On the dynamics of the separation surface in a two liquid layer system M.LaRocca 1 ,G.Sciortino 1 ,M.A.Boniforti 2 1 University RomaTRE, Via V.Volterra 62, 00146 Roma, Italy 2 University La Sapienza, Via Eudossiana 18, 00184 Roma, Italy Abstract In this paper a theoretical and experimental investigation on the slosh- ing of two liquid layers with a free-surface is performed. The mathemati- cal model is obtained by applying the Lagrangian variational formulation to the potential formulation of the fluid motion and a dynamical sys- tem which describes the dynamics of motion of the separation surface is derived. In order to account the damping of the motion, generalised dissipative forces are considered. To this aim, the logarithmic decrement coefficients are estimated by means of a wavelet analysis performed on the experimental free oscillations of the fluid system. The numerical integra- tion of the mathematical model gives results which are in good agreement with the experimental results. 1 Introduction The aim of this paper consists in investigating the motion of the separation surface between two layers of immiscible liquids inside of a prismatic container which can rotate around a horizontal axis. Colored water and transparent vase- line oil are used. The upper liquid is limited by a free surface. The theoretical problem is analysed assuming a potential formulation for the absolute fluid mo- tion, moreover suitable expansions for the velocity potentials, the separation surface and the free surface are adopted so that the variational formulation, described in La Rocca et al.(2000, 2002), can be applied to the present case. In order to take into account for the damping of the motion, a dissipative function expressed in terms of logarithmic decrement coefficients is considered. To this aim, a wavelet analysis is applied to the decaying oscillations of the fluid system which permits to experimentally detect the decrement coefficients linked to each eigenfrequency of the considered mode. For different values of the forcing frequency and amplitude an experimental and numerical investigation is performed. The agreement between numerical 1