= Diffusive nose of an advected porous gravity current
{title2=$w\sim\sqrt{a h_{\mathrm{int}}t}$}
The downstream edge of a continuously fed <porous gravity current with background flow> has a transition width proportional to $\sqrt{a h_{\mathrm{int}}t}$ around drift position $ut$. Its <similarity solution> satisfies $(FF\prime)\prime+\eta F\prime/2=0$, $F(-\infty)=1$, and $F(\eta_N)=0$. A finite front has $F\sim(\eta_N/2)(\eta_N-\eta)$. A clipped linear ramp is a useful mass-preserving approximation, but not an exact solution of this nonlinear transition equation.
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