Modulational stability of wave packets at fluid interface of layer and half-space

The modulational stability of internal wave packets propagated along the surface of a hydrodynamic system consisting of a lower half-space and an upper layer covered with a rigid lid is investigated. The study is conducted within the framework of a nonlinear low-dimensional model incorporating surface tension on an interface using the method of multi-scale expansions implemented via symbolic computation. The evolution equation of the envelope of the wave packet takes the form of the Schrodinger equation. Conditions ¨ for the modulational stability of the solution of the evolution equation are identified for various physical and geometrical characteristics of the system. Significant influence on the modulational stability of the system’s geometrical characteristics and surface tension is observed for relatively small liquid layer thicknesses. For large layer thicknesses, the stability diagram degenerates to that of a system composed of two half-spaces.

---

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki i promocja sportu (2025).