Group resonant interactions between surface and internal gravity waves in a two-layer system

Two-dimensional resonant triad interactions in a two-layer system

“…For a density ratio close to one, relevant for the ocean, the qualitative characteristics of 2-D resonant triads are similar to those shown in figures 2 and 3, except for the value of K + 2m , at which the 1-D class-III resonance is originated from the K + 2 -axis, as shown in figure 2(b). As discussed in Taklo & Choi (2020), when the density ratio approaches one, K + 2m increases rapidly for the class-III resonance. For example, for h 2 /h 1 = 4 and ρ 2 /ρ 1 = 1.01, the minimum surface wavenumber for the 1-D class-III resonance is given by K + 2m ≈ 31.198.…”

“…Unlike case A2, successive near-resonant triad interactions can occur more easily as the density ratio is close to one (Alam 2012; Taklo & Choi 2020). Through successive resonant interactions, one expects the generation of a number of surface wave modes, or sidebands, whose wavenumbers are given by () with .…”

“…As pointed out by Alam (2012), the resonance that occurs between short surface waves and long internal waves propagating in the same direction was overlooked in the work of Ball (1964). Nevertheless, due to its relevance to ocean waves such as a mechanism of short surface wave modulation by long internal waves, the class-III resonance has been studied for a few decades both experimentally and theoretically for progressive waves (Lewis, Lake & Ko 1974;Alam 2012;Tanaka & Wakayama 2015;Taklo & Choi 2020) and for standing waves (Joyce 1974). In addition, the critical case of the class-III resonance where the internal wavenumber approaches zero has been investigated for its possible application to surface expressions of internal solitary waves (Hashizume 1980;Funakoshi & Oikawa 1983;Kodaira et al 2016).…”

“…To study the time evolution of 2-D resonant triads, spectral models have been developed from the explicit Hamiltonian system obtained by Taklo & Choi (2020) for the surface and interface displacements and the density-weighted velocity potentials evaluated at the surface and interface. Starting with the spectral model for the Fourier transforms of the original dependent variables for the explicit Hamiltonian system, the surface and interface motions have been decomposed into the surface and internal wave modes using a canonical transformation.…”

Dependence of the internal wave energy flux on the parameters of a two­layer hydrodynamic system

“…Nonlinear interactions between surface and internal gravitational waves in a two-layer system were studied in [12]. The study was conducted using explicit nonlinear evolution equations of the second order in the Hamiltonian form.…”