= Rain-fed aquifer similarity solution
{title2=$h=t f(x/t)$}
For the dimensionless rainfall-driven <Boussinesq equation for an unconfined aquifer>, $h_t=(hh_x)_x+1$, balancing every time power in $h=t^af(x/t^b)$ gives $a=b=1$. The <similarity profile> obeys $(ff')'+\eta f'-f+1=0$. A river drained to base level gives $f(0)=0$, while undrained storage far away gives $f(\infty)=1$. The solution approximates a finite <aquifer> before its drainage-affected length reaches the far boundary. If $J=\lim_{\eta\downarrow0}ff'>0$, the dimensional drainage flux is $\sqrt K R^{3/2}Jt/\phi$.
Back to article page
