proposition A.765 The roll equations

open in the book · appendices/A-long-proofs.tex:37190 · p. 3166

Rests on

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 phenomenon 31.49 Dynamical similarity ¶
      - depends_on theorem D.2 Buckingham's $\Pi$ theorem ¶
    - depends_on theorem 31.37 The Navier–Stokes equations ¶
      - depends_on theorem 31.36 The Newtonian constitutive relation ¶
      - depends_on theorem 31.22 Euler's equations of motion ¶
      - proves proof ch:14-fluid-dynamics@proof-18 ¶
  - 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 ¶

Supports

depends_on proposition A.766 Nondimensionalisation ¶
- 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.

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`	→	Two-dimensional rolls	declared	appendices/A-long-proofs.tex:37204
`depends_on`	→	The Boussinesq equations	declared	appendices/A-long-proofs.tex:37204
`depends_on`	←	Nondimensionalisation	declared	appendices/A-long-proofs.tex:37289
`proves`	←	app:A-long-proofs@proof-444	declared	appendices/A-long-proofs.tex:37207