Super-critical withdrawal from a two-layer fluid through a line sink if the lower layer is of finite depth

Hocking, Graeme C.; Forbes, Lawrence K.

doi:10.1017/s0022112000002780

Cited by 32 publications

(14 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This method has been successfully applied in a number of different applications involving free-surface flows, see for example [6,7,14,15].…”

Section: Nonlinear Problem and Numerical Methodsmentioning

confidence: 99%

Waveless subcritical flow past symmetric bottom topography

Holmes¹,

Hocking²,

Forbes³

et al. 2012

Eur. J. Appl. Math

Self Cite

View full text Add to dashboard Cite

The subcritical flow of a stream over a bottom obstruction or depression is considered with particular interest in obtaining solutions with no downstream waves. In the linearised problem this can always be achieved by superposition of multiple obstructions, but it is not clear whether this is possible in a full nonlinear problem. Solutions computed here indicate that there is an effective nonlinear superposition principle at work as no special shape modifications were required to obtain wave-cancelling solutions. Waveless solutions corresponding to one or more trapped waves are computed at a range of different Froude numbers and are shown to provide a rather elaborate mosaic of solution curves in parameter space when both negative and positive obstruction heights are included.

show abstract

“…This method has been successfully applied in a number of different applications involving free-surface flows, see for example [6,7,14,15].…”

Section: Nonlinear Problem and Numerical Methodsmentioning

confidence: 99%

Waveless subcritical flow past symmetric bottom topography

Holmes¹,

Hocking²,

Forbes³

et al. 2012

Eur. J. Appl. Math

Self Cite

View full text Add to dashboard Cite

show abstract

“…For our study, the most relevant and suggestive results are that twodimensional withdrawal differs significantly from axisymmetric withdrawal (Forbes et al (2004); Stokes et al (2005)). Also, in both 2D and axisymmetric withdrawal, whether selective withdrawal or full entrainment is realized can depend crucially on the initial conditions which determine transient evolution of the interface, instead of being solely determined by the boundary conditions (Hocking & Forbes (2001)). …”

Section: Inviscid Selective Withdrawalmentioning

confidence: 99%

Liquid interfaces in viscous straining flows: numerical studies of the selective withdrawal transition

Berkenbusch¹,

Cohen²,

Zhang³

2008

J. Fluid Mech.

View full text Add to dashboard Cite

This paper presents a numerical analysis of the transition from selective withdrawal to viscous entrainment. In our model problem, an interface between two immiscible layers of equal viscosity is deformed by an axisymmetric withdrawal flow, which is driven by a point sink located some distance above the interface in the upper layer. We find that steady-state hump solutions, corresponding to selective withdrawal of liquid from the upper layer, cease to exist above a threshold withdrawal flux, and that this transition corresponds to a saddle-node bifurcation for the hump solutions. Numerical results on the shape evolution of the steady-state interface are compared against previous experimental measurements. We find good agreement where the data overlap. However, the numerical results' larger dynamic range allows us to show that the large increase in the curvature of the hump tip near transition is not consistent with an approach towards a power-law cusp shape, an interpretation previously suggested from inspection of the experimental † mkb@uchicago.edu ‡ ic64@cornell.edu ¶ wzhang@uchicago.edu measurements alone. Instead the large increase in the curvature at the hump tip reflects a logarithmic coupling between the overall height of the hump and the curvature at the tip of the hump.

show abstract

“…However, this limiting value does not always coincide with the critical drawdown flow rate as described above, and solutions with a downward cusp appear to exist at a somewhat higher value. Cusped solutions were originally thought to be the critical drawdown flows, and strong evidence for this was given by Forbes et al [7,14,15]. In spite of these results, uncertainty remains about the critical flows due to poor comparison with experiment and the existence of multiple cusped solutions for certain geometries, as seen in the work of Vanden-Broeck and Keller [26] and Hocking [12,13].…”

Section: Introductionmentioning

confidence: 99%

A rational approximation to the evolution of a free surface during fluid withdrawal through a point sink

Hocking¹,

Stokes²,

Forbes³

2010

ANZIAMJ

View full text Add to dashboard Cite

The time varying flow in which fluid is withdrawn from a reservoir through a point sink of variable strength beneath a free surface is considered. Asymptotic techniques are used to derive an approximate solution to the flow that is valid at intermediate times, giving a simple rational approximation to track changes in the free surface for any temporal variations in the sink strength. Comparisons with numerical simulations are given, showing that the approximation has wide applicability.

show abstract

Super-critical withdrawal from a two-layer fluid through a line sink if the lower layer is of finite depth

Cited by 32 publications

References 16 publications

Waveless subcritical flow past symmetric bottom topography

Waveless subcritical flow past symmetric bottom topography

Liquid interfaces in viscous straining flows: numerical studies of the selective withdrawal transition

A rational approximation to the evolution of a free surface during fluid withdrawal through a point sink

Contact Info

Product

Resources

About