 Solution

ID: 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:

h (0, t) = 0, q (L, t) = - K h (L, t) h_{x} (L, t) = 0.

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^{*}

; stopping rainfall changes the forcing but does not instantaneously remove stored water.

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