scholarly journals Steady two-dimensional free-surface flow over semi-infinite and finite-length corrugations in an open channel

2018 ◽  
Vol 3 (11) ◽  
Author(s):  
Jack S. Keeler ◽  
Benjamin J. Binder ◽  
Mark G. Blyth
Keyword(s):  
Free Surface ◽  
Finite Length ◽  
Open Channel ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Two Dimensional

scholarly journals Steady Two-Dimensional Free-Surface Flow Past Disturbances in an Open Channel: Solutions of the Korteweg–De Vries Equation and Analysis of the Weakly Nonlinear Phase Space

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 24 ◽  
Author(s):  
Benjamin Binder
Keyword(s):  
Free Surface ◽  
Open Channel ◽  
Kdv Equation ◽  
Bottom Topography ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Two Dimensional ◽  
Model Approximation ◽  
Flow Past ◽  
Channel Bottom

Two-dimensional free-surface flow past disturbances in an open channel is a classical problem in hydrodynamics—a problem that has received considerable attention over the last two centuries (e.g., see Lamb’s Treatise, 1879). With traces back to Russell’s experimental observations of the Great Wave of Translation in 1834, Korteweg and de Vries (1895), and others, derived an unforced equation to describe the balance between nonlinearity and dispersion required to model the solitary wave. More recently, Akylas (1984) derived a forced KdV equation to model a pressure distribution on the free-surface (e.g., a ship). Since then, the forced KdV equation has been shown to be a useful model approximation for two-dimensional flow past disturbances in an open channel. In this paper, we review the stationary solutions of the forced KdV equation for four types of localised disturbances: (i) a flat plate separating two free surfaces; (ii) a compact bump, or dip in the channel bottom topography; (iii) a compact distribution of pressure on the free surface and (iv) a step-wise change in the otherwise constant horizontal level of the channel bottom topography. Moreover, Dias and Vanden-Broeck (2002) developed a phase plane method to analyse flow over a bump, and this general approach has also been applied to the three other types of forcing (see Binder et al., 2005–2015, and others). In this study, we use eleven basic flow types to classify the steady solutions of the forced KdV equation using the phase plane method. Additionally, considering solutions that are wave-free both far upstream and far downstream, we compare KdV model approximations of the uniform flow conditions in the far-field with exact solutions of the full problem. In particular, we derive a new KdV model approximation for the upstream dimensionless flow-rate which is conveniently given in terms of the known downstream dimensionless flow-rate.

Minimising wave drag for free surface flow past a two-dimensional stern

2011 ◽  
Vol 23 (7) ◽  
pp. 072101 ◽  
Author(s):  
Osama Ogilat ◽  
Scott W. McCue ◽  
Ian W. Turner ◽  
John A. Belward ◽  
Benjamin J. Binder
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Wave Drag ◽  
Surface Flow ◽  
Two Dimensional ◽  
Flow Past

Free Surface Flow over Obstacles at Subcritical Froude Numbers

1978 ◽  
Vol 5 (2) ◽  
pp. 89-94
Author(s):  
J.S.C. Tong ◽  
I.G. Currie
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Finite Length ◽  
Theoretical Approach ◽  
Wave Train ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Horizontal Surface ◽  
Lee Waves ◽  
The Mean

Experiments were carried out on free-surface flow over obstacles of finite length. The obstacles were located on the otherwise horizontal surface which contained the free-surface flow. The Froude number in each case was subcritical and resulted in a train of lee waves on the surface, downstream of the obstacles. The results confirm the predicted phenomenon of ‘upstream influence’ – that the mean upstream depth and the mean downstream depth should differ. Serious discrepancies between the observed results and the results from existing theories are noted, however. Not only is the amplitude of the lee waves at variance with the theory, but the phasing of the wave train, relative to the obstacle, is different. An alternative theoretical approach is proposed, the results from which are in much better agreement with the observed results.

Explicit Approximations for Calculating Potential Flow About a Body

1983 ◽  
Vol 27 (01) ◽  
pp. 1-12
Author(s):  
F. Noblesse ◽  
G. Triantafyllou
Keyword(s):  
Free Surface ◽  
Potential Flow ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Wave Resistance ◽  
Two Dimensional ◽  
Regular Waves ◽  
Practical Applications ◽  
Flow Problems ◽  
Unbounded Fluid

Several explicit approximations for calculating nonlifting potential flow about a body in an unbounded fluid are studied. These approximations are shown to be exact in the particular cases of flows due to translations of ellipsoids, and they are compared with the exact potential for two-dimensional flows about ogives in translatory motions. Two approximations, given by formulas (31) and (32) in the conclusion, appear to be of particular interest for practical applications, and they can be extended to free-surface flow problems, for example, ship wave resistance, and radiation and diffraction of regular waves by a body.

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