The fundamental eigenfrequency is simple in the two-dimensional sloshing problem

2023/05/22 by Н. В. Кузнецов, Kuznetsov, Nikolay
Earth and Planetary Sciences · Engineering · #35P05 #Analysis of PDEs (math.AP) #Arctic and Antarctic ice dynamics #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics Simulations and Interactions #Mathematical Physics (math-ph) #Wave and Wind Energy Systems

paper · pdf · doi:10.48550/arxiv.2305.12949

openalex publication_date 2023/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The two-dimensional sloshing problem is considered; it describes the transversal free oscillations of water in an open, infinitely long canal of uniform cross-section. It is proved that the fundamental eigenfrequency is simple, whereas the corresponding velocity potential has only one nodal line connecting the free surface and the bottom; its harmonic conjugate (stream function) does not change sign under the proper choice of the additive constant.

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