A random wave process

1984 ◽  
Vol 12 (1) ◽  
pp. 97-114 ◽  
Author(s):  
D. A. Dawson ◽  
G. C. Papanicolaou
Keyword(s):  
Wave Process ◽  
Random Wave

scholarly journals On the Oval Shapes of Beach Stones

AppliedMath ◽  
2022 ◽  
Vol 2 (1) ◽  
pp. 16-38
Author(s):  
Theodore P. Hill
Keyword(s):  
Continuous Time ◽  
Basic Equation ◽  
Numerical Experiments ◽  
Physical Mechanism ◽  
Wave Process ◽  
Random Wave ◽  
Local Shape ◽  
Standard Curve ◽  
Non Local ◽  
Curve Shortening

This article introduces a new stochastic non-isotropic frictional abrasion model, in the form of a single short partial integro-differential equation, to show how frictional abrasion alone of a stone on a planar beach might lead to the oval shapes observed empirically. The underlying idea in this theory is the intuitive observation that the rate of ablation at a point on the surface of the stone is proportional to the product of the curvature of the stone at that point and the likelihood the stone is in contact with the beach at that point. Specifically, key roles in this new model are played by both the random wave process and the global (non-local) shape of the stone, i.e., its shape away from the point of contact with the beach. The underlying physical mechanism for this process is the conversion of energy from the wave process into the potential energy of the stone. No closed-form or even asymptotic solution is known for the basic equation, which is both non-linear and non-local. On the other hand, preliminary numerical experiments are presented in both the deterministic continuous-time setting using standard curve-shortening algorithms and a stochastic discrete-time polyhedral-slicing setting using Monte Carlo simulation.

Ship Capsize Risk in a Seaway Using Fitted Distributions to Roll Maxima

2000 ◽  
Vol 122 (2) ◽  
pp. 141-146 ◽  
Author(s):  
Kevin A. McTaggart
Keyword(s):  
Efficient Method ◽  
Time Domain ◽  
Wave Process ◽  
Gumbel Distribution ◽  
Roll Angle ◽  
Random Wave ◽  
Seed Number ◽  
Moderate Number ◽  
Ship Capsize

This paper presents an efficient method for determining capsize risk for a given seaway and ship operational condition using time domain simulations. The risk of capsize during 1 h exposure to a given seaway is dependent on the wave process realization, which is determined by a seed number and resulting random wave phases. The dependence of maximum roll angle on wave process can be modeled by fitting a suitable distribution to maximum roll angles from a moderate number of simulations. Sample computations for a naval frigate demonstrate that a Gumbel distribution provides a very good fit to maximum roll angles from different wave realizations. [S0892-7219(00)00402-7]

Verifications of Diffraction Modeling Capability in a Coastal Spectral Wave Model

2009 ◽  
Author(s):  
Jinhai Zheng ◽  
Yu Tang
Keyword(s):  
Balance Equation ◽  
Wave Diffraction ◽  
Process Model ◽  
Present Model ◽  
Wave Process ◽  
Wave Structure ◽  
Wave Model ◽  
Wave Action ◽  
Random Wave ◽  
Spectral Wave Model

WABED (Wave Action Balance Equation with Diffraction) is a 2-D coastal spectral wave process model and used in the development of a practice-oriented random wave prediction for coastal engineering studies at inlets, navigation projects, and wave-structure interactions. Wave diffraction is implemented by adding a term derived from the parabolic wave equation to the wave action balance equation. This paper describes the evaluation of the modeling capability to represent wave diffraction available in the WABED, which is accomplished by testing the present model for diffraction-prone cases such as the wave field of a gap in an infinitely long breakwater and that over an elliptical shoal. Computations are compared with experimental observations and Sommerfeld’s analytical solutions. Comparisons indicate that WABED performs reasonable well in these conditions and is capable of predicting wave diffraction effectively together with refraction and shoaling.

EXPERIMENTAL STUDY ON RANDOM WAVE PRESSURE AFTER WAVE BREAKING ACTING ON SEAWALL ON LAND SIDE OF SHORELINE

2018 ◽  
Vol 74 (2) ◽  
pp. I_1063-I_1068
Author(s):  
Kenya TAKAHASHI ◽  
Yu SOUMA ◽  
Toshimasa ISHII ◽  
Takeshi NISHIHATA ◽  
Takeru MICHIMAE ◽  
...  
Keyword(s):  
Experimental Study ◽  
Wave Breaking ◽  
Random Wave ◽  
Wave Pressure

Full‐field optimum detection in an uncertain, anisotropic random wave scattering environment

1995 ◽  
Vol 98 (2) ◽  
pp. 1097-1110 ◽  
Author(s):  
V. Premus ◽  
D. Alexandrou ◽  
L. W. Nolte
Keyword(s):  
Wave Scattering ◽  
Random Wave ◽  
Full Field ◽  
Optimum Detection

scholarly journals Time Scale for Scour Beneath Pipelines Due to Long-Crested and Short-Crested Nonlinear Random Waves Plus Current

2021 ◽  
Vol 9 (2) ◽  
pp. 114
Author(s):  
Dag Myrhaug ◽  
Muk Chen Ong
Keyword(s):  
Time Scale ◽  
Current Flow ◽  
Irregular Waves ◽  
Wave Crest ◽  
Random Wave ◽  
Random Waves ◽  
Flow Conditions ◽  
Regular Waves ◽  
Nonlinear Random Waves ◽  
2D And 3D

This article derives the time scale of pipeline scour caused by 2D (long-crested) and 3D (short-crested) nonlinear irregular waves and current for wave-dominant flow. The motivation is to provide a simple engineering tool suitable to use when assessing the time scale of equilibrium pipeline scour for these flow conditions. The method assumes the random wave process to be stationary and narrow banded adopting a distribution of the wave crest height representing 2D and 3D nonlinear irregular waves and a time scale formula for regular waves plus current. The presented results cover a range of random waves plus current flow conditions for which the method is valid. Results for typical field conditions are also presented. A possible application of the outcome of this study is that, e.g., consulting engineers can use it as part of assessing the on-bottom stability of seabed pipelines.

scholarly journals Experiment Investigation of Bistable Vibration Energy Harvesting with Random Wave Environment

2021 ◽  
Vol 11 (9) ◽  
pp. 3868
Author(s):  
Qiong Wu ◽  
Hairui Zhang ◽  
Jie Lian ◽  
Wei Zhao ◽  
Shijie Zhou ◽  
...  
Keyword(s):  
Renewable Energy ◽  
Energy Harvesting ◽  
Cantilever Beam ◽  
Large Scale ◽  
Low Frequency ◽  
Vibration Energy ◽  
Random Wave ◽  
Periodic Signal ◽  
Vibration Energy Harvesting ◽  
Motion Activity

The energy harvested from the renewable energy has been attracting a great potential as a source of electricity for many years; however, several challenges still exist limiting output performance, such as the package and low frequency of the wave. Here, this paper proposed a bistable vibration system for harvesting low-frequency renewable energy, the bistable vibration model consisting of an inverted cantilever beam with a mass block at the tip in a random wave environment and also develop a vibration energy harvesting system with a piezoelectric element attached to the surface of a cantilever beam. The experiment was carried out by simulating the random wave environment using the experimental equipment. The experiment result showed a mass block’s response vibration was indeed changed from a single stable vibration to a bistable oscillation when a random wave signal and a periodic signal were co-excited. It was shown that stochastic resonance phenomena can be activated reliably using the proposed bistable motion system, and, correspondingly, large-scale bistable responses can be generated to realize effective amplitude enlargement after input signals are received. Furthermore, as an important design factor, the influence of periodic excitation signals on the large-scale bistable motion activity was carefully discussed, and a solid foundation was laid for further practical energy harvesting applications.

Retrieval of wave period from altimetry: Deep learning accounting for random wave field dynamics

2021 ◽  
Vol 265 ◽  
pp. 112629
Author(s):  
Jiuke Wang ◽  
Lotfi Aouf ◽  
Sergei Badulin
Keyword(s):  
Deep Learning ◽  
Wave Field ◽  
Wave Period ◽  
Random Wave ◽  
Random Wave Field
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