A Note on Steady Flow Into a Submerged Point Sink

Abstract

The steady, axisymmetric flow induced by a point sink (or source) submerged in an unbounded inviscid fluid is computed. The resulting deformation of the free surface is obtained, and a limit of steady solutions is found that is quite different to those obtained in past work. More accurate solutions indicate that the old limiting flow rate was too high and, in fact, the breakdown of steady solutions at a lower flow rate is characterized by the appearance of spurious wavelets at the free surface.2010 Mathematics subject classification: 0102.

The effect of surface tension on free-surface flow induced by a point sink

“…As indicated above, the solutions for the case where surface tension approaches zero are identical to those obtained by Hocking et al [11]. The limiting steady value of F ≈ 3 is significantly lower than those obtained by Forbes and Hocking [3] (F ≈ 6.4) and Vanden Broeck and Keller [26] (F ≈ 5.4).…”

“…The numerical scheme is described in detail by Hocking et al [11]. For convenience, we briefly outline the derivation here.…”

“…In this work, we include the effect of surface tension, the addition of which not only adds an extra physical dimension to the problem bringing into context the earlier work without surface tension [3,26], but also has a regularizing effect on the calculations. A recent paper [11] showed that the maximum flow rate at which steady solutions to this problem exist was significantly over-estimated in the earlier work [3,26]. More accurate solutions indicate that as soon as small waves begin to form on the free surface, the steady solutions fail.…”

The Effect of Surface Tension on Free-Surface Flow Induced by a Point Sink

“…Forbes and others [3,11,12]. The numerical scheme is described in detail by Hocking et al [11]. For convenience, we briefly outline the derivation here.…”

“…A recent paper [11] showed that the maximum flow rate at which steady solutions to this problem exist was significantly over-estimated in the earlier work [3,26]. More accurate solutions indicate that as soon as small waves begin to form on the free surface, the steady solutions fail.…”