Vorticity Budget of Weak Thermal Convection in Keplerian Disks

By employing the equations of mean-square vorticity (enstrophy) fluctuations in strong shear flows, we demonstrate that unlike energy production of turbulent vorticity in non-rotating shear flows, the turbulent vorticity of weak convection in Keplerian disks cannot gain energy from vortex stretching/tilting by background shear unless the associated 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. Subject headings: accretion, accretion disks — convection — hydrodynamics — MHD — turbulence