Generalizing the Multimodal Method for the Levitating Drop Dynamics

الملخص EN

The present paper extends the multimodal method, which is well known for liquid sloshing problems, to the free-surface problem modeling the levitating drop dynamics.

The generalized Lukovsky-Miles modal equations are derived.

Based on these equations an approximate modal theory is constructed to describe weakly-nonlinear axisymmetric drop motions.

Whereas the drop performs almost-periodic oscillations with the frequency close to the lowest natural frequency, the theory takes a finite-dimensional form.

Periodic solutions of the corresponding finite-dimensional modal system are compared with experimental and numerical results obtained by other authors.

A good agreement is shown.