Taylor instability of a non-uniform free-surface flow

1975 ◽  
Vol 67 (1) ◽  
pp. 113-123 ◽  
Author(s):  
G. Dagan
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Three Dimensional ◽  
Free Surface Flow ◽  
Normal Pressure ◽  
Surface Flow ◽  
Taylor Instability ◽  
Radius Of Curvature ◽  
Order Of Magnitude ◽  
Gaseous Bubbles

The evolution of a small disturbance in a three-dimensional steady free-surface flow is investigated. The radius of curvature of the free surface and the length scale characterizing the non-uniformity of the velocity are assumed to be of the same order of magnitude. It is shown that the local rate of growth of the amplitude of the disturbance depends on both the normal pressure gradient (as in the case of Taylor instability) and the rate of strain on the free surface. Application of the theory to rising gaseous bubbles and gravity water waves is discussed.

scholarly journals A topological study of gravity free-surface waves generated by bluff bodies using the method of steepest descents

2016 ◽  
Vol 472 (2191) ◽  
pp. 20150833 ◽  
Author(s):  
Philippe H. Trinh
Keyword(s):  
Free Surface ◽  
Riemann Surface ◽  
Surface Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Free Surface Flow ◽  
Surface Flow ◽  
The Body ◽  
Bluff Bodies ◽  
Free Surface Waves

The standard analytical approach for studying steady gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its dimensions. In this paper, a methodology that avoids any such geometrical simplification is presented for the case of steady-state flows at low speeds. The approach is made possible through a reduction of the water-wave equations to a complex-valued integral equation that can be studied using the method of steepest descents. The main result is a theory that establishes a correspondence between different bluff-bodied free-surface flow configurations, with the topology of the Riemann surface formed by the steepest descent paths. Then, when a geometrical feature of the body is modified, a corresponding change to the Riemann surface is observed, and the resultant effects to the water waves can be derived. This visual procedure is demonstrated for the case of two-dimensional free-surface flow past a surface-piercing ship and over an angled step in a channel.

scholarly journals Flow from a source above a sloping base

2020 ◽  
Vol 61 ◽  
pp. C75-C88
Author(s):  
Shaymaa Mukhlif Shraida ◽  
Graeme Hocking
Keyword(s):  
Free Surface ◽  
Flow Rate ◽  
Water Waves ◽  
Line Source ◽  
Free Surface Flow ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Theoretical Research ◽  
Line Sink

We consider the outflow of water from the peak of a triangular ridge into a channel of finite depth. Solutions are computed for different flow rates and bottom angles. A numerical method is used to compute the flow from the source for small values of flow rate and it is found that there is a maximum flow rate beyond which steady solutions do not seem to exist. Limiting flows are computed for each geometrical configuration. One application of this work is as a model of saline water being returned to the ocean after desalination. References Craya, A. ''Theoretical research on the flow of nonhomogeneous fluids''. La Houille Blanche, (1):22–55, 1949. doi:10.1051/lhb/1949017 Dun, C. R. and Hocking, G. C. ''Withdrawal of fluid through a line sink beneath a free surface above a sloping boundary''. J. Eng. Math. 29:1–10, 1995. doi:10.1007/bf00046379 Hocking, G. ''Cusp-like free-surface flows due to a submerged source or sink in the presence of a flat or sloping bottom''. ANZIAM J. 26:470–486, 1985. doi:10.1017/s0334270000004665 Hocking, G. C. and Forbes, L. K. ''Subcritical free-surface flow caused by a line source in a fluid of finite depth''. J. Eng. Math. 26:455-466, 1992. doi:10.1007/bf00042763 Hocking, G. C. ''Supercritical withdrawal from a two-layer fluid through a line sink", J. Fluid Mech. 297:37–47, 1995. doi:10.1017/s0022112095002990 Hocking, G. C., Nguyen, H. H. N., Forbes, L. K. and Stokes,T. E. ''The effect of surface tension on free surface flow induced by a point sink''. ANZIAM J., 57:417–428, 2016. doi:10.1017/S1446181116000018 Landrini, M. and Tyvand, P. A. ''Generation of water waves and bores by impulsive bottom flux'', J. Eng. Math. 39(1–4):131-170, 2001. doi:10.1023/A:1004857624937 Lustri, C. J., McCue, S. W. and Chapman, S. J. ''Exponential asymptotics of free surface flow due to a line source''. IMA J. Appl. Math., 78(4):697–713, 2013. doi:10.1093/imamat/hxt016 Stokes, T. E., Hocking, G. C. and Forbes, L.K. ''Unsteady free surface flow induced by a line sink in a fluid of finite depth'', Comp. Fluids, 37(3):236–249, 2008. doi:10.1016/j.compfluid.2007.06.002 Tuck, E. O. and Vanden-Broeck, J.-M. ''A cusp-like free-surface flow due to a submerged source or sink''. ANZIAM J. 25:443–450, 1984. doi:10.1017/s0334270000004197 Vanden-Broeck, J.-M., Schwartz, L. W. and Tuck, E. O. ''Divergent low-Froude-number series expansion of nonlinear free-surface flow problems". Proc. Roy. Soc. A., 361(1705):207–224, 1978. doi:10.1098/rspa.1978.0099 Vanden-Broeck, J.-M. and Keller, J. B. ''Free surface flow due to a sink'', J. Fluid Mech, 175:109–117, 1987. doi:10.1017/s0022112087000314 Yih, C.-S. Stratified flows. Academic Press, New York, 1980. doi:10.1016/B978-0-12-771050-1.X5001-3

scholarly journals Experiments and Simulations of Free-Surface Flow behind a Finite Height Rigid Vertical Cylinder

Fluids ◽  
2021 ◽  
Vol 6 (10) ◽  
pp. 367
Author(s):  
Valentin Ageorges ◽  
Jorge Peixinho ◽  
Gaële Perret ◽  
Ghislain Lartigue ◽  
Vincent Moureau
Keyword(s):  
Free Surface ◽  
Numerical Study ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Free Surface Flow ◽  
Air Entrainment ◽  
Surface Flow ◽  
Finite Height ◽  
Wave Patterns ◽  
Different Diameters

We present the results of a combined experimental and numerical study of the free-surface flow behind a finite height rigid vertical cylinder. The experiments measure the drag and the wake angle on cylinders of different diameters for a range of velocities corresponding to 30,000 <Re< 200,000 and 0.2<Fr<2 where the Reynolds and Froude numbers are based on the diameter. The three-dimensional large eddy simulations use a conservative level-set method for the air-water interface, thus predicting the pressure, the vorticity, the free-surface elevation and the onset of air entrainment. The deep flow looks like single phase turbulent flow past a cylinder, but close to the free-surface, the interaction between the wall, the free-surface and the flow is taking place, leading to a reduced cylinder drag and the appearance of V-shaped surface wave patterns. For large velocities, vortex shedding is suppressed in a layer region behind the cylinder below the free surface. The wave patterns mostly follow the capillary-gravity theory, which predicts the crest lines cusps. Interestingly, it also indicates the regions of strong elevation fluctuations and the location of air entrainment observed in the experiments. Overall, these new simulation results, drag, wake angle and onset of air entrainment, compare quantitatively with experiments.

scholarly journals Influence of the hydrofoil inclination angle at free surface flow around junctions

2020 ◽  
Vol 43 ◽  
pp. 103-108
Author(s):  
Costel Ungureanu ◽  
Costel Iulian Mocanu
Keyword(s):  
Boundary Layer ◽  
Free Surface ◽  
Bluff Body ◽  
Three Dimensional ◽  
Free Surface Flow ◽  
Breaking Waves ◽  
Surface Flow ◽  
Vortex Structures ◽  
The Body ◽  
Flow Topology

"Free surface flow is a hydrodynamic problem with a seemingly simple geometric configuration but with a flow topology complicated by the pressure gradient due to the presence of the obstacle, the interaction between the boundary layer and the free surface, turbulence, breaking waves, surface tension effects between water and air. As the ship appendages become more and more used and larger in size, the general understanding of the flow field around the appendages and the junction between them and the hull is a topical issue for naval hydrodynamics. When flowing with a boundary layer, when the streamlines meet a bluff body mounted on a solid flat or curved surface, detachments appear in front of it due to the blocking effect. As a result, vortex structures develop in the fluid, also called horseshoe vortices, the current being one with a completely three-dimensional character, complicated by the interactions between the boundary layer and the vortex structures thus generated. Despite the importance of the topic, the literature records the lack of coherent methods for investigating free surface flow around junctions, the lack of consistent studies on the influence of the inclination of the profile mounted on the body. As a result, this paper aims to systematically study the influence of profile inclination in respect to the support plate."

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