On adjustable undular bore profiles based on the modified steady KdV–Burgers equation

Abstract

In this study, a speed parameter is introduced into the steady Korteweg–de Vries (KdV)–Burgers equation which enables the theoretical undular bore profiles to be adjustable with a proper combination of the speed parameter and the viscous damping parameter. A new criterion for identifying the above two bores is then proposed with respect to these two parameters, whose influence on the undular bore profile is then discussed. For the theoretical solution with a small damping, error after introducing the variable speed parameter is limited. A large speed parameter corresponds to a wide range of acceptable dampings. From the energy perspective, it is confirmed that the speed parameter also denotes the nonlinearity effect. In addition, comparison between the theoretical and experimental results shows the superiority of the present model over the traditional model, which also reveals the physical meanings of the present model.