Modulation-resonance mechanism for surface waves in a two-layer fluid system

Abstract

We propose a Boussinesq-type model to study the surface/interfacial wave manifestation of an underlying, slowly-varying, long-wavelength, baroclinic flow in a two-layer, density-stratified system. The results of our model show numerically that, under strong nonlinearity, surface waves, with their typical wavenumber being the resonant k res , can be generated locally at the leading edge of the underlying slowly-varying, long-wavelength baroclinic flow. Here, the resonant k res satisfies the class 3 triad resonance condition among two short-mode waves and one long-mode wave in which all waves propagate in the same direction. Moreover, when the slope of the baroclinic flow is sufficiently small, only one spatially-localized large-amplitude surface wave packet can be generated at the leading edge. This localized surface wave packet becomes high in amplitude and large in group velocity after the interaction with its surrounding waves. These results are qualitatively consistent with various experimental observations including resonant surface waves at the leading edge of an internal wave. Subsequently, we propose a mechanism, referred to as the modulation-resonance mechanism, underlying these surface phenomena, based on our numerical simulations. The proposed modulation-resonance mechanism combines the linear modulation (ray-based) theory for the spatiotemporal asymmetric behavior of surface waves and the nonlinear class 3 triad resonance theory for the energy focusing of surface waves around the resonant wavenumber k res in Fourier space.

Modulation of surface gravity waves by internal waves

“…Note, the model of Craig et al (2012) requires detailed in-situ measurements of the upper water column, while the numerical model of Hao and Shen (2020) is computationally expensive. Furthermore, recently Jiang et al (2019) investigated the generation of (weakly nonlinear) surface waves at the leading edge of an internal wave. These models do not apply to the physical scenario considered here, where we have a broad band sea state that is characterized by breaking in the rough bands (see figure 1).…”

A Model Sensitivity Study of Ocean Surface Wave Modulation Induced by Internal Waves

“…Alternatively, the two‐layer ocean model is based on the potential flow assumption and is thus less computationally expensive. The nonlinear interaction between surface waves and internal waves has been studied by several simplified models derived from the two‐layer model, including the nonlinear Schrödinger equation coupled to the Korteweg–de Vries (KdV) equation (Craig et al., 2012) and the second‐order approximation to the original governing equations (Jiang et al., 2019; Taklo & Choi, 2020). These simplifications mean that the short wave dynamics are not fully resolved.…”

“…To avoid numerical instability, we restrict our discussions to the weakly/moderately nonlinear internal waves comparable to those in HS20, such that both the surface and interface quantities can be expanded in terms of the typical wave slopes. Note that this is a necessary simplification in the phase‐resolved models to ensure that the surface wave dynamics can be captured together with the internal wave (Craig et al., 2012; Hao & Shen, 2020; Jiang et al., 2019; Taklo & Choi, 2020).…”

Laboratory Study of the Impact of the Surface Solitary Waves Created by the Internal Solitary Waves on Optical Imaging

“…We could clearly observe SSWs created by the ISWs. The depression‐type ISWs created elevation‐type SSWs (S. X. W. Jiang et al., 2019) (blue solid line in Figure 4a) that manifested in a bright‐dark pattern in the optical images, as shown in Figure 4b. In contrast, the elevation‐type ISWs created depression‐type SSWs (blue solid in Figure 4c) and had dark‐bright patterns in the optical images (see Figure 4d).…”