Author(s): Richard Jurisits

Linked Author(s):

Keywords: Solitary waves; Korteweg-de Vries equation; Turbulent flows; Free-surface flows

Abstract: We consider a two-dimensional, incompressible, turbulent open-channel flow over a plane bottom with small, constant slope. The roughness of the bottom may vary with the space coordinate in main direction of the flow, giving rise to small variations in the bottom friction coefficient. The flow is assumed to be slightly supercritical with Froude numbers close to 1. In an asymptotic analysis given in Schneider (2013), an extended Kortewegde Vries (KdV) equation was derived to describe the surface elevation of the fluid. While stationary solutions as perturbed forms of the classical solitary wave type have been studied intensively in the past, we focus on a a travelling wave solution for a novel single wave solution type. This new solution type is characterized by a smaller amplitude as compared to the classical solitary wave and exhibits a slow decay in downstream direction (shallow tail).

DOI: https://doi.org/10.3850/978-90-833476-1-5_iahr40wc-p0445-cd

Year: 2023