Dispersive and dispersive-like bores in channels with sloping banks

Abstract

In this paper a detailed analysis of undular bore dynamics in channels of variable cross-section is presented. Two undular bore regimes, low Froude number (LFN) and high Froude number (HFN), are simulated with a Serre–Green–Naghdi model, and the results are compared with the experiments by Treske (1994). We show that contrary to Favre waves and HFN bores, which are controlled by dispersive non-hydrostatic mechanisms, LFN bores correspond to a hydrostatic phenomenon. The dispersive-like properties of the LFN bores is related to wave refraction on the banks in a way similar to that of edge waves in the near shore. A fully hydrostatic asymptotic model for these dispersive-like bores is derived and compared to the observations, confirming our claim.