 Solution

ID: past-exam-of-the-physics-of-the-earth-as-a-planet-course-of-the-university-of-cambridge/2014/paper-1/2/b/solution

Unsteady inertial force density scales as

ρ v / τ

, whereas viscous force density scales as

η v / λ^{2}

. Using the preceding timescale gives

\frac{unsteady inertia}{viscosity} \sim \frac{ρ λ ^{2}}{η τ} \sim \frac{ρ ^{2} g λ ^{3}}{η ^{2}} .

Convective inertia has ratio

ρ v λ / η

. Since

v \sim h / τ

, this is smaller by

h / λ

for small relief. Thus the displayed estimate controls the larger inertial contribution in this model.

 New to topics? Read the docs here!