Breaking of shoaling internal solitary waves

TLDR

High‑resolution two‑dimensional simulations of narrow‑crested, fully nonlinear internal solitary waves of depression shoaling on a uniformly sloping boundary in a smoothed two‑layer density field were performed over a wide range of slopes (S = 0.01–0.3), with breaking location modeled as a function of wave amplitude, wavelength, and isopycnal length, and the effects of grid resolution and Reynolds number on instability and reflection were investigated. On steep slopes (S ≥ 0.1) the waves exhibited surging, plunging, and collapsing breakers linked to reflection, convective instability, and boundary‑layer separation, while on mild slopes (S ≤ 0.05) they fissioned into trains of elevation waves; the breaker type was mapped in S_w–S space, the reflection coefficient R matched other studies, and high Reynolds numbers (~10⁴) triggered a global instability that increased R by about 10 %.

Abstract

The breaking of fully nonlinear internal solitary waves of depression shoaling upon a uniformly sloping boundary in a smoothed two-layer density field was investigated using high-resolution two-dimensional simulations. Our simulations were limited to narrow-crested waves, which are more common than broad-crested waves in geophysical flows. The simulations were performed for a wide range of boundary slopes S ∈ [0.01, 0.3] and wave slopes extending the parameter range to weaker slopes than considered in previous laboratory and numerical studies. Over steep slopes ( S ≥ 0.1), three distinct breaking processes were observed: surging, plunging and collapsing breakers which are associated with reflection, convective instability and boundary-layer separation, respectively. Over mild slopes ( S ≤ 0.05), nonlinearity varies gradually and the wave fissions into a train of waves of elevation as it passes through the turning point where solitary waves reverse polarity. The dynamics of each breaker type were investigated and the predominance of a particular mechanism was associated with a relative developmental time scale. The breaking location was modelled as a function of wave amplitude ( a ), characteristic wave length and the isopycnal length along the slope. The breaker type was characterized in wave slope ( S w = a / L w , where L w is a measure of half of the wavelength) versus S space, and the reflection coefficient ( R ), modelled as a function of the internal Iribarren number, was in agreement with other studies. The effects of grid resolution and wave Reynolds number ( Re w ) on R , boundary-layer separation and the evolution of global instability were studied. High Reynolds numbers ( Re w ~ 10 4 ) were found to trigger a global instability, which modifies the breaking process relative to the lower Re w case, but not necessarily the breaking location, and results in a ~ 10 % increase in R , relative to the Re w ~ 10 3 case.