This book covers a new approach to analyzing hydrodynamic stability.With the use of standard remedies of functional analysis, theory of boundary value problems and infinitesimal Lie algebras, it is shown in the book that large vortex mushrooms of an ideal incompressible fluid in a vertical strip behind a water hammer proves to be 2D (plane-parallel) nonlinear (for arbitrary disturbances of initial velocities) and long wave stable. It is one of the many examples provided in the book discussing hydrodynamic stability.
Author(s): Oleg V. Troshkin
Publisher: World Scientific Publishing
Year: 2021
Language: English
Pages: 281
City: Singapore
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
