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2025 | OriginalPaper | Chapter

2. Understanding Sloshing as a Complex Asymptotically Reduced Dynamical System

Author : Alexander N. Timokha

Published in: Interfacial Flows—The Power and Beauty of Asymptotic Methods

Publisher: Springer Nature Switzerland

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Abstract

The chapter presents a detailed examination of sloshing dynamics, focusing on the complex interactions between liquid motion and container movements. It begins by discussing the fundamental principles of sloshing, emphasizing how liquid sloshing in partially filled containers can generate significant hydrodynamic forces and moments, posing risks to structural integrity. The text delves into the mathematical modeling of sloshing, utilizing the Bateman-Luke variational principle and multimodal modeling techniques to derive the Miles-Lukovsky-type modal equations. These equations are crucial for understanding the resonant behaviors and stability of sloshing systems. The chapter also explores the linear and nonlinear theories of sloshing, including the Duffing equation and single-dominant modal theories, which are essential for predicting and controlling sloshing phenomena. Additionally, it covers the application of these theories to various container shapes and motion types, providing insights into the practical challenges and solutions related to sloshing in real-world scenarios. The chapter concludes with a discussion on the implications of sloshing for structural design and control systems, highlighting the importance of accurate modeling and analysis in ensuring the safety and efficiency of liquid-containing structures.
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previous chapter Introduction: Applying Perturbation and Related Methods to Rationally Describe the “Teapot Effect” Under Capillary and Weak Viscous Action
next chapter Thin-Film Flows: Classical Examples, Marangoni Motions, and Viscous Membranes
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Metadata
Title
Understanding Sloshing as a Complex Asymptotically Reduced Dynamical System
Author
Alexander N. Timokha
Copyright Year
2025
Book
Interfacial Flows—The Power and Beauty of Asymptotic Methods

Print ISBN: 978-3-031-78763-8

Electronic ISBN: 978-3-031-78764-5

Copyright Year: 2025

DOI
https://doi.org/10.1007/978-3-031-78764-5_2

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