Numerical Comparison for Focused Wave Propagation Between the Fully Nonlinear Potential Flow and the Viscous Fluid Flow Models

Jiang, Sheng-Chao; Liu, Changfeng; Sun, Lei

doi:10.1007/s13344-020-0026-4

Cited by 2 publications

(1 citation statement)

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“…A great number of studies have been conducted on gravity-capillary surface waves and there have been notable advancements in the study of nonlinear and dispersive gravitycapillary surface waves, with a particular focus on the effect of viscosity [1][2][3][4][5][6][7][8][9][10][11]. Several linear and weakly nonlinear equations have been suggested to represent the propagation of surface waves and dispersion relations [11][12][13][14]. The study of the nonlinear properties of capillary-gravity waves in infinitely deep water was initiated by Harrison [15] using a perturbation expansion.…”

Section: Introductionmentioning

confidence: 99%

Comprehensive Perturbation Approach to Nonlinear Viscous Gravity–Capillary Surface Waves at Arbitrary Wavelengths in Finite Depth

Ghahraman

Bene

2023

Fluids

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This study presents a comprehensive analysis of the second-order perturbation theory applied to the Navier–Stokes equations governing free surface flows. We focus on gravity–capillary surface waves in incompressible viscous fluids of finite depth over a flat bottom. The amplitude of these waves is regarded as the perturbation parameter. A systematic derivation of a nonlinear-surface-wave equation is presented that fully takes into account dispersion, while nonlinearity is included in the leading order. However, the presence of infinitely many over-damped modes has been neglected and only the two least-damped modes are considered. The new surface-wave equation is formulated in wave-number space rather than real space and nonlinear terms contain convolutions making the equation an integro-differential equation. Some preliminary numerical results are compared with computational-modelling data obtained via open source CFD software OpenFOAM.

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