Shoaling of internal solitary waves over linear slopes with variable topography

Abstract

This study investigates the influence of variable topography on the kinematics of internal solitary wave shoaling across various breaking regimes under the unifying condition of a slope-intersecting pycnocline. It is demonstrated that bottom corrugations can significantly modify the dynamics: in plunging, collapsing and fission cases, variable topography alters wave shape and induces Kelvin–Helmholtz billows within the pycnocline; in surging scenarios, it impedes upslope propagation and generates a reflected mode-2 wave offshore. Despite these pronounced mechanical effects during the breaking phase, analysis of density and enstrophy fields via a user-defined scatter plot method suggests that potential post-wave mixing distributions remain largely unaffected by changes in the topography parameter, indicating a transient influence confined to the active shoaling region. In the fission case, the length scale of the topography can be much larger than the wavelength. In this case, undulating topography locally modifies layer depths, potentially arresting and restarting the fission process as critical depth ratios are traversed. A comparison between two- and three-dimensional simulations is made in the collapsing case and it is shown that the two-dimensional simulations accurately capture the dynamics of wave breaking at onset.