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High Spots for the Ice-Fishing Problem with Surface Tension

In the ice-fishing problem, a half-space of fluid lies below an infinite rigid plate (``the ice'') with a hole. We investigate the ice-fishing problem including the effects of surface tension on the free surface. The dimensionless number that describes the effect of surface tension is called the Bond number. For holes that are infinite parallel strips or circular holes, we transform the problem to an equivalent eigenvalue integro-differential equation on an interval and expand in the appropriate basis (Legendre and radial polynomials, respectively). We use computational methods to demonstrate that the high spot, i.e., the maximal elevation of the fundamental sloshing profile, for the ice-fishing problem is in the interior of the free surface for large Bond numbers, but for a sufficiently small Bond number the high spot is on the boundary of the free surface. While several papers have proven high spot results in the absence of surface tension as it depends on the shape of the container, to the best of our knowledge, this is the first study investigating the effects of surface tension on the location of the high spot.

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Informasi Detail

Judul Seri

SIAM JOURNAL ON APPLIED MATHEMATICS; Vol.82 No.4 July-August 2022

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 1312-1335

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

SURFACE TENSION
GENERALIZED EIGENVALUE PROBLEM
ORTHOGONAL POLYNOMIALS
FLUID SLOSHING
HIGH SPOTS CONJECTURE

Info Detail Spesifik

https://doi.org/10.1137/21M1458879

Pernyataan Tanggungjawab

Nathan Willis, Chee Han Tan, Christel Hohenegger, Braxton Osting

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