scholarly journals FULLY NONLINEAR MODELING OF NEARSHORE WAVE PROPAGATION INCLUDING THE EFFECTS OF WAVE BREAKING

2018 ◽  
pp. 78 ◽  
Author(s):  
Christos E. Papoutsellis ◽  
Marissa L. Yates ◽  
Bruno Simon ◽  
Michel Benoit
Keyword(s):  
Wave Breaking ◽  
Velocity Potential ◽  
Model Simulation ◽  
Spatial Scales ◽  
Nonlinear Modeling ◽  
Series Representation ◽  
Wave System ◽  
Regular Waves ◽  
Fully Nonlinear ◽  
Weakly Nonlinear

Nearshore wave modeling over spatial scales of several kilometers requires balancing the fine-scale modeling of physical processes with the model’s accuracy and efficiency. In this work, a fully nonlinear potential flow model is proposed as a compromise between simplified linear, weakly nonlinear or weakly dispersive models and direct CFD approaches. The core of present approach is the use of a series representation for the velocity potential. This series contains prescribed vertical functions and allows the determination of the velocity potential in terms of unknown horizontal functions. The resulting dimensionally reduced model retains the structure of the Hamiltonian water wave system Zakharov (1968), Craig & Sulem (1993), avoiding the solution of the Laplace problem for the potential. Instead, a numerically convenient linear system of horizontal equations needs to be solved at each step in the temporal evolution. No simplifications concerning the deformation of the physical boundaries are introduced, apart from the typical requirement of a smooth, non-overturning free surface and seabed. The main limitation of this formulation is its inability to account for wave breaking. The treatment of this process is the subject of the present work. Two different techniques are implemented in the present model. Simulation results are compared to laboratory measurements for two test cases: (1) shoaling and breaking of regular waves over a barred bathymetry Beji & Battjes (1993) and (2) shoaling and breaking of regular waves on a plane beach Ting & Kirby (1994).

Non-Linear Dynamics of Parametric Roll of Container Ship in Irregular Seas

2014 ◽  
Author(s):  
Abhilash S. Somayajula ◽  
Jeffrey M. Falzarano
Keyword(s):  
Volterra Series ◽  
Nonlinear Modeling ◽  
Series Representation ◽  
Nonlinear Damping ◽  
Regular Waves ◽  
Parametric Roll ◽  
Linear Dynamics ◽  
Following Seas ◽  
Ergodic Behavior ◽  
Non Linear

Parametric motion is the phenomenon where a structure is excited into large amplitude motion even when there is no direct excitation. A well-known example of this type of motion is the parametric roll of ships in head or following seas. Parametric roll of container ships in head seas is relatively a new problem which has gained much importance after the catastrophic incidence of APL China in 1998. Many studies have investigated this phenomenon in the case of a ship being excited in regular waves. However, ships do not encounter regular waves in the actual ocean. So, it is imperative to study the importance of parametric roll in irregular seas. In this paper the analysis of roll equation of motion is performed by nonlinear modeling. The problem of parametric roll is approached as a non-linear dynamics problem with due consideration to nonlinear time varying hydrostatics as well as the nonlinear damping. A nonlinear damping model is used to approximate the actual viscous damping in the system. The variation of the roll righting arm with time has been modeled using a Volterra series representation which includes the hydrostatic non-linearity. Various realizations of the roll motion have been simulated and analyzed to study the ergodic behavior of the phenomenon. The paper also discusses future ideas of how to analyze parametric roll in irregular seaways.

scholarly journals Anomalous width variation of rarefactive ion acoustic solitary waves in the context of auroral plasmas

2004 ◽  
Vol 11 (2) ◽  
pp. 219-228 ◽  
Author(s):  
S. S. Ghosh ◽  
G. S. Lakhina
Keyword(s):  
Solitary Waves ◽  
Nonlinear Theory ◽  
Acoustic Waves ◽  
Large Amplitude ◽  
Magnetized Plasma ◽  
Amplitude Variation ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
Ion Acoustic Solitary Waves ◽  
Ion Acoustic

Abstract. The presence of dynamic, large amplitude solitary waves in the auroral regions of space is well known. Since their velocities are of the order of the ion acoustic speed, they may well be considered as being generated from the nonlinear evolution of ion acoustic waves. However, they do not show the expected width-amplitude correlation for K-dV solitons. Recent POLAR observations have actually revealed that the low altitude rarefactive ion acoustic solitary waves are associated with an increase in the width with increasing amplitude. This indicates that a weakly nonlinear theory is not appropriate to describe the solitary structures in the auroral regions. In the present work, a fully nonlinear analysis based on Sagdeev pseudopotential technique has been adopted for both parallel and oblique propagation of rarefactive solitary waves in a two electron temperature multi-ion plasma. The large amplitude solutions have consistently shown an increase in the width with increasing amplitude. The width-amplitude variation profile of obliquely propagating rarefactive solitary waves in a magnetized plasma have been compared with the recent POLAR observations. The width-amplitude variation pattern is found to fit well with the analytical results. It indicates that a fully nonlinear theory of ion acoustic solitary waves may well explain the observed anomalous width variations of large amplitude structures in the auroral region.

scholarly journals Steep unidirectional wave groups – fully nonlinear simulations vs. experiments

2015 ◽  
Vol 2 (4) ◽  
pp. 1159-1195 ◽  
Author(s):  
L. Shemer ◽  
B. K. Ee
Keyword(s):  
Wave Breaking ◽  
Surface Elevation ◽  
Computational Results ◽  
Local Surface ◽  
Qualitative Comparison ◽  
Wave Groups ◽  
Fully Nonlinear ◽  
Nonlinear Simulations ◽  
Velocity Of Propagation ◽  
Steep Waves

Abstract. A method was developed to carry out detailed qualitative comparison of fully nonlinear computations with the measurements of unidirectional wave groups. Computational results on evolving wave groups were compared with the available experiments. The local surface elevation variation, evolution of envelope shapes, the velocity of propagation of the steepest crests in the group and their relation to the height of the crests were obtained numerically and experimentally. Conditions corresponding to incipient wave breaking were investigated in greater detail. The results shed additional light on the limits of applicability of the computational results, as well as on mechanisms leading to the breaking of steep waves.

Finite-amplitude internal wavepacket dispersion and breaking

2001 ◽  
Vol 429 ◽  
pp. 343-380 ◽  
Author(s):  
BRUCE R. SUTHERLAND
Keyword(s):  
Numerical Simulations ◽  
Internal Waves ◽  
Large Amplitude ◽  
Finite Amplitude ◽  
Critical Amplitude ◽  
Fully Nonlinear ◽  
Weakly Nonlinear ◽  
The Stability ◽  
The Waves ◽  
Horizontal Wavelength

The evolution and stability of two-dimensional, large-amplitude, non-hydrostatic internal wavepackets are examined analytically and by numerical simulations. The weakly nonlinear dispersion relation for horizontally periodic, vertically compact internal waves is derived and the results are applied to assess the stability of weakly nonlinear wavepackets to vertical modulations. In terms of Θ, the angle that lines of constant phase make with the vertical, the wavepackets are predicted to be unstable if [mid ]Θ[mid ] < Θc, where Θc = cos−1 (2/3)1/2 ≃ 35.3° is the angle corresponding to internal waves with the fastest vertical group velocity. Fully nonlinear numerical simulations of finite-amplitude wavepackets confirm this prediction: the amplitude of wavepackets with [mid ]Θ[mid ] > Θc decreases over time; the amplitude of wavepackets with [mid ]Θ[mid ] < Θc increases initially, but then decreases as the wavepacket subdivides into a wave train, following the well-known Fermi–Pasta–Ulam recurrence phenomenon.If the initial wavepacket is of sufficiently large amplitude, it becomes unstable in the sense that eventually it convectively overturns. Two new analytic conditions for the stability of quasi-plane large-amplitude internal waves are proposed. These are qualitatively and quantitatively different from the parametric instability of plane periodic internal waves. The ‘breaking condition’ requires not only that the wave is statically unstable but that the convective instability growth rate is greater than the frequency of the waves. The critical amplitude for breaking to occur is found to be ACV = cot Θ (1 + cos2 Θ)/2π, where ACV is the ratio of the maximum vertical displacement of the wave to its horizontal wavelength. A second instability condition proposes that a statically stable wavepacket may evolve so that it becomes convectively unstable due to resonant interactions between the waves and the wave-induced mean flow. This hypothesis is based on the assumption that the resonant long wave–short wave interaction, which Grimshaw (1977) has shown amplifies the waves linearly in time, continues to amplify the waves in the fully nonlinear regime. Using linear theory estimates, the critical amplitude for instability is ASA = sin 2Θ/(8π2)1/2. The results of numerical simulations of horizontally periodic, vertically compact wavepackets show excellent agreement with this latter stability condition. However, for wavepackets with horizontal extent comparable with the horizontal wavelength, the wavepacket is found to be stable at larger amplitudes than predicted if Θ [lsim ] 45°. It is proposed that these results may explain why internal waves generated by turbulence in laboratory experiments are often observed to be excited within a narrow frequency band corresponding to Θ less than approximately 45°.

The Interaction of Katabatic Flow and Mountain Waves. Part II: Case Study Analysis and Conceptual Model

2007 ◽  
Vol 64 (6) ◽  
pp. 1857-1879 ◽  
Author(s):  
Gregory S. Poulos ◽  
James E. Bossert ◽  
Thomas B. McKee ◽  
Roger A. Pielke
Keyword(s):  
Conceptual Model ◽  
Gravity Wave ◽  
Wave Breaking ◽  
Gradient Force ◽  
Pressure Gradient Force ◽  
Wave System ◽  
Katabatic Flow ◽  
Mountain Wave ◽  
Mountain Waves ◽  
Wave Evolution

Via numerical analysis of detailed simulations of an early September 1993 case night, the authors develop a conceptual model of the interaction of katabatic flow in the nocturnal boundary layer with mountain waves (MKI). A companion paper (Part I) describes the synoptic and mesoscale observations of the case night from the Atmospheric Studies in Complex Terrain (ASCOT) experiment and idealized numerical simulations that manifest components of the conceptual model of MKI presented herein. The reader is also referred to Part I for detailed scientific background and motivation. The interaction of these phenomena is complicated and nonlinear since the amplitude, wavelength, and vertical structure of the mountain-wave system developed by flow over the barrier owes some portion of its morphology to the evolving atmospheric stability in which the drainage flows develop. Simultaneously, katabatic flows are impacted by the topographically induced gravity wave evolution, which may include significantly changing wavelength, amplitude, flow magnitude, and wave breaking behavior. In addition to effects caused by turbulence (including scouring), perturbations to the leeside gravity wave structure at altitudes physically distant from the surface-based katabatic flow layer can be reflected in the katabatic flow by transmission through the atmospheric column. The simulations show that the evolution of atmospheric structure aloft can create local variability in the surface pressure gradient force governing katabatic flow. Variability is found to occur on two scales, on the meso-β due to evolution of the mountain-wave system on the order of one hour, and on the microscale due to rapid wave evolution (short wavelength) and wave breaking–induced fluctuations. It is proposed that the MKI mechanism explains a portion of the variability in observational records of katabatic flow.

Nonlinear behaviour of contained inertia waves

1996 ◽  
Vol 315 ◽  
pp. 151-173 ◽  
Author(s):  
Richard Manasseh
Keyword(s):  
Fundamental Mode ◽  
Experimental Studies ◽  
Higher Order ◽  
Time Dependent ◽  
Linear Wave ◽  
Wave System ◽  
Nonlinear Behaviour ◽  
Rotating Fluid ◽  
Weakly Nonlinear ◽  
Higher Order Modes

Rotating fluid-filled containers are systems which admit inertial oscillations, which at appropriate frequencies can be represented as inertia wave modes. When forced by a time-dependent perturbation, systems of contained inertia waves have been shown, in a number of experimental studies, to exhibit complex and varied breakdown phenomena. It is particularly hard to determine a forcing amplitude below which breakdowns do not occur but at which linear wave behaviour is still measurable. In this paper, experiments are presented where modes of higher order than the fundamental are forced. These modes exhibit more complex departures from linear inviscid behaviour than the fundamental mode. However, the experiments on higher-order modes show that instabilities begin at nodal planes. It is shown that even a weakly nonlinear contained inertia-wave system is one in which unexpectedly efficient interactions with higher-order modes can occur, leading to ubiquitous breakdowns. An experiment with the fundamental mode illustrates the system's preference for complex transitions to chaos.

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 Analysis of Added Resistance on Ship in Parametric Roll Motions

2016 ◽  
Author(s):  
Jae-Hoon Lee ◽  
Yonghwan Kim ◽  
Min-Guk Seo
Keyword(s):  
Near Field ◽  
Three Dimensional ◽  
Field Method ◽  
Roll Motion ◽  
Added Resistance ◽  
Regular Waves ◽  
Nonlinear Formulation ◽  
Parametric Roll ◽  
Weakly Nonlinear ◽  
Rankine Panel Method

In the present study, the added resistance of a containership in parametric roll motion is investigated. The numerical simulation is carried out using a three dimensional Rankine panel method along with the weakly nonlinear formulation. The added resistance is evaluated by a near-field method, namely, the direct integration of the 2nd-order pressure on a body surface. To calculate the component resulting from the large-amplitude roll motion, the higher-order restoring and Froude-Krylov forces on wetted hull surfaces are taken into account. With or without parametric roll in regular waves, the components of added resistance classified with respect to integral terms are compared to figure out the important of each term. Through the investigation, the correlation between the added resistance and parametric roll is derived from coupling and decoupling the components of roll motion and vertical motions.

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