Modal Method for Solving the Nonlinear Sloshing of Two Superposed Fluids in a Rectangular Tank - Meziani, Bachir; Ourrad, Ouerdia (Journal of Applied Nonlinear Dynamics, 2026)
The nonlinear sloshing of two superposed fluids in a rectangular tank is studied. The equations governing the nonlinear motion of the interface and the free surface have been resolved at first and second order. The shape of these surfaces depends on the perturbation parameter ε and density ratio ρ of the fluids. The analysis of nonlinear effects shows new aspects that are not pre-viously observed. Linear theory is still valid for very small sloshing amplitude. When the amplitude increases, nonlinear effects can not be neglected. Superposed fluids with neighbors densities are more sensitive to nonlinear effects. they occurs in this case, by sub harmonic instabilities in space and beats phenomena in time. The first non-linear effects are observed at the interface. when ε increases, the influence of terms related to the first order eigenfrequency ω11 decreases and the influence of terms related to the eigenfrequency 2ω11 increases faster than those relating to the second order eigenfrequency ω21. At the free surface, the influence of terms related to the second order eigenfrequency ω21 is more pronounced when they appear as the influence of those relating to the eigenfrequency 2ω11.