Dynamic boundary condition for an inviscid interface
= Dynamic boundary condition for an inviscid interface
At an interface between two inviscid fluids without surface tension, the pressure is continuous. For potential flows of equal density, the <Unsteady Bernoulli equation> therefore equates
$$
\partial_t\phi+\frac12|\nabla\phi|^2
$$
on the two sides, up to a removable function of time.