= Upstream basin profile of a sediment-lubricated mountain
{title2=$x/\ell=P(d/d_\infty)-P(3)$}
In front of the contact line in the <sediment-lubricated viscous mountain model>, $h=d$ and $d_x=3\mu_sU(d-d_\infty)/(\rho gd^3)$. For $\delta=d/d_\infty$ and $\ell=\rho gd_\infty^3/(3\mu_sU)$, integration gives $x/\ell=P(\delta)-P(3)$, with $P(\delta)=\delta^3/3+\delta^2/2+\delta+\ln(\delta-1)$. The branch $1<\delta\leq3$ is unique and tends exponentially to the uniform far-field depth.
Back to article page
