On the shape of the fundamental sloshing mode in axisymmetric containers

TL;DR

This paper numerically investigates the high spot positions of the fundamental sloshing mode in axisymmetric tanks, introducing new computational methods and linking the problem to the hot spots conjecture.

Contribution

It presents a novel numerical scheme for calculating sloshing modes and a new imaging method, connecting fluid oscillation problems to spectral graph theory.

Findings

Identified the high spot locations in axisymmetric tanks

Developed a new numerical approach for sloshing mode computation

Linked the high spot problem to the hot spots conjecture

Abstract

In the paper we numerically study positions of high spots (extrema) of the fundamental sloshing mode of liquid in an axisymmetric tank. Our approach is based on a linear model reducing the problem to appropriate Steklov eigenvalue problem. We propose a numerical scheme for calculating sloshing modes and a novel method of making images of oscillating fluid. We also describe the relation of the high spot problem to the celebrated hot spots conjecture.