Numerical Methods for Nonlinear Waves

Fenton, John D.

doi:10.1142/9789812797544_0005

Cited by 46 publications

(33 citation statements)

References 121 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although numerical models for surface gravity waves are undergoing constant improvement -in terms of speed, accuracy and generality (Fenton 1999;Dias & Bridges 2006) -simplified analytical models remain (and will remain) in common use. Indeed, such models provide insight and are also accurate enough for many practical applications.…”

Section: Introductionmentioning

confidence: 99%

On the Lagrangian description of steady surface gravity waves

Clamond¹

2007

J. Fluid Mech.

View full text Add to dashboard Cite

This paper concerns the mathematical formulation of two-dimensional steady surface gravity waves in a Lagrangian description of motion. It is demonstrated first that classical second-order Lagrangian Stokes-like approximations do not exactly represent a steady wave motion in the presence of net mass transport (Stokes drift). A general mathematically correct formulation is then derived. This derivation leads naturally to a Lagrangian Stokes-like perturbation scheme that is uniformly valid for all time -in other words, without secular terms. This scheme is illustrated, both for irrotational waves, with seventh-order and third-order approximations in deep water and finite depth, respectively, and for rotational waves with a third-order approximation of the Gerstner-like wave on finite depth. It is also shown that the Lagrangian approximations are more accurate than their Eulerian counterparts of the same order.

show abstract

Section: Introductionmentioning

confidence: 99%

On the Lagrangian description of steady surface gravity waves

Clamond¹

2007

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…In particular, three nonlinear wave theories are used for nonlinear wave generation: the fifth-order Stokes wave theory [46], the Fourier series method for Stokes and cnoidal waves [47] and McCowan's theory for solitary waves [48,49].…”

Section: Model Descriptionmentioning

confidence: 99%

Computational Fluid Dynamics for Modeling Gravity Currents in the Presence of Oscillatory Ambient Flow

Stancanelli¹,

Musumeci²,

Foti³

2018

Water

View full text Add to dashboard Cite

Gravity currents generated by lock release are studied in the case of initially quiescent ambient fluid and oscillating ambient fluid (regular surface waves). In particular, the dynamics of the density currents are investigated by means of CFD numerical simulations. The aim is to evaluate the influence of the ambient fluid velocity field on the observed mixing and turbulent processes. Results of two different turbulence closure models, namely the standard k − ε turbulence model and the LES model, are analyzed. Model predictions are validated through comparison with laboratory measurements. Results show that the k − ε model is able to catch the main current propagation parameters (e.g., front velocity at the different phases of the evolution of the current, gravity current depth, etc.), but that a LES model provides more realistic insights into the turbulent processes (e.g., formation of interfacial Kelvin-Helmholtz billows, vortex stretching and eventual break up into 3D turbulence). The ambient fluid velocity field strongly influences the dynamics of the gravity currents. In particular, the presence of an oscillatory motion induces a relative increase of mixing at the front (up to 25%) in proximity of the bottom layer, and further upstream, an increase of the mixing process (up to 60%) is observed due to the mass transport generated by waves. The observed mixing phenomena observed are also affected by the ratio between the gravity current velocity v f and the horizontal orbital velocity induced by waves u w , which has a stronger impact in the wave dominated regime (v f /u w < 1).

show abstract

“…The ability of SWASH model in simulating nonlinear waves can be verified by using solutions of Fourier approximation method [Fenton, 1999], which expands the stream function into a series that inherently satisfies Laplace's equation throughout the whole flow field. With the kinematic and dynamic boundary conditions, parameters of the series are computed numerically.…”

Section: Appendix D Verification Of Swash Modelmentioning

confidence: 99%

“…With the kinematic and dynamic boundary conditions, parameters of the series are computed numerically. Since any periodic process can be precisely approximated by Fourier series, the method can provide very accurate solutions for waves up to limited wave-height [Fenton, 1999]. The steady wave profile simulated by SWASH model is compared with that computed by Fourier approximation method with 20 Fourier components.…”

Section: Appendix D Verification Of Swash Modelmentioning

confidence: 99%

Resolution of Incident and Reflected Components of Nonlinear Regular Waves

Liu

2016

Coastal Engineering Journal

View full text Add to dashboard Cite

The method of Lin and Huang [Lin and Huang [2004] "Decomposition of incident and reflected higher harmonic waves using four wave gauges," Coast. Eng. 51(5), 395-406.] (LH) is improved for resolution of incident and reflected strongly nonlinear regular waves in shallow waters with measurements of four stationary wave gauges. For first harmonics, wavenumbers, amplitudes and initial phases are obtained by using a nonlinear least squares method. For higher harmonics, wavenumbers of free and bound modes are determined from linear dispersion relation and multiple of first-harmonic wavenumbers, respectively, and the other unknowns are solved by using a linear least squares method. Auto-correlation function is used to determine fundamental wave period for gaining a good performance of Fourier transform. The efficiency and accuracy of the present method are demonstrated by using artificial data and numerical flume data. It is also demonstrated that the present method is less sensitive to signal noise and gauge spacings. Comparison between the present method and the LH method indicates the necessity of employing nonlinear method in determining fundamental wavenumbers of nonlinear shallow-water waves. Finally, the present method is extended to account for obliquely-incident waves. Sensitivity tests indicate the robustness of the extended method with respect to incident angles. Relative position of gauges in the array for avoiding singularity is suggested.

show abstract

Numerical Methods for Nonlinear Waves

Cited by 46 publications

References 121 publications

On the Lagrangian description of steady surface gravity waves

On the Lagrangian description of steady surface gravity waves

Computational Fluid Dynamics for Modeling Gravity Currents in the Presence of Oscillatory Ambient Flow

Resolution of Incident and Reflected Components of Nonlinear Regular Waves

Contact Info

Product

Resources

About