Birth, interactions, and evolution over topography of solitons in Serre-Green-Naghdi model

TL;DR

This paper demonstrates the robustness and complex interactions of solitons in the Serre-Green-Naghdi equations through high-resolution simulations, revealing their resilience and behavior over topography.

Contribution

It introduces a novel well-balanced finite-volume method and provides new insights into soliton interactions and topographic effects in the SGN model.

Findings

SGN solitons resemble KdV solitons

Solitons exit collisions with minimal residuals

Solitons survive topographic obstacles and generate secondary waves

Abstract

New evidence of surprising robustness of solitary-wave solutions of the Serre-Green-Naghdi (SGN) equations is presented on the basis of high-resolution numerical simulations conducted using a novel well-balanced finite-volume method. SGN solitons exhibit a striking resemblance with their celebrated Korteweg-deVries (KdV) counterparts. Co-moving solitons are shown to exit intact from double and triple collisions with a remarkably small wave-wake residual. The counter-propagating solitons experiencing frontal collisions and solitons hitting a wall, non-existing in KdV case configurations, are shown to also recover, but with a much larger than in co-moving case residual, confirming with higher precision the results known in the literature. Multiple SGN solitons emerging from localized initial conditions are exhibited, and it is demonstrated that SGN solitons survive hitting localized topographic obstacles, and generate secondary solitons when they encounter a rising escarpment.