proposition 31.80 Rayleigh's circulation criterion

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:2661 · p. 1072

Rests on

depends_on proposition 31.40 Circular Couette flow ¶
- depends_on proposition 31.39 Plane Couette flow ¶
  - depends_on theorem 31.37 The Navier–Stokes equations ¶
    - depends_on theorem 31.36 The Newtonian constitutive relation ¶
      - depends_on definition 31.32 Newtonian fluid; dynamic and kinematic viscosity ¶
      - depends_on proposition 31.9 Cauchy–Stokes decomposition ¶
      - proves proof ch:14-fluid-dynamics@proof-17 ¶
    - depends_on theorem 31.22 Euler's equations of motion ¶
      - depends_on definition 31.21 Ideal fluid ¶
      - depends_on lemma 31.11 Transport theorem for a material volume ¶
      - depends_on theorem 30.21 Cauchy's equation of motion ¶
      - proves proof ch:14-fluid-dynamics@proof-11 ¶
    - proves proof ch:14-fluid-dynamics@proof-18 ¶
  - proves proof ch:14-fluid-dynamics@proof-19 ¶
- depends_on theorem 31.37 The Navier–Stokes equations ¶ ↺
- proves proof ch:14-fluid-dynamics@proof-20 ¶
depends_on theorem 31.22 Euler's equations of motion ¶ ↺
proves proof ch:14-fluid-dynamics@proof-40 ¶

Supports

depends_on remark 31.81 Where the threshold comes from, and what it costs ¶

Neighborhood

Every logical edge within two steps of this node.

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partly declared
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Edges

type	direction	node	provenance	where
`depends_on`	→	Circular Couette flow	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2677
`depends_on`	→	Euler's equations of motion	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2677
`depends_on`	←	Where the threshold comes from, and what it costs	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2754
`proves`	←	ch:14-fluid-dynamics@proof-40	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2680