proposition A.766 Nondimensionalisation

open in the book · appendices/A-long-proofs.tex:37259 · p. 3167

Rests on

depends_on definition 31.51 The other similarity groups ¶
- depends_on phenomenon 31.49 Dynamical similarity ¶
  - 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-24 ¶
- depends_on theorem D.2 Buckingham's $\Pi$ theorem ¶
  - depends_on equation D.3 eq:E-kernel-condition ¶
  - proves proof app:E-dimensionless@proof-1 ¶
depends_on proposition A.765 The roll equations ¶
- depends_on definition A.763 Two-dimensional rolls ¶
  - depends_on equation 31.11 eq:fluid-incompressible ¶
  - depends_on proposition A.761 The Boussinesq equations ¶
    - depends_on definition A.760 The convecting layer ¶
      - depends_on definition 31.51 The other similarity groups ¶ ↺
      - depends_on theorem 31.37 The Navier–Stokes equations ¶ ↺
    - depends_on phenomenon 31.78 Convective onset at a computed threshold ¶
      - depends_on definition 31.51 The other similarity groups ¶ ↺
      - depends_on theorem 31.37 The Navier–Stokes equations ¶ ↺
      - proves proof ch:14-fluid-dynamics@proof-39 ¶
    - depends_on theorem 31.37 The Navier–Stokes equations ¶ ↺
    - proves proof app:A-long-proofs@proof-443 ¶
- depends_on proposition A.761 The Boussinesq equations ¶ ↺
- proves proof app:A-long-proofs@proof-444 ¶
proves proof app:A-long-proofs@proof-445 ¶

Supports

depends_on theorem A.767 Marginal stability of the conducting state ¶
- depends_on remark A.768 Two conventions for the wavenumber ¶
- depends_on theorem A.769 The Lorenz system ¶
  - depends_on remark A.771 What was assumed, and where it fails ¶
  - depends_on remark A.770 What the three variables and three parameters are ¶
depends_on theorem A.769 The Lorenz system ¶ ↺

Neighborhood

Every logical edge within two steps of this node.

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partly declared
a check failed
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inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	The other similarity groups	declared	appendices/A-long-proofs.tex:37289
`depends_on`	→	The roll equations	declared	appendices/A-long-proofs.tex:37289
`depends_on`	←	Marginal stability of the conducting state	declared	appendices/A-long-proofs.tex:37369
`depends_on`	←	The Lorenz system	declared	appendices/A-long-proofs.tex:37487
`proves`	←	app:A-long-proofs@proof-445	declared	appendices/A-long-proofs.tex:37292