Coupled problem of dam-break flow
Abstract
Initial stage of the flow with a free surface generated by a vertical
wall moving from a liquid of finite depth in a gravitational field is
studied. The liquid is inviscid and incompressible, and its flow is
irrotational. Initially the liquid is at rest. The wall starts to move
from the liquid with a constant acceleration.
It is shown that, if the acceleration of the plate is small, then the
liquid free surface separates from the wall only along an
exponentially small interval. The interval on the wall, along which
the free surface instantly separates for moderate acceleration of the
wall, is determined by using the condition that the displacements of
liquid particles are finite. During the initial stage the original
problem of hydrodynamics is reduced to a mixed boundary-value problem
with respect to the velocity field with unknown in advance position of
the separation point. The solution of this
problem is derived in terms of complete elliptic integrals. The
initial shape of the separated free surface is calculated and compared
with that predicted by the small-time solution of the dam break
problem. It is shown that the free surface at the separation point is
orthogonal to the moving plate.
Initial acceleration of a dam, which is suddenly released, is calculated.