Interfacial gravity waves in a two-fluid system

In this work a theoretical and experimental investigation is performed on the sloshing of two immiscible liquid layers inside of a closed square-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 coordinates. These coordinates are the time depending coefficients of the modal expansions adopted for the separation surface of the two fluids and for the velocity potentials of the fluid layers. Dissipative effects are taken into account by considering generalised dissipative forces derived by a dissipative model extensively treated in the paper. Numerical integration of the dynamical system furnish solutions which well reproduce the examined experimental configurations.