By employing the equations of mean-square vorticity (enstrophy) fluctuation
s in strong shear flows, we demonstrate that, unlike energy production of t
urbulent vorticity in nonrotating shear flows, the turbulent vorticity of w
eak convection in Keplerian disks cannot gain energy from vortex stretching
/tilting by background shear unless the associated Reynolds stresses are ne
gative. This is because the epicyclic motion is an energy sink of the radia
l component of mean-square turbulent vorticity in Keplerian disks when Reyn
olds stresses are positive. Consequently, weak convection cannot be self-su
stained in Keplerian flows. This agrees with the results implied from the e
quations of mean-square velocity fluctuations in strong shear flows. Our an
alysis also sheds light on the explanation of the simulation result in whic
h 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 azimut
hal pressure perturbations and directions of energy cascade.