  In this dissertation, several components of large-scale solar flows are
studied observationally: solar equatorial Rossby waves (waves of radial
vorticity), large-scale convection, and surface flows around active regions.
Maps of horizontal flows are derived from photospheric observations by the
Helioseismic and Magnetic Imager (HMI) aboard the Solar Dynamics Observatory
(SDO) using two different techniques: granulation tracking and local
helioseismology. First, the eigenfunctions of solar Rossby waves are measured
from helioseismic ring-diagram flow maps with a correlation method and a
spectral analysis. Down to $9$ Mm below the surface, the dependence of the
radial vorticity with radius $r$ is consistent with $r^{m-1}$, for a given
longitudinal wavenumber $m$. At the surface, the eigenfunctions are
complex-valued. The real part decreases away from the equator and switches sign
around $\pm 20-30^\circ$. The imaginary part is small, but nonzero, and may be
due to wave attenuation. This may have implications for the transport of
angular momentum in the latitudinal direction. Second, we revisit previous
measurements of power spectra of longitudinal velocities near the solar
surface, obtained from time-distance and ring-diagram helioseismology. Several
issues in these past helioseismic analyses are identified and corrected. The
corrections are not sufficient to remove the discrepancy between the
measurements. I thus present new velocity power spectra from granulation
tracking and ring-diagram helioseismology. The two new measurements are close
to each other near the solar surface, and the corresponding kinetic energy
decreases with increasing spatial scale.
