On the shape of the fundamental sloshing mode in axisymmetric containers

2014/11/10 by Kulczycki, Tadeusz, Kwaśnicki, Mateusz, Siudeja, Bartłomiej
#65N25 #65N30 #76M10 #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1411.2572

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.

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