A Comparative Study of Nonlinear Shallow-Water Wave Loads on a Submerged Horizontal Box

2014 ◽  
Author(s):  
Masoud Hayatdavoodi ◽  
R. Cengiz Ertekin
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Wave Forces ◽  
Two Dimensional ◽  
Wave Loads ◽  
Laboratory Measurements ◽  
Linear Solution ◽  
Coastal Bridges ◽  
Inviscid Incompressible Fluid ◽  
Level I

This paper is concerned with calculations of the two-dimensional nonlinear vertical and horizontal forces and overturning moment due to the unsteady flow of an inviscid, incompressible fluid over a fully-submerged horizontal, fixed box. The problem is approached on the basis of the Level I Green-Naghdi (GN) theory of shallow-water waves. The main objective of this paper is to present a comparison of the solitary and cnoidal wave loads calculated by use of the GN equations, with those computed by Euler’s equations and the recent laboratory measurements, and also with a linear solution of the problem for small-amplitude waves. The results show a remarkable similarity between the GN and Euler’s models and the laboratory measurements. In particular, the calculations predict that the thickness of the box has no effect on the vertical forces and only a slight influence on the two-dimensional horizontal positive force. The calculations also predict that viscosity of the fluid has a small effect on these loads. The results have applications to various physical problems such as wave forces on submerged coastal bridges and submerged breakwaters.

Nonlinear Wave Loads on a Submerged Deck by the Green–Naghdi Equations

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Masoud Hayatdavoodi ◽  
R. Cengiz Ertekin
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Periodic Wave ◽  
Wave Forces ◽  
Two Dimensional ◽  
Wave Loads ◽  
Laboratory Measurements ◽  
Coastal Bridges ◽  
Inviscid Incompressible Fluid ◽  
Level I

We present a comparative study of the two-dimensional linear and nonlinear vertical and horizontal wave forces and overturning moment due to the unsteady flow of an inviscid, incompressible fluid over a fully submerged horizontal, fixed deck in shallow-water. The problem is approached on the basis of the level I Green–Naghdi (G–N) theory of shallow-water waves. The main objective of this paper is to present a comparison of the solitary and periodic wave loads calculated by use of the G–N equations, with those computed by the Euler equations and the existing laboratory measurements, and also with linear solutions of the problem for small-amplitude waves. The results show a remarkable similarity between the G–N and the Euler solutions and the laboratory measurements. In particular, the calculations predict that the thickness of the deck, if it is not “too thick,” has no effect on the vertical forces and has only a slight influence on the two-dimensional horizontal positive force. The calculations also predict that viscosity of the fluid has a small effect on these loads. The results have applications to various physical problems such as wave forces on submerged coastal bridges and submerged breakwaters.

Manoeuvring Study of a Container Ship in Shallow Water Waves

2018 ◽  
Author(s):  
Manases Tello Ruiz ◽  
Marc Mansuy ◽  
Guillaume Delefortrie ◽  
Marc Vantorre
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Numerical Study ◽  
Scale Model ◽  
Wave Forces ◽  
Shallow Water Waves ◽  
The North ◽  
Captive Model Tests ◽  
Calm Water ◽  
Large Container

When approaching or leaving a port a ship often needs to perform manoeuvres in the presence of waves. At the same time the water depth is still limited for deep drafted vessels. For manoeuvring simulation purposes this requires a manoeuvring model which includes phenomena such as short crested waves and squat effects. The present paper addresses the manoeuvring problem in shallow water waves numerically and experimentally. The numerical study is conducted by means of potential theory, incorporating first and second order exciting wave forces, and their superposition to the calm water manoeuvring models. The applicability of such an approach is also investigated. The experimental work has been conducted at Flanders Hydraulics Research (in cooperation with Ghent University) with a scale model of an ultra large container vessel. Captive model tests comprise harmonic yaw tests and steady straight line tests with and without waves, at different forward speeds, wave frequencies and amplitudes, in head and following waves. Waves are chosen to represent conditions commonly met by ships in the Belgian coastal zone of the North Sea.

scholarly journals On the Benjamin–Lighthill conjecture for water waves with vorticity

2017 ◽  
Vol 825 ◽  
pp. 961-1001 ◽  
Author(s):  
V. Kozlov ◽  
N. Kuznetsov ◽  
E. Lokharu
Keyword(s):  
Water Waves ◽  
Finite Depth ◽  
Two Dimensional ◽  
Constant Depth ◽  
Lipschitz Continuous ◽  
Vorticity Distribution ◽  
Inviscid Incompressible Fluid ◽  
Two Dimensional Flow ◽  
Wave Heights ◽  
Gravity Driven

We consider the nonlinear problem of steady gravity-driven waves on the free surface of a two-dimensional flow of an inviscid, incompressible fluid (say, water). The water motion is supposed to be rotational with a Lipschitz continuous vorticity distribution, whereas the flow of finite depth is assumed to be unidirectional. We verify the Benjamin–Lighthill conjecture for flows with values of Bernoulli’s constant close to the critical one. For this purpose it is shown that a set of near-critical waves consists only of Stokes and solitary waves provided their slopes are bounded by a constant. Moreover, the subset of waves with crests located on a fixed vertical is uniquely parametrised by the flow force, which varies between its values for the supercritical and subcritical shear flows of constant depth. There exists another parametrisation for this set; it involves wave heights varying between the constant depth of the subcritical shear flow and the height of a solitary wave.

Two-dimensional periodic waves in shallow water

1989 ◽  
Vol 209 ◽  
pp. 567-589 ◽  
Author(s):  
Joe Hammack ◽  
Norman Scheffner ◽  
Harvey Segur
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Two Dimensional ◽  
Reasonable Accuracy ◽  
Kp Equation ◽  
Petviashvili Equation ◽  
Stable Manner ◽  
Genus 2 ◽  
Surface Patterns ◽  
The Waves

Experimental data are presented that demonstrate the existence of a family of gravitational water waves that propagate practically without change of form on the surface of shallow water of uniform depth. The surface patterns of these waves are genuinely two-dimensional and fully periodic, i.e. they are periodic in two spatial directions and in time. The amplitudes of these waves need not be small; their form persists even up to breaking. The waves are easy to generate experimentally, and they are observed to propagate in a stable manner, even when perturbed significantly. The measured waves are described with reasonable accuracy by a family of exact solutions of the Kadomtsev-Petviashvili equation (KP solutions of genus 2) over the entire parameter range of the experiments, including waves well outside the putative range of validity of the KP equation. These genus-2 solutions of the KP equation may be viewed as two-dimensional generalizations of cnoidal waves.

scholarly journals NUMERICAL MODELLING OF SOLITARY AND FOCUSED WAVE FORCES ON COASTAL-BRIDGE DECK

2018 ◽  
pp. 12 ◽  
Author(s):  
Rameeza Moideen ◽  
Manasa Ranjan Behera ◽  
Arun Kamath ◽  
Hans Bihs
Keyword(s):  
Water Waves ◽  
Bridge Deck ◽  
Experimental Studies ◽  
Wave Forces ◽  
Extreme Waves ◽  
Shallow Water Waves ◽  
Wave Impact ◽  
Coastal Bridges ◽  
Focused Wave ◽  
The Impact

In the recent past, coastal bridges have been subjected to critical damage due to extreme wave attacks during natural calamities like storm surge and tsunami. Various numerical and experimental studies have suggested different empirical equations for wave impact on deck. However, they do not account the velocities of the wave type properly, which requires a detailed investigation to study the impact of extreme waves on decks. Solitary wave assumption is more suitable for shallow water waves, while the focused wave has been used widely to represent extreme waves. The present study aims to investigate the focused wave impact on coastal bridge deck using REEF3D (Bihs et al., 2016).

scholarly journals Comment on “Two-dimensional third-and fifth-order nonlinear evolution equations for shallow water waves with surface tension” [Nonlinear Dyn,  doi:10.1007/s11071-017-3938-7]

2021 ◽  
Author(s):  
Piotr Rozmej ◽  
Anna Karczewska
Keyword(s):  
Surface Tension ◽  
Shallow Water ◽  
Water Waves ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Two Dimensional ◽  
Shallow Water Waves ◽  
Small Parameters ◽  
Fifth Order

AbstractThe authors of the paper “Two-dimensional third-and fifth-order nonlinear evolution equations for shallow water waves with surface tension” Fokou et al. (Nonlinear Dyn 91:1177–1189, 2018) claim that they derived the equation which generalizes the KdV equation to two space dimensions both in first and second order in small parameters. Moreover, they claim to obtain soliton solution to the derived first-order (2+1)-dimensional equation. The equation has been obtained by applying the perturbation method Burde (J Phys A: Math Theor 46:075501, 2013) for small parameters of the same order. The results, if correct, would be significant. In this comment, it is shown that the derivation presented in Fokou et al. (Nonlinear Dyn 91:1177–1189, 2018) is inconsistent because it violates fundamental properties of the velocity potential. Therefore, the results, particularly the new evolution equation and the dynamics that it describes, bear no relation to the problem under consideration.

Hydroelastic Response of a Floating Mat-Type Structure in Oblique, Shallow-Water Waves

1999 ◽  
Vol 43 (04) ◽  
pp. 241-254
Author(s):  
R. Cengiz Ertekin ◽  
Jang Whan Kim
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Wave Equations ◽  
Plate Theory ◽  
Integral Equation Method ◽  
Field Method ◽  
Boundary Integral ◽  
Incoming Wave ◽  
Level I ◽  
Hydroelastic Response

The linear, Level I Green-Naghdi (GN) theory is developed to study the hydroelastic behavior of a rectangular airport or runway whose draft is "small" and which floats in a near-shore area. The new theoretical and numerical model uses the linear, shallow-water wave equations of the GN type for the fluid dynamics and the thin-plate theory for the structural dynamics. The governing equations are matched at the juncture boundary and the resulting partial differential equations are solved by the boundary-integral-equation method, and the finite-difference method is used for discretizing the boundary conditions at the edges of the plate. The method devised here is proven to be very efficient in a parametric study of the hydroelastic response of a mat-type floating runway in regular, oblique waves. The main parameters varied in the problem are the stiffness, length and beam of the mat. The deflections of the mat are calculated for various incoming wave frequencies and heading angles in water of "shallow" depth. The results are compared with the available experimental data and numerical calculations by others. The mean drift loads on the mat are also calculated by following Maruo's far-field method.

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