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2025 | OriginalPaper | Chapter

4. Free Surface Singularities: From Singular Points to Spatio-Temporal Complexity

Author : Jens Eggers

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

Publisher: Springer Nature Switzerland

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Abstract

The chapter explores the fascinating realm of free surface singularities, focusing on both time-dependent and persistent phenomena. It begins by classifying singularities into time-dependent, such as the breakup of a fluid drop, and time-independent, like the caustic lines observed in a coffee cup. The text delves into the dynamics of these singularities, highlighting how they organize the surrounding behavior and exhibit universal properties. It discusses the formation of drops, the coalescence of fluids, and the development of shock waves, illustrating the rich variety of singularities and their underlying mechanisms. The chapter also examines the concept of self-similarity, where the structure of a singularity remains invariant under scaling transformations, and explores the conditions under which this property holds. It further investigates the stability of similarity solutions, revealing how small perturbations can lead to complex, time-dependent behaviors. The text also touches on the eikonal equation and its role in describing wavefront dynamics, including the formation of caustics and the application of catastrophe theory to classify optical singularities. Additionally, it discusses the transition from one-dimensional to multi-dimensional singularities, highlighting the conditions under which pointlike or quasi-one-dimensional behaviors emerge. The chapter concludes by tying together these concepts to describe the spatial and temporal complexity observed in turbulent systems, providing a comprehensive overview of the emergent behaviors and universal properties of free surface singularities.
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previous chapter Thin-Film Flows: Classical Examples, Marangoni Motions, and Viscous Membranes
next chapter Viscoelastic Lubrication Using the Second-Order Fluid
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Metadata
Title
Free Surface Singularities: From Singular Points to Spatio-Temporal Complexity
Author
Jens Eggers
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_4

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