proposition 31.40 Circular Couette flow

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:1172 · p. 1054

Rests on

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 definition 31.1 Fluid ¶
      - depends_on definition 31.8 Rate of strain and vorticity ¶
    - depends_on proposition 31.9 Cauchy–Stokes decomposition ¶
      - depends_on definition 31.8 Rate of strain and vorticity ¶ ↺
      - proves proof ch:14-fluid-dynamics@proof-3 ¶
    - 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 definition 31.1 Fluid ¶ ↺
    - depends_on lemma 31.11 Transport theorem for a material volume ¶
      - depends_on definition 31.4 Material derivative ¶
      - depends_on theorem 7.133 Gauss ¶
      - proves proof ch:14-fluid-dynamics@proof-4 ¶
    - depends_on theorem 30.21 Cauchy's equation of motion ¶
      - depends_on theorem 7.133 Gauss ¶ ↺
      - depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
      - proves proof ch:13-continuum-elasticity@proof-9 ¶
    - 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 ¶

Supports

depends_on proposition 31.80 Rayleigh's circulation criterion ¶
- depends_on remark 31.81 Where the threshold comes from, and what it costs ¶
depends_on remark 31.79 Bénard's own cells, and Taylor's cylinders ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Plane Couette flow	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:1185
`depends_on`	→	The Navier–Stokes equations	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:1185
`depends_on`	←	Rayleigh's circulation criterion	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2677
`depends_on`	←	Bénard's own cells, and Taylor's cylinders	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2658
`proves`	←	ch:14-fluid-dynamics@proof-20	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:1188