M.A. Boniforti

A fully nonlinear model for sloshing in a rotating container

In this paper a theoretical and experimental analysis of sloshing in 2D and 3D free-surface configurations is performed. In particular, the case of a tank rotating around a horizontal axis has been considered. The fluid is assumed to be incompressible and inviscid. A fully nonlinear mathematical model is defined by applying the variational method to the sloshing. The damping of gravity waves has been accounted by introducing a suitable dissipation function from which generalized dissipative forces are derived. A modal decomposition is then adopted for the unknowns and a dynamical system is derived to describe the evolution of the physical system. An experimental technique has been applied to select the leading modes, whose evolution characterizes the physical process, i.e. captures the most of the kinetic energy of the process. A very good agreement between experimental and numerical results confirms the validity of the methodological approach followed.

A two-layer shallow water model for 3D gravity currents

A two-layer, shallow-water model for three-dimensional (3D) gravity currents is proposed. The formulation results from the shallow-water-equations for two layers of immiscible liquids, subjected by the rigid-lid condition, so that the upper surface of the lighter layer remains perfectly flat during the motion. The arising pressure must be determined by solving the equations of motion, which is no problem for two-dimensional and axisymmetric gravity currents because the pressure is easily eliminated. In 3D gravity currents, the pressure is determined by solving a Poisson equation, together with momentum and mass balance equations. By means of a suitable scaling and a perturbation expansion, the equations are uncoupled from each other so that the problem is considerably simplified. Numerical results are compared with 3D lock-exchange release experiments. A comparison between numerical and experimental results of the gravity current indicates a fairly good agreement, whereas the results concerning the upper layer field variables shows that the numerical results are consistent with the experiments.

Experimental and theoretical investigation on the sloshing of a two-liquid system with free surface

In this paper a theoretical and experimental investigation is performed on the sloshing of a two-liquid system with both separation and free surface. The experimental configuration consists of an oscillating tank filled with two layers of immiscible liquids. The mathematical model is obtained by applying the Lagrangian variational approach to the potential formulation of the fluid motion, and a dynamical system which describes the dynamics of motion is derived. In order to account for the damping of the motion, generalized dissipative forces are considered. For this purpose, the logarithmic decrement coefficients are estimated by means of a wavelet analysis performed on the experimental free oscillations of the fluid system. Numerical integration of the mathematical model gives results which are in a fair agreement with the experimental results.

Interfacial gravity waves in a two-fluid system

Abstract 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.

Hamiltonian formulation for the motion of a two fluid system with free surface

In this work, a theoretical investigation is performed on modeling interfacial and surface waves in a layered fluid system. The physical system consists of two immiscible liquid layers of different densities ρ1 > ρ2 with an interfacial surface and a free surface, inside a prismatic-section tank. On the basis of the potential formulation of the fluid motion, we derive a nonlinear system of partial differential equations using the Hamiltonian formulation for irrotational flow of the two fluids of different density subject to conservative force. As a consequence of the assumption of potential velocity, the dynamics of the system can be described in terms of variables evaluated only at the boundary of the fluid system, namely the separation surface and the free surface. This Hamiltonian formulation enables one to define the evolution equations of the system in a canonical form by using the functional derivatives.

Triadic resonant modes :dynamical model and truncation criterion

In the present paper we propose a three-dimensional theoretical model describing the local evolution of any two- or three-dimensional disturbance superimposed on a basic shear flow. A numerical investigation, using a truncated form of the evolution model, was performed to select resonant three-dimensional disturbance in a transitional cylinder wake. A truncation criterion of non-linear triadic resonance, which is a generalisation of the standard linear-resonance condition, allowed us to locate some triadic sets of linear eigenmodes. Numerical integration of the corresponding low-dimensional dynamical systems showed interesting results that are in qualitative agreement with those performed by Williamson and Prasad [J. Fluid Mech. 256 (1993) 269.] This seems to validate the truncation criterion which, together with the theoretical model, proved to be an appropriate tool for describing the local evolution of large-scale structures in shear flows.

Transitional flow as a nonlinear dynamical system

Investigation performed over the past twenty years have clearly pointed out the importance of large scale coherent structures in mixing, in transition dynamics and in turbulence of free shear flows.

Dynamics Of Interfacial And Surface Waves In A Layered Fluid

In this paper the dynamics of a layered fluid system, constituted by two superimposed immiscible liquid layers inside a moving container, is considered. Such layered fluid system presents two moving boundaries: the separation surface and the free surface. The motion imposed to the container an oscillating rotation with given amplitude and frequency generates waves on the moving surfaces, whose dynamics is analysed by means of a suitable visualisation device. Several wave configurations are obtained by varying the angular frequency of the exciting motion and some of them compared with those obtained by numerical simulations.

Sinuous and Varicose Modes in Phase-Locked Interaction

The aim of this paper is to propose an identification technique of dynamical systems in order to describe the local evolution of modes which dominate the dynamics of transitional shear flows. By using the linear eigenmodes of viscous flows, a numerical investigation was performed to model the dynamical evolution of disturbances which arise in a transitional symmetric shear flow when a planar mode interacts in a phase-locked mechanism with one or more oblique three-dimensional modes. Numerical results highlighted a good qualitative agreement with the experimental ones and showed furthermore some interesting correspondences with the phenomenological conclusion of recent theoretical investigations obtained by spatial stability of inviscid flows. Our investigation confirmed that only some nonlinear triadic interactions can be active, depending on the sinuous or varicose nature of the selected modes. In particular, mechanisms of coupling among more triadic systems turned out to be of remarkable interest, in that they can induce a preferential amplification of oblique modes in spite of their dumped-varicose nature.