  Spectra of the cellular photospheric flows are determined from full-disk
Doppler velocity observations acquired by the Helioseismic and Magnetic Imager
(HMI) instrument on the Solar Dynamics Observatory (SDO) spacecraft. Three
different analysis methods are used to separately determine spectral
coefficients representing the poloidal flows, the toroidal flows, and the
radial flows. The amplitudes of these spectral coefficients are constrained by
simulated data analyzed with the same procedures as the HMI data. We find that
the total velocity spectrum rises smoothly to a peak at a wavenumber of about
120 (wavelength of about 35 Mm), which is typical of supergranules. The
spectrum levels off out to wavenumbers of about 400, and then rises again to a
peak at a wavenumber of about 3500 (wavelength of about 1200 km), which is
typical of granules. The velocity spectrum is dominated by the poloidal flow
component (horizontal flows with divergence but no curl) at wavenumbers above
30. The toroidal flow component (horizontal flows with curl but no divergence)
dominates at wavenumbers less than 30. The radial flow velocity is only about
3\% of the total flow velocity at the lowest wavenumbers, but increases in
strength to become about 50\% at wavenumbers near 4000. The spectrum compares
well with the spectrum of giant cell flows at the lowest wavenumbers and with
the spectrum of granulation from a 3D radiative-hydrodynamic simulation at the
highest wavenumbers.
