Computations of fully nonlinear three-dimensional wave–wave and wave–body interactions. Part 2. Nonlinear waves and forces on a body

2001 ◽  
Vol 438 ◽  
pp. 41-66 ◽  
Author(s):  
YUMING LIU ◽  
MING XUE ◽  
DICK K. P. YUE
Keyword(s):  
Steady State ◽  
Wave Diffraction ◽  
High Harmonic ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Fully Nonlinear ◽  
Bow Wave ◽  
Stokes Waves ◽  
State Force ◽  
Dimensional Wave

The mixed-Eulerian–Lagrangian method using high-order boundary elements, described in Xue et al. (2001) for the simulation of fully nonlinear three-dimensional wave–wave and wave–body interactions, is here extended and applied to the study of two nonlinear three-dimensional wave–body problems: (a) the development of bow waves on an advancing ship; and (b) the steep wave diffraction and nonlinear high-harmonic loads on a surface-piercing vertical cylinder. For (a), we obtain convergent steady-state bow wave profiles for a flared wedge, and the Wigley and Series 60 hulls. We compare our predictions with experimental measurements and find good agreement. It is shown that upstream influence, typically not accounted for in quasi-two-dimensional theory, plays an important role in bow wave prediction even for fine bows. For (b), the primary interest is in the higher-harmonic ‘ringing’ excitations observed and quantified in experiments. From simulations, we obtain fully nonlinear steady-state force histories on the cylinder in incident Stokes waves. Fourier analysis of such histories provides accurate predictions of harmonic loads for which excellent comparisons to experiments are obtained even at third order. This confirms that ‘ringing’ excitations are directly a result of nonlinear wave diffraction.

Computations of fully nonlinear three-dimensional wave–wave and wave–body interactions. Part 1. Dynamics of steep three-dimensional waves

2001 ◽  
Vol 438 ◽  
pp. 11-39 ◽  
Author(s):  
MING XUE ◽  
HONGBO XÜ ◽  
YUMING LIU ◽  
DICK K. P. YUE
Keyword(s):  
Three Dimensional ◽  
Breaking Waves ◽  
Stokes Wave ◽  
Two Dimensional ◽  
Wave Instability ◽  
Fully Nonlinear ◽  
Stokes Waves ◽  
Distinct Features ◽  
Wave Problems ◽  
Dimensional Wave

We develop an efficient high-order boundary-element method with the mixed-Eulerian–Lagrangian approach for the simulation of fully nonlinear three-dimensional wave–wave and wave–body interactions. For illustration, we apply this method to the study of two three-dimensional steep wave problems. (The application to wave–body interactions is addressed in an accompanying paper: Liu, Xue & Yue 2001.) In the first problem, we investigate the dynamics of three-dimensional overturning breaking waves. We obtain detailed kinematics and full quantification of three-dimensional effects upon wave plunging. Systematic simulations show that, compared to two-dimensional waves, three-dimensional waves generally break at higher surface elevations and greater maximum longitudinal accelerations, but with smaller tip velocities and less arched front faces. For the second problem, we study the generation mechanism of steep crescent waves. We show that the development of such waves is a result of three-dimensional (class II) Stokes wave instability. Starting with two-dimensional Stokes waves with small three-dimensional perturbations, we obtain direct simulations of the evolution of both L2 and L3 crescent waves. Our results compare quantitatively well with experimental measurements for all the distinct features and geometric properties of such waves.

Three-Dimensional Periodic Fully Nonlinear Potential Waves

2013 ◽  
Author(s):  
Dmitry Chalikov ◽  
Alexander V. Babanin
Keyword(s):  
Wave Field ◽  
Degrees Of Freedom ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Transform Method ◽  
Fully Nonlinear ◽  
Stokes Waves ◽  
Nonlinear Potential ◽  
The Fourier Transform

An exact numerical scheme for a long-term simulation of three-dimensional potential fully-nonlinear periodic gravity waves is suggested. The scheme is based on a surface-following non-orthogonal curvilinear coordinate system and does not use the technique based on expansion of the velocity potential. The Poisson equation for the velocity potential is solved iteratively. The Fourier transform method, the second-order accuracy approximation of the vertical derivatives on a stretched vertical grid and the fourth-order Runge-Kutta time stepping are used. The scheme is validated by simulation of steep Stokes waves. The model requires considerable computer resources, but the one-processor version of the model for PC allows us to simulate an evolution of a wave field with thousands degrees of freedom for hundreds of wave periods. The scheme is designed for investigation of the nonlinear two-dimensional surface waves, for generation of extreme waves as well as for the direct calculations of a nonlinear interaction rate. After implementation of the wave breaking parameterization and wind input, the model can be used for the direct simulation of a two-dimensional wave field evolution under the action of wind, nonlinear wave-wave interactions and dissipation. The model can be used for verification of different types of simplified models.

Numerical Simulation of Nonlinear Wave Diffraction by a Vertical Cylinder

1992 ◽  
Vol 114 (1) ◽  
pp. 36-44 ◽  
Author(s):  
C. Yang ◽  
R. C. Ertekin
Keyword(s):  
Experimental Data ◽  
Circular Cylinder ◽  
Nonlinear Wave ◽  
Wave Diffraction ◽  
Three Dimensional ◽  
Vertical Cylinder ◽  
Radiation Condition ◽  
Wave Force ◽  
Second Order ◽  
Time Stepping

A three-dimensional time domain approach is used to study nonlinear wave diffraction by a fixed, vertical circular-cylinder that extends to the sea floor. In this approach, the development of the flow can be obtained by a time-stepping procedure, in which the velocity potential of the flow at any instant of time is obtained by the boundary-element method. In the numerical calculations, the exact body-boundary condition is satisfied on the instantaneous wetted surface of the cylinder, and an extended Sommerfeld condition is developed and used as the numerical radiation condition. The fourth-order Adams-Bashford method is employed in the time stepping scheme. Calculations are done to obtain the nonlinear diffraction of solitary waves and Stokes second-order waves by a vertical circular-cylinder. Numerical results are compared with the available linear and second-order wave-force predictions for some given wave height and wavelength conditions, and also with experimental data. Present horizontal force results agree better with the experimental data than the previous predictions.

scholarly journals Hydroelastic wave diffraction by a vertical cylinder

2011 ◽  
Vol 369 (1947) ◽  
pp. 2832-2851 ◽  
Author(s):  
Paul Brocklehurst ◽  
Alexander Korobkin ◽  
Emilian I. Părău
Keyword(s):  
Incident Wave ◽  
Wave Diffraction ◽  
Plate Theory ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Vertical Cylinder ◽  
Finite Depth ◽  
Cylinder Surface ◽  
Linear Elastic ◽  
Potential Flow Model

A linear three-dimensional problem of hydroelastic wave diffraction by a bottom-mounted circular cylinder is analysed. The fluid is of finite depth and is covered by an ice sheet, which is clamped to the cylinder surface. The ice stretches from the cylinder to infinity in all lateral directions. The hydroelastic behaviour of the ice sheet is described by linear elastic plate theory, and the fluid flow by a potential flow model. The two-dimensional incident wave is regular and has small amplitude. An analytical solution of the coupled problem of hydroelasticity is found by using a Weber transform. We determine the ice deflection and the vertical and horizontal forces acting on the cylinder and analyse the strain in the ice sheet caused by the incident wave.

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