Vorticity budget of weak thermal convection in Keplerian disks

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.