Interfacial gravity waves in a two-fluid system

Abstract

In this work a theoretical and experimental investigation is performed on the sloshing\ud of two immiscible liquid layers inside of a closed square-section tank. By applying a\ud variational approach to the potential formulation of the fluid motion, a nonlinear\ud dynamical system is derived applying the Lagrange equations to the Lagrangian of\ud motion defined in terms of suitable generalised coordinates. These coordinates are\ud the time depending coefficients of the modal expansions adopted for the separation\ud surface of the two fluids and for the velocity potentials of the fluid layers. Dissipative\ud effects are taken into account by considering generalised dissipative forces derived\ud by a dissipative model extensively treated in the paper.\ud Numerical integration of the dynamical system furnish solutions which well\ud reproduce the examined experimental configurations

Dynamic coupling between horizontal vessel motion and two-layer shallow-water sloshing

“…Another example is the work of LA ROCCA ET AL. [39,40] which includes both experiments and theory showing excellent agreement between a Lagrangian reduction to a large system of ODEs and the experimental results for a rigid lid container [39], and two layers with a free surface [40]. However, as far as we are aware there are no results in the literature which consider the dynamic coupling between a sloshing two-layer fluid and vessel motion.…”

Two-dimensional variational vibroequilibria and Faraday?s drops

“…The surveys by Nevolin (1984) [43], Lukovsky & Timokha (1999) [33], Perlin & Schultz (2000) [44], Faltinsen & Timokha (2001, 2002 [7,8], Ibrahim et al (2001) [16] and La Rocca et al (2002) [25] include detailed description of theoretical and experimental results from this scientific field emphasising mainly nonlinear gravity/capillary-gravity waves due to resonant forcing. When forcing frequency is close to the lowest natural frequency, the resonant waves occur relative to potential equilibria caused by surface tension and gravitation.…”

Sloshing of a layered fluid with a free surface as a Hamiltonian system

“…22. The motions of both the separation and free surfaces were measured by recording the motion by a charge coupled device ͑CCD͒ camera, extracting from the movie a series of images and determining from the images the instantaneous position of each point of the moving surfaces.…”

“…La Rocca et al 21 developed a fully nonlinear model based on a variational Lagrangian approach, avoiding any perturbative expansion and taking into account all the nonlinear effects. The sloshing of a layered fluid system without and with a free surface was recently investigated by a variational Lagrangian approach, respectively by La Rocca et al 22,23 Both experimental and theoretical analyses were performed by modeling a tank with a squared base. The mathematical model was applied to the potential formulation of the fluid motion and a dynamical system was derived in order to describe sloshing's dynamics.…”