Nonlinear internal waves in a two-liquids system

In this work a theoretical and experimental investigation is performed on the sloshing of two immiscible liquid layers inside of a closed, squared-section tank. By applying a variational approach to the potential formulation of the fluid motion, a nonlinear dynamical system is derived applying the Lagrange equations to the Lagrangian of motion defined in terms of suitable generalised co-ordinates. Such coordinates are the time-depending coefficients of the series expansions adopted for the surface of separation and for the velocity potentials of the fluid layers. Dissipative effects are taken into account by considering generalised dissipative forces added to the Lagrange equations. Numerical integration of the nonlinear dynamical system gives solutions in good agreement with experimental data.