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Volume-Preserving Flows of an Ideal Fluid
https://doi.org/10.1142/9789812565747_0008Cited by:0 (Source: Crossref)
Abstract:
The following sections are included:
Fundamental Concepts
Volume-preserving diffeomorphisms
Right-invariant fields
Basic Tools
Commutator
Divergence-free connection
Coadjoint action ad*
Formulas in ℝ3 space
Geodesic Equation
Jacobi Equation and Frozen Field
Interpretation of Riemannian Curvature of Fluid Flows
Flat connection
Pressure gradient as an agent yielding curvature
Instability in Lagrangian particle sense
Time evolution of Jacobi field
Stretching of line-elements
Flows on a Cubic Space (Fourier Representation)
Lagrangian Instability of Parallel Shear Flows
Negative sectional curvatures
Stability of a plane Couette flow
Other parallel shear flows
Steady Flows and Beltrami Flows
Steady flows
A Beltrami flow
ABC flow
Theorem:
