Dynamically Coupled Rigid Body-Fluid Flow Systems

✍ Scribed by Banavara N. Shashikanth

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 192
• Edition: 1
• Category: Library

✦ Synopsis

This book presents a unified study of dynamically coupled systems involving a rigid body and an ideal fluid flow from the perspective of Lagrangian and Hamiltonian mechanics. It compiles theoretical investigations on the topic of dynamically coupled systems using a framework grounded in Kirchhoff’s equations. The text achieves a balance between geometric mechanics, or the modern theories of reduction of Lagrangian and Hamiltonian systems, and classical fluid mechanics, with a special focus on the applications of these principles. Following an introduction to Kirchhoff’s equations of motion, the book discusses several extensions of Kirchhoff’s work, particularly related to vortices. It addresses the equations of motions of these systems and their Lagrangian and Hamiltonian formulations. The book is suitable to mathematicians, physicists and engineers with a background in Lagrangian and Hamiltonian mechanics and theoretical fluid mechanics. It includes a brief introductory overview of geometric mechanics in the appendix.

✦ Table of Contents

Preface
Contents
1 Kirchhoff's Insufficiently-Celebrated Equations of Motion
1.1 Introduction
1.2 Kirchhoff's Equations
1.3 The Legacy of Kirchhoff's Equations
1.4 The Geometric Mechanics of Kirchhoff's Equations
1.4.1 The Euler–Lagrange and Hamilton's Equations in the Spatially-Fixed Frame
1.5 Extending Kirchhoff's Model
1.5.1 The Sum Poisson Bracket
2 The Addition of Vortices
2.1 The Importance of Vorticity
2.2 Singular Vortex Models
2.2.1 The N-Point-Vortex Model
2.2.2 The N Vortex Ring Model
3 Dynamically Coupled Rigid Body+Point Vortices in R2
3.1 N-Point-Vortices and Stationary Rigid Boundaries: C. C. Lin's Problem
3.2 N-Point-Vortices Dynamically Coupled with a Single Rigid Contour of Arbitrary Shape
3.2.1 The Euler–Lagrange Equations in a Spatially-FixedFrame
3.2.2 The Vortical Momenta and Reciprocity Relations
3.3 N-Point-Vortices Dynamically Coupled with a Single Rigid Circular Contour
3.3.1 The Half-Space Model
4 Dynamically Coupled Rigid Body+Vortex Rings in R3
4.1 N Vortex Rings and a Single Stationary Rigid Boundary
4.2 N Vortex Rings Dynamically Coupled with a Single Rigid Body of Arbitrary Shape
4.2.1 The Euler–Lagrange Equations in a Spatially-FixedFrame
4.2.2 The Vortical Momenta and Reciprocity Relations
4.3 N Vortex Rings Dynamically Coupled with a Rigid Sphere
4.3.1 The Axisymmetric Model of a Sphere and N CircularRings
5 Viscous Effects and Their Modeling
5.1 System Momentum Balance Laws in the Viscous Setting
5.2 Some Experimental and Numerical Work of Vortex Rings Colliding with Rigid Bodies
6 Miscellaneous Extensions
6.1 Dynamically Coupled Rigid Body+free Surface
6.1.1 A Free Surface Dynamically Coupled with a Completely Submerged Single Rigid Body of Arbitrary Shape
6.1.1.1 Phase Space and Hamiltonian Formalism
6.2 Dynamically Coupled N Rigid Bodies in the Absenceof Vorticity
6.2.1 The Euler–Lagrange Equations in a Spatially-FixedFrame
6.3 A Single Buoyant Rigid Body Above an Impermeable FlatBoundary
A Brief Introduction to Geometric Mechanics
B Leading Order Behavior of Velocity and Vector Potential Fields of a Curved Vortex Filament
C Hamiltonian Function and Vector Field in the Half-space Model for Np=2 Sh2006
References
Index