• Corpus ID: 244478052

High Spots for the Ice-Fishing Problem with Surface Tension

@article{Willis2021HighSF,
  title={High Spots for the Ice-Fishing Problem with Surface Tension},
  author={N. Parker Willis and Chee Han Tan and Christel Hohenegger and Braxton Osting},
  journal={ArXiv},
  year={2021},
  volume={abs/2111.10727}
}
In the ice-fishing problem, a half-space of fluid lies below an infinite rigid plate (“the ice”) with a hole. In this paper, 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… 

References

SHOWING 1-10 OF 30 REFERENCES
An Isoperimetric Sloshing Problem in a Shallow Container with Surface Tension
In 1965, B. A. Troesch solved the isoperimetric sloshing problem of determining the container shape that maximizes the fundamental sloshing frequency among two classes of shallow containers:
The damping of capillary–gravity waves at a rigid boundary
The frequency and damping rate of surface capillary-gravity waves in a bounded region depend on the conditions imposed where the free surface makes contact with the boundary. Extreme cases are when
Gravity-capillary waves with edge constraints
This paper presents a theoretical and experimental investigation into a novel class of water-wave motions in narrow open channels. The distinctive condition on these motions is that the lines of
A Variational Characterization of Fluid Sloshing with Surface Tension
TLDR
In the limit of zero surface tension, the variational formulation of the mixed Steklov-Neumann eigenvalue problem is recovered and it is proved a domain monotonicity result for the fundamental sloshing eigen value.
‘High spots’ theorems for sloshing problems
We investigate several 2D and 3D cases of the classical eigenvalue problem that arises in hydrodynamics and is referred to as the sloshing problem. In particular, for a domain W ⊂ R2 (canal's
Capillary hysteresis in sloshing dynamics: a weakly nonlinear analysis
The sloshing of water waves in a vertical cylindrical tank is an archetypal damped oscillator in fluid mechanics. The wave frequency is traditionally derived in the potential flow limit (Lamb,
Experimental investigation of capillarity effects on surface gravity waves: non-wetting boundary conditions
Damping and eigenfrequencies of surface capillary—gravity waves greatly depend on the boundary conditions. To the best of our knowledge, so far no direct measurement has been made of the dynamic
LIQUIDS ON SOLID SURFACES: STATIC AND DYNAMIC CONTACT LINES
A contact line is formed at the intersection of two immiscible fluids and a solid. That the mutual interaction between the three materials in the immediate vicinity of a contact line can
On the eigenvalue problem for fluid sloshing in a half-space
SummaryThe boundary-value problem for free oscillations of a liquid in a half-space, which is bounded above by a rigid plane that contains a circular aperture, is transformed to a homogeneous,
On the ‘high spots’ of fundamental sloshing modes in a trough
  • T. Kulczycki, N. Kuznetsov
  • Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2010
We study an eigenvalue problem with a spectral parameter in a boundary condition. The problem describes sloshing of a heavy liquid in a container, which means that the unknowns are the frequencies
...
1
2
3
...