  By employing the equations of mean-square vorticity (enstrophy) fluctuations
in strong shear flows, we demonstrate that unlike energy production of
turbulent vorticity in nonrotating shear flows, the turbulent vorticity of weak
convection in Keplerian disks cannot gain energy from vortex stretching/tilting
by background shear unless the asscoiated Reynolds stresses are negative. This
is because the epicyclic motion is an energy sink of the radial component of
mean-square turbulent vorticity in Keplerian disks when Reynolds stresses are
positive. Consequently, weak convection cannot be self-sustained in Keplerian
flows. This agrees with the results implied from the equations of mean-square
velocity fluctuations in strong shear flows. Our analysis also sheds light on
the explanation of the simulation result in which positive kinetic helicity is
produced by the Balbus-Hawley instability in a vertically stratified Keplerian
disk. We also comment on the possibility of outward angular momentum transport
by strong convection based on azimuthal pressure perturbations and directions
of energy cascade.
