The base of the cooling oceanic thermal boundary layer becomes unstable when its…

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

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

Problem

The base of the cooling oceanic thermal boundary layer becomes unstable when its local Rayleigh number Raδ=ρgαVΔTδ3/(ηvκ)\mathrm{Ra}_\delta = \rho g\alpha_V\Delta T\delta^3/(\eta_v\kappa) reaches 10310^3, with the layer thickness growing as δ=2.32κt\delta = 2.32\sqrt{\kappa t}. Take ρ=3300 kg m−3\rho = 3300\,\mathrm{kg\,m^{-3}}, g=10 m s−2g = 10\,\mathrm{m\,s^{-2}}, αV=3×10−5 K−1\alpha_V = 3\times10^{-5}\,\mathrm{K^{-1}}, ΔT=1300 K\Delta T = 1300\,\mathrm{K} and κ=10−6 m2 s−1\kappa = 10^{-6}\,\mathrm{m^2\,s^{-1}}. ((a)) Find the onset thickness δc\delta_c and onset age tct_c for ηv=5×1020 Pa s\eta_v = 5\times10^{20}\,\mathrm{Pa\,s}. ((b)) Repeat for ηv=2.5×1021 Pa s\eta_v = 2.5\times10^{21}\,\mathrm{Pa\,s}.

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