Sloshing in vertical cylinders with circular walls: the effect of radial baffles

TL;DR

This study investigates how radial baffles in vertical cylindrical containers influence sloshing eigenvalues and eigenfunctions, revealing significant changes in eigenvalue multiplicity and surface behavior due to symmetry breaking.

Contribution

It provides a detailed analysis of the impact of radial baffles on sloshing eigenvalues, eigenfunctions, and surface patterns, highlighting new effects of symmetry breaking.

Findings

Radial baffles lower the lowest eigenvalues.

Baffles cause all eigenvalues to become simple.

Surface maxima, minima, and nodes are affected by baffle presence.

Abstract

The behaviour of sloshing eigenvalues and eigenfunctions is studied for vertical cylindrical containers that have circular walls and constant (possibly infinite) depth. The effect of breaking the axial symmetry due to the presence of radial baffles is analysed. It occurs that the lowest eigenvalues are substantially smaller for containers with baffles going throughout the depth; moreover, all eigenvalues are simple in this case. On the other hand, the lowest eigenvalue has multiplicity two in the absence of baffle. It is shown how these properties affect the location of maxima and minima of the free surface elevation and the location of its nodes.