scholarly journals ACTION OF NON-LINEAR WAVES AT A SOLID WALL

1976 ◽  
Vol 1 (15) ◽  
pp. 46
Author(s):  
Mohamed S. Nasser ◽  
John A. McCorquodale
Keyword(s):  
Water Waves ◽  
Solid Wall ◽  
Shallow Water Waves ◽  
Difference Model ◽  
One Dimensional ◽  
Numerical Predictions ◽  
Linear Waves ◽  
Damping Parameter ◽  
Non Linear ◽  
Run Up

A one-dimensional finite difference model is developed to simulate the action of long non-linear shallow water waves at a solid barrier. A damping parameter is introduced to account for the centrifugal effects in the incident wave. A stability criterion for At/Ax is suggested. The numerical predictions of reflection and run-up compare satisfactorily with experimental results.

Action of Non-Linear Waves at a Solid Wall

1977 ◽  
Author(s):  
Mohamed S. Nasser ◽  
John A. McCorquodale
Keyword(s):  
Solid Wall ◽  
Linear Waves ◽  
Non Linear

scholarly journals Detecting nonlinearity in run-up on a natural beach

2007 ◽  
Vol 14 (4) ◽  
pp. 385-393 ◽  
Author(s):  
K. R. Bryan ◽  
G. Coco
Keyword(s):  
Water Waves ◽  
Nonlinear Behaviour ◽  
Correlated Noise ◽  
Incoming Wave ◽  
Linear Interaction ◽  
Natural Systems ◽  
Relative Contribution ◽  
Cyclic Behaviour ◽  
Non Linear ◽  
Run Up

Abstract. Natural geophysical timeseries bear the signature of a number of complex, possibly inseparable, and generally unknown combination of linear, stable non-linear and chaotic processes. Quantifying the relative contribution of, in particular, the non-linear components will allow improved modelling and prediction of natural systems, or at least define some limitations on predictability. However, difficulties arise; for example, in cases where the series are naturally cyclic (e.g. water waves), it is most unclear how this cyclic behaviour impacts on the techniques commonly used to detect the nonlinear behaviour in other fields. Here a non-linear autoregressive forecasting technique which has had success in demonstrating nonlinearity in non-cyclical geophysical timeseries, is applied to a timeseries generated by videoing the waterline on a natural beach (run-up), which has some irregular oscillatory behaviour that is in part induced by the incoming wave field. In such cases, the deterministic shape of each run-up cycle has a strong influence on forecasting results, causing questionable results at small (within a cycle) prediction distances. However, the technique can clearly differentiate between random surrogate series and natural timeseries at larger prediction distances (greater than one cycle). Therefore it was possible to clearly identify nonlinearity in the relationship between observed run-up cycles in that a local autoregressive model was more adept at predicting run-up cycles than a global one. Results suggest that despite forcing from waves impacting on the beach, each run-up cycle evolves somewhat independently, depending on a non-linear interaction with previous run-up cycles. More generally, a key outcome of the study is that oscillatory data provide a similar challenge to differentiating chaotic signals from correlated noise in that the deterministic shape causes an additional source of autocorrelation which in turn influences the predictability at small forecasting distances.

scholarly journals Observation of broad-band water waveguiding in shallow water: a revival

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Fabián Sepúlveda-Soto ◽  
Diego Guzmán-Silva ◽  
Edgardo Rosas ◽  
Rodrigo A. Vicencio ◽  
Claudio Falcón
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Open Channel ◽  
Fluid Layer ◽  
Broad Band ◽  
Shallow Water Waves ◽  
One Dimensional ◽  
The One ◽  
Complex Phenomena

Abstract We report on the observation and characterization of broad-band waveguiding of surface gravity waves in an open channel, in the shallow water limit. The waveguide is constructed by changing locally the depth of the fluid layer, which creates conditions for surface waves to propagate along the generated guide. We present experimental and numerical results of this shallow water waveguiding, which can be straightforwardly matched to the one-dimensional water wave equation of shallow water waves. Our work revitalizes water waveguiding research as a relevant and controllable experimental setup to study complex phenomena using waveguide geometries.

scholarly journals Head-on collision of internal waves with trapped cores

2017 ◽  
Vol 24 (4) ◽  
pp. 751-762 ◽  
Author(s):  
Vladimir Maderich ◽  
Kyung Tae Jung ◽  
Kateryna Terletska ◽  
Kyeong Ok Kim
Keyword(s):  
Wave Amplitude ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Class Iii ◽  
Navier Stokes Equations ◽  
Linear Waves ◽  
Non Linear ◽  
Conservation Of Momentum ◽  
Run Up ◽  
The Waves

Abstract. The dynamics and energetics of a head-on collision of internal solitary waves (ISWs) with trapped cores propagating in a thin pycnocline were studied numerically within the framework of the Navier–Stokes equations for a stratified fluid. The peculiarity of this collision is that it involves trapped masses of a fluid. The interaction of ISWs differs for three classes of ISWs: (i) weakly non-linear waves without trapped cores, (ii) stable strongly non-linear waves with trapped cores, and (iii) shear unstable strongly non-linear waves. The wave phase shift of the colliding waves with equal amplitude grows as the amplitudes increase for colliding waves of classes (i) and (ii) and remains almost constant for those of class (iii). The excess of the maximum run-up amplitude, normalized by the amplitude of the waves, over the sum of the amplitudes of the equal colliding waves increases almost linearly with increasing amplitude of the interacting waves belonging to classes (i) and (ii); however, it decreases somewhat for those of class (iii). The colliding waves of class (ii) lose fluid trapped by the wave cores when amplitudes normalized by the thickness of the pycnocline are in the range of approximately between 1 and 1.75. The interacting stable waves of higher amplitude capture cores and carry trapped fluid in opposite directions with little mass loss. The collision of locally shear unstable waves of class (iii) is accompanied by the development of instability. The dependence of loss of energy on the wave amplitude is not monotonic. Initially, the energy loss due to the interaction increases as the wave amplitude increases. Then, the energy losses reach a maximum due to the loss of potential energy of the cores upon collision and then start to decrease. With further amplitude growth, collision is accompanied by the development of instability and an increase in the loss of energy. The collision process is modified for waves of different amplitudes because of the exchange of trapped fluid between colliding waves due to the conservation of momentum.

scholarly journals Nonlinear self adjointness, conservation laws and exact solutions of ill-posed Boussinesq equation

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 37-43 ◽  
Author(s):  
Emrullah Yaşar ◽  
Sait San ◽  
Yeşim Sağlam Özkan
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Shallow Water ◽  
Water Waves ◽  
Function Method ◽  
Boussinesq Equation ◽  
Lie Point Symmetries ◽  
Shallow Water Waves ◽  
Non Linear ◽  
Ill Posed

AbstractIn this work, we consider the ill-posed Boussinesq equation which arises in shallow water waves and non-linear lattices. We prove that the ill-posed Boussinesq equation is nonlinearly self-adjoint. Using this property and Lie point symmetries, we construct conservation laws for the underlying equation. In addition, the generalized solitonary, periodic and compact-like solutions are constructed by the exp-function method.

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