= Shear-to-slip transition in a shallow ice current
{title2=$H_*=3/\beta$}
The two mobilities in the <shallow-ice flux with linear basal drag> are equal at thickness $H_*=3/\beta$. A conserved half-volume $V_g$ gives length $L_*=V_g/H_*$ and time $T_*=3\mu L_*^2/(\rho gH_*^3)$. Nondimensional thick profiles spread as $\tau^{1/5}$; thin sliding profiles spread as $\tau^{1/4}$. Matching the centre of the mass-normalized early <planar volume-conserving nonlinear-diffusion similarity> to unit depth estimates $\tau_{\mathrm{tr}}=3/(10I_3^2)\simeq0.42385$. The numerical estimate depends on the matching convention and the initial-profile relaxation.
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