{c}

Condition (1b) is the <kinematic boundary condition>: surface particles remain on the moving free-surface graph. Condition (1c) is the <dynamic boundary condition for an inviscid interface> from unsteady <Bernoulli's equation>, with the surface pressure fixed at the atmospheric value and absorbed into the potential's time gauge. Condition (1d) is impermeability of the fixed horizontal bed, so its normal velocity vanishes.

Solution

Past exam of the probability, statistics and options I course of the University of Oxford / 2008 / K / 2 / i / Solution

 Solution (source code)