Spatial eigenfunctions q_α, mode(r, θ, m) for the ζ_z-symmetric columnar convective modes with m = 2. By definition, modes are of the form q_α, mode(r, θ, m)exp[i(mϕ−ωt)], where q_α is either v_r, v_θ, v_ϕ, or p₁. (a) Meridional cuts of the radial velocity v_r, latitudinal velocity v_θ, longitudinal velocity v_ϕ, and pressure perturbation p₁ extracted from the convection simulation (lower panels) and obtained from our linear calculation (upper panels). (b) Radial dependence of the eigenfunction v_ϕ at the equator. The black solid and red dashed lines represent the simulation and linear calculation, respectively. (c) Latitudinal eigenfunction of v_ϕ at the surface normalized near the equator.