Synopses & Reviews
Fluid dynamics, the behavior of liquids and gases, is a field of broad impact—in physics, engineering, oceanography, and meteorology for example—yet full understanding demands fluency in higher mathematics, the only language fluid dynamics speaks. Dr. Richard Meyer's work is indeed introductory, while written for advanced undergraduate and graduate students in applied mathematics, engineering, and the physical sciences. A knowledge of calculus and vector analysis is presupposed.
The author develops basic concepts from a semi-axiomatic foundation, noting that "for mathematics students such a treatment helps to dispel the all too common impression that the whole subject is built on a quicksand of assorted intuitions." Contents include:
Kinematics: Lagrangian and Eulerian descriptions, Circulation and Vorticity.
Momentum Principle and Ideal Fluid: Conservation examples, Euler equations, D'Alembert's and Kelvin's theorems.
Newtonian Fluid: Constitutive and Kinetic theories, exact solutions.
Fluids of Small Viscosity: Singular Perturbation, Boundary Layers.
Some Aspects of Rotating Fluids: Rossby number, Ekman layer, Taylor-Proudman Blocking.
Some Effects of Compressibility: Thermodynamics, Waves, Shock relations and structure, Navier-Stokes equations.
Dr. Meyer writes, "This core of our knowledge concerns the relation between inviscid and viscous fluids, and the bulk of this book is devoted to a discussion of that relation."
Excellent coverage of kinematics, momentum principle, Newtonian fluid, rotating fluids, compressibility, and more. Geared toward advanced undergraduate and graduate students of mathematics and science; prerequisites include calculus and vector analysis. 1971 edition.
Excellent coverage of kinematics, momentum principle, Newtonian fluid, rotating fluids, compressibility, more. Geared toward advanced undergraduate and graduate students of mathematics and science; prerequisites include calculus and vector analysis. 1971 edition.
Introductory text to highly sophisticated mathematical discipline. Applied math undergrads, science grads will find excellent coverage of kinematics, Newtonian fluids, compressibility, etc.
Table of Contents
2 Lagrangian description
3 Eulerian description
4 Conservation of mass
6 Some potential flows
8 Line vortex
9 Vortex sheet
2 Momentum Principle and Ideal Fluid
10 Conservation of linear momentum
11 Mixing and lift
12 Equations of motion
13 D'Alembert's theorem
14 Kelvin's theorem
15 Conservation of angular momentum
3 Newtonian Fluid
16 The Couette experiment
17 Constitutive equation
18 Kinetic theory
19 Some viscous fluid motions
4 Fluids of Small Viscosity
20 Reynolds number
21 A singular perturbation example
22 Limit equations for the flat plate
23 Discussion of Blasius' solution
24 Limit equations with pressure gradient and wall curvature
25 Similarity solutions
26 Momentum integral
5 Some Aspects of Rotating Fluids
29 Bjerknes' theorem
30 Rossby number
31 Ekman layer
32 Taylor-Proudman theorem
6 Some Effects of Compressibility
33 Thermodynamic state
34 Flow initiation
35 Conservation of energy
36 Shock relations
37 Shock structure
38 Navier-Stokes equations