Experiments on nonlinear cross waves

1986 ◽  
Vol 29 (12) ◽  
pp. 3971 ◽  
Author(s):  
S. Lichter ◽  
L. Shemer
Keyword(s):  
Cross Waves

The mode number dependence of neutral stability of cross-waves

1990 ◽  
Vol 9 (3) ◽  
pp. 148-152 ◽  
Author(s):  
L. Shemer ◽  
S. Lichter
Keyword(s):  
Mode Number ◽  
Neutral Stability ◽  
Cross Waves

Long-time evolution and regions of existence of parametrically excited nonlinear cross-waves in a tank

1989 ◽  
Vol 209 ◽  
pp. 249-263 ◽  
Author(s):  
Lev Shemer ◽  
Eliezer Kit
Keyword(s):  
Boundary Condition ◽  
Parametric Excitation ◽  
Wave Breaking ◽  
Model Equation ◽  
Numerical Study ◽  
Parametrically Excited ◽  
Numerical Studies ◽  
Scaling Procedure ◽  
Long Time ◽  
Cross Waves

Results of an experimental and numerical study of parametrically excited nonlinear cross-waves in the vicinity of the cut-off frequency, are reported. Experiments are performed at three cross-wave modes and in the whole range of existence of cross-waves. Numerical studies are based on the solution of the nonlinear Schrödinger equation with a boundary condition at the wavemaker which corresponds to parametric excitation. The validity of the scaling procedure adopted in the model is verified experimentally. Dissipation is incorporated in the model equation and in the wavemaker boundary condition. The influence of the wave breaking on the range of existence of cross-waves is discussed and the relation between the maximum possible steepness of cross-waves and the limits of their existence is obtained.

Subharmonic resonant interaction of a gravity–capillary progressive axially symmetric wave with a radial cross-wave

2019 ◽  
Vol 869 ◽  
pp. 439-467 ◽  
Author(s):  
Meng Shen ◽  
Yuming Liu
Keyword(s):  
Free Surface ◽  
Evolution Equation ◽  
Threshold Value ◽  
Resonant Interaction ◽  
The Body ◽  
Wave Radiation ◽  
Axially Symmetric ◽  
Damping Term ◽  
The Cross ◽  
Cross Waves

We theoretically investigate the problem of subharmonic resonant interaction of a progressive (axially symmetric) ring wave with a radial cross-wave in the context of the potential-flow formulation for gravity-capillary waves. The objective is to understand the nonlinear mechanism governing energy transfer from a progressive ring wave to its subharmonic cross-waves through triadic resonant interactions. We first show that for an arbitrary three-dimensional body floating in an unbounded free surface, there exists a set of homogeneous solutions at any frequency in the gravity-capillary wave context. The homogeneous solution depends solely on the mean free-surface slope at the waterline of the body and physically represents a progressive radial cross-wave. Unlike standing cross-waves, a progressive cross-wave loses energy during propagation by overcoming the work done by surface tension at the waterline and through wave radiation. We then consider the subharmonic interaction of a progressive ring wave, which is forced by a radial swelling–contraction deformation of a vertical circular cylinder, with subharmonic cross-waves. We derive the nonlinear spatial–temporal evolution equation governing the motion of the cross-wave by use of the average Lagrangian method. In addition to energy-input terms from the interaction with the forced ring wave, the evolution equation contains a damping term associated with energy loss in cross-wave propagation. We show that the presence of the damping term leads to a non-trivial threshold value of the ring wave steepness (or amplitude) beyond which the cross-wave becomes unstable and grows with time by taking energy from the ring wave. Finally, we extend this analysis to the experimental case of Tatsuno et al. (Rep. Res. Inst. Appl. Mech. Kyushu University, vol. 17, 1969, pp. 195–215) in which asymmetric wave patterns are observed during high-frequency vertical oscillations of a surface-piercing sphere. The theoretical prediction of the threshold value of oscillation amplitude and characteristic features of generated radial cross-waves agrees reasonably well with experimental observations.

Chaotic analyses of weakly damped parametrically excited cross waves with surface tension

2005 ◽  
Vol 175 (1-4) ◽  
pp. 139-179
Author(s):  
R. T. Hudspeth ◽  
R. B. Guenther ◽  
S. Fadel
Keyword(s):  
Surface Tension ◽  
Parametrically Excited ◽  
Cross Waves

Parametrically excited, standing cross-waves

1988 ◽  
Vol 186 ◽  
pp. 119-127 ◽  
Author(s):  
John Miles
Keyword(s):  
Surface Waves ◽  
Phase Plane ◽  
Evolution Equations ◽  
Plane Waves ◽  
Wave Problem ◽  
Parametrically Excited ◽  
The Cross ◽  
The Stability ◽  
Cross Waves

Luke's (1967) variational formulation for surface waves is extended to incorporate the motion of a wavemaker and applied to the cross-wave problem. Whitham's average-Lagrangian method then is invoked to obtain the evolution equations for the slowly varying complex amplitude of the parametrically excited cross-wave that is associated with symmetric excitation of standing waves in a rectangular tank of width π/k, length l and depth d for which kl = O(1) and kd [Gt ] 1. These evolution equations are Hamiltonian and isomorphic to those for parametric excitation of surface waves in a cylinder that is subjected to a vertical oscillation, for which phase-plane trajectories, stability criteria and the effects of damping are known (Miles 1984a). The formulation and results differ from those of Garrett (1970) in consequence of his linearization of the boundary condition at the wavemaker and his neglect of self-interaction of the cross-waves in the free-surface conditions (although Garrett does incorporate self-interaction in his calculation of the equilibrium amplitude of the cross-waves). These differences have only a small effect on the criterion for the stability of plane waves, but the self-interaction is crucial for the determination of the stability of the cross-waves.

scholarly journals CFD Simulation of Ship Seakeeping Performance and Slamming Loads in Bi-Directional Cross Wave

2020 ◽  
Vol 8 (5) ◽  
pp. 312 ◽  
Author(s):  
Jialong Jiao ◽  
Songxing Huang
Keyword(s):  
Cfd Simulation ◽  
Wave Length ◽  
Green Water ◽  
Navier Stokes ◽  
Transverse Motion ◽  
Linear Superposition ◽  
Motion Responses ◽  
Seakeeping Performance ◽  
Ocean Environment ◽  
Cross Waves

Accurate prediction of ship seakeeping performance in complex ocean environment is a fundamental requirement for ship design and actual operation in seaways. In this paper, an unsteady Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD) solver with overset grid technique was applied to estimate the seakeeping performance of an S175 containership operating in bi-directional cross waves. The cross wave is reproduced by linear superposition of two orthogonal regular waves in a rectangle numerical wave tank. The ship nonlinear motion responses, bow slamming loads, and green water on deck induced by cross wave with different control parameters such as wave length and wave heading angle are systemically analyzed. The results demonstrate that both vertical and transverse motion responses, as well as slamming pressure of ship induced by cross wave, can be quite large, and they are quite different from those in regular wave. Therefore, ship navigational safety when suffering cross waves should be further concerned.

The Sloshing Motion of Cross-Waves

1995 ◽  
Vol 95 (2) ◽  
pp. 171-191
Author(s):  
Jianke Yang
Keyword(s):  
Cross Waves

scholarly journals THE MEASURED PROPERTIES OF IRREGULAR WAVE BREAKING AND WAVE HEIGHT CHANGE AFTER BREAKING ON THE SLOPE

1988 ◽  
Vol 1 (21) ◽  
pp. 29 ◽  
Author(s):  
Akira Seyama ◽  
Akira Kimura
Keyword(s):  
Wave Height ◽  
Water Depth ◽  
Wave Theory ◽  
Irregular Waves ◽  
Linear Wave ◽  
Periodic Waves ◽  
Zero Crossing ◽  
Irregular Wave ◽  
Height Change ◽  
Cross Waves

Wave height change of the zero-down-cross waves on uniform slopes were examined experimentally. The properties of shoaling, breaking and decay after breaking for a total of about 4,000 irregular waves of the Pierson-Moskowitz type on 4 different slopes (1/10, 1/20, 1/30 and 1/50) were investigated. The shoaling property of the zero-down-cross waves can be approximated by the linear wave theory. However, the properties of breaking and decay after breaking differ considerably from those for periodic waves. The wave height water depth ratio (H/d) at the breaking point for the zero-down-cross waves is about 30% smaller than that for periodic waves on average despite the slopes. Wave height decay after breaking also differs from that for periodic waves and can be classified into three regions, i.e. shoaling, plunging and bore regions. Experimental equations for the breaking condition and wave height change after breaking are proposed in the study. A new definition of water depth for the zero-crossing wave analysis which can reduce the fluctuation in the plotted data is also proposed.

The interaction between capillary waves and a current and wave decay

1977 ◽  
Vol 81 (2) ◽  
pp. 241-256 ◽  
Author(s):  
F. Y. Sorrell ◽  
G. V. Sturm
Keyword(s):  
Wave Train ◽  
Capillary Waves ◽  
Constant Current ◽  
Progressive Wave ◽  
First Order Theory ◽  
Wave Decay ◽  
Wave Maker ◽  
The Cross ◽  
Spatially Varying ◽  
Cross Waves

Results of experiments on capillary-wave decay and energy transfer to mean currents are presented. The conditions investigated were those of a progressive wave train propagating on still water, on a constant current and on a spatially varying current. The waves were generated by either a mechanical or a pneumatic wave maker and the wave maker usually excited cross-wave motion. Thus the study also provides data on cross-wave generation and growth under these conditions. In particular these results indicate that the cross-waves obtain energy from a constant current as well as a spatially varying current. The progressive-wave energy was separated from that in the cross-waves by spatial averaging. When this is done the wave-current interaction and wave decay can be described by a first-order theory which includes viscous dissipation.

Sign in / Sign up

Export Citation Format

Share Document