A hotspot swell beneath a slow-moving plate is wide and high

PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics · Seismology, tectonics and geodynamics

The Solid Earth, Ch Plates, creep and convection: the mantle in motion

Problem

A hotspot swell beneath a slow-moving plate is ws=700 kmw_s = 700\,\mathrm{km} wide and hs=500 mh_s = 500\,\mathrm{m} high, and the plate moves over the plume at up=30 mm yr−1u_{\rm p} = 30\,\mathrm{mm\,yr^{-1}}. Take ρm−ρw=2300 kg m−3\rho_m - \rho_w = 2300\,\mathrm{kg\,m^{-3}}, cp=1250 J kg−1 K−1c_p = 1250\,\mathrm{J\,kg^{-1}\,K^{-1}}, αV=3×10−5 K−1\alpha_V = 3\times10^{-5}\,\mathrm{K^{-1}} and 1 yr=3.156×107 s1\,\mathrm{yr} = 3.156\times10^{7}\,\mathrm{s}. ((a)) Find the plume's buoyancy flux BB. ((b)) Find the heat flux QQ it carries. ((c)) By what factor does this plume fall short of the Hawaiian plume's 0.30 TW0.30\,\mathrm{TW}, and which two of the three swell quantities wsw_s, hsh_s and upu_{\rm p} account for most of that factor? Take the Hawaiian swell as ws=1000 kmw_s=1000\,\mathrm{km}, hs=1 kmh_s=1\,\mathrm{km} and up=100 mm yr−1u_{\rm p}=100\,\mathrm{mm\,yr^{-1}}.

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