Diffraction of sea waves by a slender body. Part 2. Water of finite depth

1990 ◽  
Vol 216 ◽  
pp. 133-160 ◽  
Author(s):  
J. A. P. Aranha ◽  
C. A. Martins
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Body Part ◽  
Finite Depth ◽  
Second Order ◽  
Slender Body ◽  
Sea Waves ◽  
Finite Water Depth

A uniformly valid theory (all wavelengths and angles of incidence) for the diffraction of sea waves by a slender body, correct to second order in the slenderness parameter, has been derived for the shallow-water limit. This theory is now extended to the finite water depth case, with the same results and accuracy.

Experimental Investigation of Trimaran Models in Shallow Water

2014 ◽  
Vol 30 (02) ◽  
pp. 66-78
Author(s):  
Mark Pavkov ◽  
Morabito Morabitob
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Critical Speed ◽  
Water Effect ◽  
Finite Water Depth ◽  
Speed Regime ◽  
Displacement Speed ◽  
Littoral Combat Ship ◽  
Shallow Water Effect ◽  
The U.S

Experiments were conducted at the U.S. Naval Academy's Hydromechanics Laboratory to determine the effect of finite water depth on the resistance, heave, and trim of two different trimaran models. The models were tested at the same length to water depth ratios over a range of Froude numbers in the displacement speed regime. The models were also towed in deep water for comparison. Additionally, the side hulls were adjusted to two different longitudinal positions to investigate possible differences resulting from position. Near critical speed, a large increase in resistance and sinkage was observed, consistent with observations of conventional displacement hulls. The data from the two models are scaled up to a notional 125-m length to illustrate the effects that would be observed for actual ships similar in size to the U.S. Navy's Independence Class Littoral Combat Ship. Faired plots are developed to allow for rapid estimation of shallow water effect on trimaran resistance and under keel clearance. An example is provided.

Nonlinear Crest Height Distribution in Three-Dimensional Ocean Waves

2008 ◽  
Author(s):  
Felice Arena ◽  
Alfredo Ascanelli
Keyword(s):  
Water Depth ◽  
Three Dimensional ◽  
Ocean Waves ◽  
Second Order ◽  
Wave Crest ◽  
Height Distribution ◽  
Order Model ◽  
Rayleigh Law ◽  
Wave Trough ◽  
Finite Water Depth

The interest and the studies on nonlinear waves are increased recently for their importance in the interaction with floating and fixed bodies. It is also well known that nonlinearities influence wave crest and wave trough distributions, both deviating from Rayleigh law. In this paper a theoretical crest distribution is obtained taking into account the extension of Boccotti’s Quasi Determinism theory, up to the second order for the case of three-dimensional waves, in finite water depth. To this purpose the Fedele & Arena [2005] distribution is generalized to three-dimensional waves on an arbitrary water depth. The comparison with Forristall second order model shows the theoretical confirmation of his conclusion: the crest distribution in deep water for long-crested and short crested waves are very close to each other; in shallow water the crest heights in three dimensional waves are greater than values given by long-crested model.

Linear Evolution of a Narrow-Banded Surface Gravity Wavepacket Over an Infinite Step

2019 ◽  
Author(s):  
Yan Li ◽  
Thomas A. A. Adcock ◽  
Ton S. van den Bremer
Keyword(s):  
Water Depth ◽  
Evolution Equations ◽  
Multiple Scales ◽  
Fundamental Problem ◽  
Wave Theory ◽  
Second Order ◽  
Order Effects ◽  
Linear Evolution ◽  
Finite Water Depth ◽  
Higher Order Effects

Abstract This paper focuses on the classical and fundamental problem of waves propagating over an infinite step in finite water depth. Specifically, this paper aims to extend classical narrow-banded wave theory for constant water depth which uses a multiple-scales expansion to the case of an abrupt change in the water depth, known as an infinite step. This paper derives the linear evolution equations and is the first step towards the calculation of second-order and higher-order effects for wavepackets travelling over a step using commonly employed envelope-type evolution equations, in particular the bound sub- and super-harmonics at second order.

scholarly journals Experimental particle paths and drift velocity in steep waves at finite water depth

2016 ◽  
Vol 810 ◽  
Author(s):  
John Grue ◽  
Jostein Kolaas
Keyword(s):  
Drift Velocity ◽  
Water Depth ◽  
Order Theory ◽  
Second Order ◽  
Velocity Shear ◽  
Vertical Position ◽  
Functional Relationships ◽  
Finite Water Depth ◽  
Particle Paths ◽  
Experimental Particle

The Lagrangian paths, horizontal Lagrangian drift velocity, $U_{L}$, and the Lagrangian excess period, $T_{L}-T_{0}$, where $T_{L}$ is the Lagrangian period and $T_{0}$ the Eulerian linear period, are obtained by particle tracking velocimetry (PTV) in non-breaking periodic laboratory waves at a finite water depth of $h=0.2~\text{m}$, wave height of $H=0.49h$ and wavenumber of $k=0.785/h$. Both $U_{L}$ and $T_{L}-T_{0}$ are functions of the average vertical position of the paths, $\bar{Y}$, where $-1<\bar{Y}/h<0$. The functional relationships $U_{L}(\bar{Y})$ and $T_{L}-T_{0}=f(\bar{Y})$ are very similar. Comparisons to calculations by the inviscid strongly nonlinear Fenton method and the second-order theory show that the streaming velocities in the boundary layers below the wave surface and above the fluid bottom contribute to a strongly enhanced forward drift velocity and excess period. The experimental drift velocity shear becomes more than twice that obtained by the Fenton method, which again is approximately twice that of the second-order theory close to the surface. There is no mass flux of the periodic experimental waves and no pressure gradient. The results from a total number of 80 000 experimental particle paths in the different phases and vertical positions of the waves show a strong collapse. The particle paths are closed at the two vertical positions where $U_{L}=0$.

scholarly journals SHOALING PROPERTIES OF BOUNDED LONG WAVES

1984 ◽  
Vol 1 (19) ◽  
pp. 54 ◽  
Author(s):  
E.P.D. Mansard ◽  
V. Barthel
Keyword(s):  
Shallow Water ◽  
Water Depth ◽  
Second Order ◽  
Long Waves ◽  
Experimental Results ◽  
Wave Groups ◽  
Good Insight ◽  
Set Up ◽  
Theoretical Considerations ◽  
Insight Into

Group bounded long waves which appear as a set-down under a group of high waves and a set-up in between groups are well described for constant water depth. However, their propagation into shallow water and their interaction with the constituent wave groups are not well understood and theoretically described yet. Therefore, model investigations were carried out to study shoaling properties of these second order waves in terms of amplitudes and phases. The tests give a good insight into the phenomenon and suggest distinct shoaling properties. Moreover, experimental results provide a valuable basis for future theoretical considerations.

On Zakharov's kernel and the interaction of non-collinear wavetrains in finite water depth

2009 ◽  
Vol 639 ◽  
pp. 433-442 ◽  
Author(s):  
MICHAEL STIASSNIE ◽  
ODIN GRAMSTAD
Keyword(s):  
Gravity Waves ◽  
Water Depth ◽  
Finite Depth ◽  
Mean Flow ◽  
Finite Water Depth ◽  
Physical Insight

The non-uniqueness of Zakharov's kernel T(ka, kb, ka, kb) for gravity waves in water of finite depth is resolved. This goal is achieved by the physical insight gained from the study of the induced mean flow generated by two interacting wavetrains.

Shallow Water Intercomparison of Wave Models — Part I Three Different Concepts to Model Surface Waves in Finite Water Depth

1985 ◽  
pp. 201-205 ◽  
Author(s):  
E. Bouws ◽  
J. J. Ephraums ◽  
J. A. Ewing ◽  
P. E. Francis ◽  
H. Günther ◽  
...  
Keyword(s):  
Surface Waves ◽  
Shallow Water ◽  
Water Depth ◽  
Model Surface ◽  
Finite Water Depth ◽  
Wave Models
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