This paper discusses the stochastic analysis of spatially complex, time-dependent flows in spherical and cylindrical geometries where the reference states, internal heating rates, and boundary conditions are temporally invariant and rotationally symmetric. Snapshots of the aspherical temperature anomalies ΔT(r,&OHgr;,t) from a single convention run are taken to be samples of a stationary, rotationally invariant random field, and the spatial two-point correlation function CTT(r,r',Δ) is constructed by averaging over rotational transformations of this ensemble. Three subfunctions are extracted: the rms variation, &sgr;T(r)=√CTT(r,r,0), the radial correlation function, RT(r,r')=CTT(r,r', 0)/&sgr;T(r)&sgr;T(r'), and the angular correlation function AT(r,Δ)=CTT(r,r,Δ)/&sgr;2T(r). All three are useful in assessing the structural differences among mantle convection simulations, but the diagnostic properties of RT and its robustness with respect to low-pass filtering recommend it as a tool for testing stratification hypotheses against whole-mantle tomographic models.