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The Sun's Photospheric Convection Spectrum

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.