Abstract: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… Show more
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