical accretion disk. It is found that such
stochastically driven flows exhibit large temporal and spatial correlations of
perturbation velocities, and hence large energy dissipations of perturbation,
which presumably generate instability. A range of angular velocity (\Omega)
profiles of background flow, starting from that of constant specific angular
momentum (\lambda = \Omega r^2 ; r being the radial coordinate) to that of
constant circular velocity (v_\phi = \Omega r), is explored. However, all the
background angular velocities exhibit identical growth and roughness exponents
of perturbations, revealing a unique universality class for the stochastically
forced hydrodynamics of rotating shear flows. This work, to the best of our
knowledge, is the first attempt to understand origin of instability and
turbulence in the three-dimensional Rayleigh stable rotating shear flows by
introducing additive noise to the underlying linearized governing equations.
This has important implications to resolve the turbulence problem in
astrophysical hydrodynamic flows such as accretion disks.
