  We provide a consistent theory of turbulence in the presence of shear and
rotation. Starting from a quasi-linear equation for the fluctuating fields, we
derive turbulence amplitude and turbulent transport coefficients, taking into
account the effect of shear and rotation on turbulence. We show that the shear
reduces both turbulence amplitude and transport, more strongly in the direction
parallel to the shear than in the perpendicular one, effectively inducing an
anisotropic turbulence. The rotation further reduces turbulence amplitude and
transport. The interaction between the shear and the rotation is shown to give
rise to a novel non-diffusive flux of angular momentum ($\Lambda$-effect),
providing a mechanism for the permanence of shearing structure in astrophysical
and geophysical systems.
