Dynamics of thermal plumes in three‐dimensional isoviscous thermal convection

SUMMARY The dynamics of mantle plumes are important for understanding intraplate volcanism and heat transfer in the mantle. Using 3‐D numerical models and scaling analyses, we investigated the controls of convective vigour or Ra (Rayleigh number) on the dynamics of thermal plumes in isoviscous and basal heating thermal convection. We examined the Ra dependence of plume number, plume spacing, plume vertical velocity and plume radius. We found that plume number does not increase monotonically with Ra . At relatively small Ra (≤10 6 ) , plume number is insensitive to Ra . For 3 × 10 6 ≤ Ra ≤ 3 × 10 7 , plume number scales as Ra 0.31 and plume spacing λ∼ Ra −0.16 ∼δ 1/2 , where δ is the thickness of the thermal boundary layer. However, for larger Ra (∼10 8 ) plume number and plume spacing again become insensitive to Ra . This indicates that the box depth poses a limit on plume spacing and plume number. We demonstrate from both scaling analyses and numerical experiments that the scaling exponents for plume number, n , heat flux, β, and average velocity on the bottom boundary, v , satisfy n = 4β− 2 v . Our scaling analyses also suggest that vertical velocity in upwelling plumes V up ∼ Ra 2(1− n +β/2)/3 and that plume radius R up ∼ Ra (β−1− n /2)/3 , which differ from the scalings for the bottom boundary velocity and boundary layer thickness.