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Your search keyword '"Yates, Marissa L."' showing total 3 results
Start Over Author "Yates, Marissa L." Topic nonlinear waves
3 results on '"Yates, Marissa L."'

1. Accuracy and efficiency of two numerical methods of solving the potential flow problem for highly nonlinear and dispersive water waves.

Author

Yates, Marissa L. and Benoit, Michel

Subjects
HYDRODYNAMICS, NONLINEAR dynamical systems, FLUIDS, NONLINEAR waves, PARTIAL differential equations, MATHEMATICAL models
Abstract

The accuracy and efficiency of two methods of resolving the exact potential flow problem for nonlinear waves are compared using three different one horizontal dimension (1DH) test cases. The two model approaches use high-order finite difference schemes in the horizontal dimension and differ in the resolution of the vertical dimension. The first model uses high-order finite difference schemes also in the vertical, while the second model applies a spectral approach. The convergence, accuracy, and efficiency of the two models are demonstrated as a function of the temporal, horizontal, and vertical resolutions for the following: (1) the propagation of regular nonlinear waves in a periodic domain; (2) the motion of nonlinear standing waves in a domain with fully reflective boundaries; and (3) the propagation and shoaling of a train of waves on a slope. The spectral model approach converges more rapidly as a function of the vertical resolution. In addition, with equivalent vertical resolution, the spectral model approach shows enhanced accuracy and efficiency in the parameter range used for practical model applications. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Published
2015
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2. Analysis of the linear version of a highly dispersive potential water wave model using a spectral approach in the vertical.

Author

Benoit, Michel, Raoult, Cécile, and Yates, Marissa L.

Subjects
*WATER waves, *NONLINEAR waves, *BATHYMETRY, *FLUID dynamics, *BOUSSINESQ equations, *SPECTRUM analysis
Abstract

The properties and accuracy of the linearized version of the fully dispersive and nonlinear wave model developed in Yates and Benoit (2015) and Raoult et al. (2016) are analyzed for both flat and variable bottom bathymetries. This model considers only a single layer of fluid and uses a basis of orthogonal Chebyshev polynomials to project the vertical structure of the potential. This approach results in an exponential convergence rate with the maximum degree of the Chebyshev polynomial, denoted N T , while only first- and second-order derivatives in space need to be evaluated. For the constant water depth case, the linear dispersion relation of the model is derived analytically, and expressions are established for N T ranging from 2 to 15. The analysis shows a rapid increase in accuracy in the deep water range with increasing N T . For instance, the relative error in the calculated wave celerity (in comparison with Stokes’ analytical solution) remains smaller than 2.5% for deep water cases with k h up to 100 using N T ≥ 9 ( k and h are the representative wavenumber and water depth, respectively). The wave kinematics, vertical profiles of the horizontal and vertical orbital velocities, converge to the Stokes profiles for k h up to 60 when using a sufficiently high value of N T . The vertically-averaged relative errors of the horizontal and vertical velocities remain below 6% and 3%, respectively, for k h up to 60 when using N T ≥ 11 . The presented model shows better dispersive properties in deep water than several high-order Boussinesq-type models. For variable bottom bathymetries, the shoaling properties of the model are studied numerically, exhibiting good agreement with results from Stokes linear theory in the case of mild bottom slopes, using a sufficiently high value of N T with respect to the offshore relative water depth. For an offshore water depth of k h = 10 (i.e. more than 3 times the deep water limit), accurate wave heights in shallow water ( k h = 0 . 25 ) are obtained with N T = 6 (or higher). Finally, the linear version of the model is validated with comparisons to analytical solutions of the reflection and transmission coefficients of regular waves over Roseau-type bathymetric profiles. Two bottom profiles are considered, including one with a steep slope, whose maximum value reaches about 1:0.7 (i.e. an angle of about 54.9 deg.). Using N T = 7 , small differences ( < 0 . 4 % ) with the analytical solution are observed for the four considered cases, confirming the ability of the linear model to represent accurately the effects of steep bottom gradients on wave propagation dynamics. [ABSTRACT FROM AUTHOR]

Published
2017
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3. Validation of a fully nonlinear and dispersive wave model with laboratory non-breaking experiments.

Author

Raoult, Cécile, Benoit, Michel, and Yates, Marissa L.

Subjects
*NONLINEAR waves, *DISPERSIVE interactions, *WATER waves, *CHEBYSHEV polynomials, *COMPUTER simulation, *POTENTIAL flow
Abstract

With the objective of modeling coastal wave dynamics taking into account nonlinear and dispersive effects, a highly accurate nonlinear potential flow model was developed. The model is based on the time evolution of two surface quantities: the free surface position and the free surface velocity potential. A spectral approach is used to resolve vertically the velocity potential in the domain, by decomposing the potential using an orthogonal basis of Chebyshev polynomials. With this approach, a wide range of relative water depths can be simulated, as demonstrated here with the propagation of nonlinear regular waves over a flat bottom with kh = 2 π and 4 π (where k is the wave number and h the water depth). The model is then validated by comparing the simulation results to experimental data for four non-breaking wave test cases: (1) nonlinear dynamics of a wave train generated by a piston-type wavemaker in constant water depth, (2) shoaling of a regular wave train on beach with constant slope up to the breaking point, (3) propagation of regular waves over a submerged bar, and (4) propagation of nonlinear irregular waves over a barred beach. The test cases show the ability of the model to reproduce well nonlinear wave interactions and the dynamics of higher-order bound and free harmonics. The simulation results agree well with the experimental data, confirming the model's ability to simulate accurately nonlinear and dispersive effects for non-breaking waves. [ABSTRACT FROM AUTHOR]

Published
2016
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