Experimental study on transformation and energy properties of depression internal solitary wave over a bottom step

Abstract

Waveform deformation and breaking are widespread phenomena when internal solitary waves (ISWs) encounter changing topographies, which have been observed in many parts of oceans. In this study, experiments are performed in a series of combinations of bottom step topographies with different heights and ISWs in different amplitudes within a two-layer stratified fluid system. According to experimental results, the evolution processes of ISWs over the bottom step are classified into four typical regimes as the wave–step interaction varying from weak to strong, which are the transmission regime, transitional regime, breaking regime, and reflection regime, corresponding to the evolution patterns of steady passage, deformation, breaking, and strong reflection, respectively. To describe the intensity of wave–step interaction, a new improved interaction parameter is proposed, which takes both relative amplitude of ISWs and relative topography changes into consideration, and achieved better effectiveness in defining the boundaries between different regimes. In terms of energy properties, with the wave–step interaction becoming stronger, the transmission ratio keeps decreasing throughout all regimes, while the reflection wave starts to appear since the breaking regime and its energy keeps increasing. At the critical point between the breaking regime and reflection regime, the reflection ratio equals the transmission ratio, and the energy loss ratio reaches its maximum.

Laboratory Investigation of Energy Dissipation and Turbulent Mixing During Internal Solitary Wave Breaking on the Rough Shelf Slope

“…while the two terms on the right side of the equation represent the potential energy and kinetic energy carried by the internal solitary wave respectively (Zou et al., 2021), where $$c$$ is the wave speed, g is the gravitational acceleration, A is the incline ISW amplitude, η ( t ) is the time history of the wave profile of the ISW, ∆ ρ is the density difference between two layers. The startpoint ( t 1 ) and endpoint are defined as the earliest and latest moments corresponding to the wave surface deviation from the equilibrium position at a distance with 5% of the wave height from the beginning and the end of the waveform, respectively (Figure 4c).…”

“…So the dissapated energy ( E loss ) can be calculated using Equation , and the ratio of energy dissipated during the ISW breaking event R loss is defined as Zou et al. (2021): $$$\begin{array}{c}{R}_{\text{loss}}=\frac{{E}_{\text{loss}}}{{E}_{i}}.\end{array}$$$ …”

“…The energy for an ISW ( E i or E r ) can be computed by the time integral of wave profiles according to the definition from Michallet and Ivey (1999) and Zou et al. (2021) as follows: $$$\begin{array}{c}E=cAg{\increment}\rho \underset{t1{}}{\overset{t2}{\int }}\eta (t)dt+cg{\increment}\rho \underset{t1{}}{\overset{t2}{\int }}{\eta (t)}^{2}\,dt,\end{array}$$$ …”

“…where E with subscript i , r , out , and loss represent incident ISW, reflected ISW, outflow and dissipated energy, respectively. The energy for an ISW (E i or E r ) can be computed by the time integral of wave profiles according to the definition from Michallet and Ivey (1999) and Zou et al (2021) as follows:…”

“…The magnitude of E out is small, accounting for only 1 ∼ 2% of E i in all experiments. So the dissapated energy (E loss ) can be calculated using Equation 11, and the ratio of energy dissipated during the ISW breaking event R loss is defined as Zou et al (2021):…”