Comprehensive Perturbation Approach to Nonlinear Viscous Gravity–Capillary Surface Waves at Arbitrary Wavelengths in Finite Depth
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 r...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-07-01
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| Series: | Fluids |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2311-5521/8/8/218 |
| Summary: | 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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| ISSN: | 2311-5521 |