  Our Sun, primarily composed of ionized hydrogen and helium, has a surface
temperature of 5777~K and a radius $R_\odot \approx 696,000$ km. In the outer
$R_\odot/3$, energy transport is accomplished primarily by convection. Using
typical convective velocities $u\sim100\,\rm{m\,s^{-1}}$ and kinematic
viscosities of order $10^{-4}$ m$^{2}$s$^{-1}$, we obtain a Reynolds number $Re
\sim 10^{14}$. Convection is thus turbulent, causing a vast range of scales to
be excited. The Prandtl number, $Pr$, of the convecting fluid is very low, of
order $10^{-7}$\,--\,$10^{-4}$, so that the Rayleigh number ($\sim Re^2 Pr$) is
on the order of $10^{21}\,-\,10^{24}$. Solar convection thus lies in
extraordinary regime of dynamical parameters, highly untypical of fluid flows
on Earth. Convective processes in the Sun drive global fluid circulations and
magnetic fields, which in turn affect its visible outer layers ("solar
activity") and, more broadly, the heliosphere ("space weather"). The precise
determination of the depth of solar convection zone, departures from
adiabaticity of the temperature gradient, and the internal rotation rate as a
function of latitude and depth are among the seminal contributions of
helioseismology towards understanding convection in the Sun. Contemporary
helioseismology, which is focused on inferring the properties of
three-dimensional convective features, suggests that transport velocities are
substantially smaller than theoretical predictions. Furthermore,
helioseismology provides important constraints on the anisotropic Reynolds
stresses that control the global dynamics of the solar convection zone. This
review discusses the state of our understanding of convection in the Sun, with
a focus on helioseismic diagnostics. We present our considerations with the
interests of fluid dynamicists in mind.
