Mechanics of Fluid Deformations: Rigid Body Rotations and Plane Channel Flow Stability

Contents
Introduction
Part 1. Velocity Strain
	Chapter 1. Vector Objects and Operations
		1.1. The initial metric and screw
		1.2. Matrices as double vectors
		1.3. Metric and convolution
		1.4. Orthogonal decompositions
		1.5. Area of the contact force
	Chapter 2. Continuum Motion
		2.1. A smooth substance
		2.2. Metric of deformation
		2.3. Rates of orts and deformation measure resolution
		2.4. Least measure motions
		2.5. Alternative measure resolution
		2.6. Bulk acceleration
	Chapter 3. Flows of Elements
		3.1. Kinematic structure of a moving body point
		3.2. Rates of length, area, and volume elements
		3.3. Contour, contact, and volume flows
Part 2. Rigid Body Rotations
	Chapter 4. Angular Momentum Equilibrium
		4.1. A point pendulum
		4.2. The ideal top, or Euler’s dynamic equations
		4.3. Inertia forms
		4.4. Polhodes
		4.5. Principal rotations
	Chapter 5. Angular Friction
		5.1. A dissipative top
		5.2. Even stability
		5.3. Odd stability
		5.4. Extreme stability
Part 3. Conservation Laws
	Chapter 6. Fluid and Gas Momentums
		6.1. Pressure force
		6.2. Euler equations
		6.3. Vorticity equation
		6.4. Vortex law
		6.5. Cyclones and anticyclones
	Chapter 7. Viscosity
		7.1. Strain–stress dependence
		7.2. Power identity
		7.3. Axial symmetry
		7.4. Helical flow and viscosity integral
		7.5. Pressure head rate
	Chapter 8. Heat Conductivity
		8.1. Heat balance
		8.2. The heat source in a fluid and a gas
		8.3. The set of conservation laws
	Chapter 9. A Centrifuge
		9.1. A caught tornado
		9.2. Rigid-body and torsional rotations of a gas tube
		9.4. Temperature separation in a counter-flow vortex
Part 4. Turbulence
	Chapter 10. Stress of Pulsations
		10.1. Vortex cascades of instabilities
		10.2. Turbulence as a turbulent force
		10.3. Generation, relaxation, and diffusion
		10.4. Laminar–turbulent transition
	Chapter 11. Stress–Flow Interaction
		11.1. Discrepancy angles of turbulent outflow
		11.2. Turbulence wave characteristics
		11.3. Electromagnetic structure
		11.4. Dark medium source, sink, and light pulsations
Part 5. Plane Channel Flow Stability
	Chapter 12. Flows as Infinitely Dimensional Rotations
		12.1. Plane eddy lifetime
		12.2. Vortex stability
		12.3. Non-commutative inertia and dissipation
		12.4. Direct and reverse basic flows in problems D and E
		12.5. Vortex strip in F and velocity profiles in P,S
	Chapter 13. Ideal Analytic Stability
		13.1. Unconditional and long-wave stabilities in problems D–F
		13.2. Analytical uniqueness
		13.3. Vortex phantoms
		13.4. Smooth vortex catastrophe
	Chapter 14. Viscous Asymptotic Stability
		14.1. Unconditional stability in P
		14.2. The adjoined spectral problem
		14.3. The least moment indicator
		14.4. Refined spectral estimates
		14.5. Short-wave stability in S
		14.6. The spectrum of compact imbedding
References
Index