Past exam of the topics in fluid mechanics course of the University of Oxford / 2023 / 2 / c / i / Solution

Return to dimensional variables. The river at base level imposes the drained boundary condition, while the right-hand end is impermeable:As long as the right-hand end remains wet, the latter is $h_x(L,t)=0$. The initial condition for the drought is the height profile inherited at $t=t^{\ast }$; stopping rainfall changes the forcing but does not instantaneously remove stored water.