  Time-distance helioseismology provides information about vector flows in the
near-surface layers of the Sun by measuring wave travel times between points on
the solar surface. Specific spatial averages of travel times have been proposed
for distinguishing between flows in the east-west and north-south directions
and measuring the horizontal divergence of the flows. No specific measurement
technique has, however, been developed to measure flow vorticity. Here we
propose a new measurement technique tailored to measuring the vertical
component of vorticity. Fluid vorticity is a fundamental property of solar
convection zone dynamics and of rotating turbulent convection in particular.
The method consists of measuring the travel time of waves along a closed
contour on the solar surface in order to approximate the circulation of the
flow along this contour. Vertical vorticity is related to the difference
between clockwise and counter-clockwise travel times. We applied the method to
characterize the vortical motions of solar convection using helioseismic data
from the Helioseismic and Magnetic Imager onboard the Solar Dynamics
Observatory (SDO/HMI) and from the Michelson Doppler Imager onboard the Solar
and Heliospheric Observatory (SOHO/MDI). Away from the equator, a clear
correlation between vertical vorticity and horizontal divergence is detected.
Horizontal outflows are associated with negative vorticity in the northern
hemisphere and positive vorticity in the southern hemisphere. The signal is
much stronger for HMI than for MDI observations. We characterize the spatial
power spectrum of the signal by comparison with a noise model. Vertical
vorticity at horizontal wavenumbers below 250/R_Sun can be probed with this
helioseismic technique.
