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Mathematical Modeling of Unsteady Inviscid Flows

Jeff D. Eldredge
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[Reviewed by
Sarah Patterson
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Mathematical Modeling of Unsteady Inviscid Flows by Jeff D. Eldredge is a research monograph intended to extend the instruction of flow potential into the modern era. A variety of unsteady flows including flows induced by moving bodies and the influence of added mass, vortex-vortex, and vortex-body dynamics are discussed. These are introduced by analyzing the dynamics of agile aerial and aquatic vehicles, wind harvesting devices, locomotion of large creatures in fluid, and interactions of individuals into systems. 
This self-contained book is a good choice for graduate students or researchers with a solid background in potential flow theory who want to extend their knowledge beyond steady flows. It would be appropriate for self-study. There are many full-color images for each chapter to aid the reader in visualizing the concepts.  Standard notations such as vector notation (for 2D and 3D flows), complex notation (for flows in the plane), and Plücker notation (for analysis of ridged bodies) are introduced in early chapters and then used throughout. The use of vector notation allows for a consideration of three-dimensional inviscid flow whenever possible.  Sufficient reviews of background mathematical tools for calculating force and moment on the body and foundational concepts of potential flow theory are included in the appendix and some of chapter 3 respectively. Important results of each chapter and clarifying notes are offset for the reader’s convenience in each chapter. 
There are three model components that are introduced in chapter 1 and are revisited throughout the later chapters: a means of introducing vorticity into the fluid, a representation of vorticity in the fluid, and a transport model for this fluid vorticity.  Another useful concept that is highlighted throughout the text is the influence on the overall motion of the fluid of a flow contributor. Some measures of fluid motion can even be linearly decomposed into the effects of such contributors. 
Sarah Patterson is an assistant professor of applied mathematics at the Virginia Military Institute. She received her PhD from Duke University in 2019 under the direction of Anita Layton. Her thesis focused on renal hemodynamic models and the immersed interface method for open interfaces. Sarah’s other research interests include computational fluid dynamics, fluid-structure interactions, numerical analysis, and mathematical modeling.