A line sink in a flowing stream with surface tension effects

Abstract

We examine a problem in which a line sink causes a disturbance to an otherwise uniform flowing stream of infinite depth. We consider the fully non-linear problem with the inclusion of surface tension and find the maximum sink strength at which steady solutions exist for a given stream flow, before examining non-unique solutions. The addition of surface tension allows for a more thorough investigation into the characteristics of the solutions. The breakdown of steady solutions with surface tension appears to be caused by a curvature singularity as the flow rate approaches the maximum. The non-uniqueness in solutions is shown to occur for a range of parameter values in all cases with non-zero surface tension.

The effect of surface tension on free surface flow induced by a point sink in a fluid of finite depth

“…where This behaviour was described in more detail in the unbounded case by Hocking et al (2015). Larger values of truncation resulted in increasing wave activity on the surface and a decrease in the maximum Froude number.…”

“…tension was considered in Forbes & Hocking (1993), and withdrawal in the presence of a background flow by Holmes & Hocking (2015). In both cases non-uniqueness was found in the solution space.…”

“…A recent, more thorough analysis of the integral equation method was given in Hocking et al (2014), and it was shown that the limiting steady solutions occur at much lower values of flow rate than initial calculations suggest. Surface tension was included in Hocking et al (2015) and was found to have a regularizing effect on both the solutions and the existence space, so that much higher flow rates could be obtained with significant surface tension included.…”

Efficient computation of two‐dimensional steady free‐surface flows

“…For example, the number of mesh points typically used is roughly 500 < N < 2000. [30][31][32][33][34][35][36][37] The increased number of points can allow for a solution with much higher resolution or over a much larger domain. In an attempt to quantify the benefits of using a large number of grid points, we perform a brief convergence study.…”

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

“…In the two-dimensional case (line sink [4,9]), this was found to provide considerable information about the flows including nonuniqueness in the solution space. Holmes and Hocking [14] recently showed that this nonuniqueness also occurs when the submerged sink is situated in a flowing stream.…”