= Solution
Condition (1b) is the <kinematic boundary condition for a free-surface graph>[kinematic free-surface boundary condition]: fluid particles on the surface remain there, since the material derivative of $y-\eta(x,t)$ vanishes. Condition (1c) is the <dynamic boundary condition for an inviscid interface>[dynamic free-surface boundary condition], obtained from the unsteady Bernoulli equation with constant atmospheric pressure and a choice of potential gauge. Condition (1d) is <impermeability condition>[impermeability]: no normal flow through the horizontal bed.
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