Generation Solitary Waves for Viscous Flow over a Hole

Authors: Mohammed Daher Albalwi

Abstract:

This study examines the transcritical flow of a stratified fluid over topography under negative forcing amplitude (hole). This generates upstream and downstream flows connected by an unsteady solution. The phenomenon is modeled using a forced Korteweg-de Vries–Burgers equation, which takes into account weak nonlinearity and weak dispersion by considering the fluid’s viscosity beyond the Korteweg–de Vries approximation. The findings demonstrate that viscosity has a significant impact on various wave characteristics, including the amplitudes of solitary waves both upstream and downstream, as well as the widths of the bores. The focus of this study is on weak damping, and the results are applicable to transcritical, supercritical, and subcritical flows. In general, as the viscosity increases, there are notable qualitative differences from the predictions of the forced Korteweg-de Vries equation.

Keywords: Korteweg-de Vries-Burgers’ equation, soliton, viscous flow, transcritical (resonant) flow, solitary waves