The unsteady fully nonlinear free-surface flow due to an impulsively
started
submerged point sink is studied in the context of incompressible potential
flow. For
a fixed (initial) submergence h of the point sink in otherwise
unbounded fluid, the
problem is governed by a single non-dimensional physical parameter, the
Froude number,
[Fscr ]≡Q/4π(gh5)1/2,
where Q is the (constant) volume flux rate and g the
gravitational acceleration. We assume axisymmetry and perform a numerical
study
using a mixed-Eulerian–Lagrangian boundary-integral-equation scheme.
We conduct
systematic simulations varying the parameter [Fscr ]
to obtain a complete quantification of the solution of the problem. Depending
on
[Fscr ], there are three distinct flow regimes: (i)
[Fscr ]<[Fscr ]1≈0.1924 – a ‘sub-critical’
regime marked by a damped wave-like behaviour of the free surface which
reaches an asymptotic steady state; (ii)
[Fscr ]1<[Fscr ]<[Fscr ]2≈0.1930 – the
‘trans-critical’ regime characterized by a reversal of
the downward motion of the free surface above the sink, eventually developing
into
a sharp upward jet; (iii) [Fscr ]>[Fscr ]2 – a ‘super-critical’
regime marked by the cusp-like
collapse of the free surface towards the sink. Mechanisms behind such flow
behaviour
are discussed and hydrodynamic quantities such as pressure, power and force
are
obtained in each case. This investigation resolves the question of validity
of a
steady-state assumption for this problem and also shows that a small-time
expansion may
be inadequate for predicting the eventual behaviour of the flow.
Three-dimensional free-surface flow over arbitrary bottom topography