Journal topic
Nonlin. Processes Geophys., 16, 33–42, 2009
https://doi.org/10.5194/npg-16-33-2009

Special issue: Extreme surface and internal waves

Nonlin. Processes Geophys., 16, 33–42, 2009
https://doi.org/10.5194/npg-16-33-2009

05 Feb 2009

05 Feb 2009

# The transformation of an interfacial solitary wave of elevation at a bottom step

V. Maderich1, T. Talipova2, R. Grimshaw3, E. Pelinovsky2,3, B. H. Choi4, I. Brovchenko1, K. Terletska1, and D. C. Kim4 V. Maderich et al.
• 1Department of Marine and River Systems, Institute of Mathematical Machine and System Problems, Kiev, Ukraine
• 2Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Nizhny Novgorod, Russia
• 3Department of Mathematical Sciences, Loughborough University, Loughborough, UK
• 4Department of Civil and Environmental Engineering, Sungkyunwan University, Suwon, Korea

Abstract. In this paper we study the transformation of an internal solitary wave at a bottom step in the framework of two-layer flow, for the case when the interface lies close to the bottom, and so the solitary waves are elevation waves. The outcome is the formation of solitary waves and dispersive wave trains in both the reflected and transmitted fields. We use a two-pronged approach, based on numerical simulations of the fully nonlinear equations using a version of the Princeton Ocean Model on the one hand, and a theoretical and numerical study of the Gardner equation on the other hand. In the numerical experiments, the ratio of the initial wave amplitude to the layer thickness is varied up one-half, and nonlinear effects are then essential. In general, the characteristics of the generated solitary waves obtained in the fully nonlinear simulations are in reasonable agreement with the predictions of our theoretical model, which is based on matching linear shallow-water theory in the vicinity of a step with solutions of the Gardner equation for waves far from the step.