# On sloshing modes in a circular tank

@article{Faltinsen2012OnSM, title={On sloshing modes in a circular tank}, author={Odd Magnus Faltinsen and Alexander N. Timokha}, journal={Journal of Fluid Mechanics}, year={2012}, volume={695}, pages={467 - 477} }

Abstract Employing the multipole-type functions given by Faltinsen & Timokha (J. Fluid Mech., vol. 665, 2010, pp. 457–479), we derive a Trefftz-type representation of the velocity potential for the liquid sloshing problem in a two-dimensional circular tank. This representation defines a continuation of the velocity potential into the ‘air’ area confined by the ‘dry’ tank surface. Its usage facilitates an effective approximation of the natural sloshing modes for all tank fillings.

## 23 Citations

### Analytical studies of sloshing in half-cylindrical tanks

- Engineering
- 2013

The technically important problem of two-dimensional inviscid standing-wave motion of a fluid in a semi-cylindrical vessel is examined using a variety of the Boussinesq wave equation as well as the…

### Analytically approximate natural sloshing modes for a spherical tank shape

- EngineeringJournal of Fluid Mechanics
- 2012

Abstract The multimodal method requires analytical (exact or approximate) natural sloshing modes that exactly satisfy the Laplace equation and boundary condition on the wetted tank surface. When…

### Analytically approximate natural sloshing modes and frequencies in two-dimensional tanks

- Engineering
- 2014

### Some aspects of the eigenfrequency computation in a two-dimensional tank filled with two non miscible fluids

- Engineering
- 2015

Determining the natural frequencies of the sloshing modes in a two-dimensional tank is a well-known problem in potential theory (see Ibrahim, 2005, or Faltinsen and Timokha, 2009, among recent…

### The Narimanov–Moiseev Multimodal Analysis of Nonlinear Sloshing in Circular Conical Tanks

- EngineeringApplied Mathematical Analysis: Theory, Methods, and Applications
- 2019

The chapter reports mathematical aspects of the Narimanov–Moiseev multimodal modelling for the liquid sloshing in rigid circular conical tanks, which perform small-magnitude oscillatory motions with…

### Multimodal Method in Sloshing

- Engineering
- 2017

The multimodal method reduces the sloshing problem with free surface to a (modal) system of nonlinear ordinary differential equations. The method was originally proposed for nonimpulsive hydrodynamic…

### Sloshing impact simulation with material point method and its experimental validations

- Engineering
- 2014

### A variational domain decomposition scheme for the natural sloshing modes in the baffled tanks

- Engineering
- 2021

### Propriétés des valeurs propres de ballotement pour contenants symétriques

- Mathematics
- 2013

The study of liquid sloshing in a container is a classical problem of hydrodynamics that has been actively investigated by mathematicians and engineers over the past 150 years. The present thesis is…

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최근 다루어지고 있는 sloshing에 관한 연구에 대하여 고찰하여 보았다. 탱크내의 유체운동의 추정에 관해서는 수치해석법에 의한 추정에 대하여는 어느 정도의 가능성을 제시하게 되었다. 그러나 구조강도상 중요한 유체충격에 의한 충격압의 추정에 대해서는 새로운 정량적 검토가 필요하다. 즉 수치계산법으로는 한계가 있기 때문에 이를 극복하기 위해서는 경험이나…