Transient Free Surface Flow Past a Two-dimensional Flat Stern

2015 ◽  
Vol 4 (3) ◽  
pp. 353-369 ◽  
Author(s):  
Osama Ogilat ◽  
Yury Stepanyants
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Two Dimensional ◽  
Flow Past

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

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.

Free-surface flow past oscillating singularities at resonant frequency

1982 ◽  
Vol 120 ◽  
pp. 139-154 ◽  
Author(s):  
G. Dagan ◽  
T. Miloh
Keyword(s):  
Free Surface ◽  
Resonant Frequency ◽  
Free Surface Flow ◽  
Generalized Solution ◽  
Surface Flow ◽  
Third Order ◽  
Large Wave ◽  
Drag Forces ◽  
Flow Past ◽  
Lift And Drag

This paper analyses the problem of a flow past an oscillating body moving with constant velocity, below and parallel to a free surface. Special attention is given to frequencies of oscillation in the neighbourhood of the critical frequency ωc= 0.25 g/U, where the classical linearized solution yields infinitely large wave amplitude. As a result both the lift and drag forces acting on the oscillating body at the resonant frequency are singular. It is demonstrated in the paper how this resonance is elimi- nated by considering higher-order free-surface effects, in particular the interaction between the first- and third-order terms. The resulting generalized solution yields finite wave amplitudes at the resonant frequency which are O(ε½) and O(εlogε) for 2 and 3 dimensions respectively. Here 6 is a measure of the singularity strength. It is also shown that inclusion of third-order terms causes a shift in the wavenumber and group velocity which eliminates the singularity in the lift and drag expressions at the resonant frequency. These results are illustrated by computing the lift and drag experienced by a submerged oscillating horizontal doublet in a uniform flow.

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