theorem A.767 Marginal stability of the conducting state

open in the book · appendices/A-long-proofs.tex:37349 · p. 3168

Rests on

depends_on phenomenon 31.78 Convective onset at a computed threshold ¶
- 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 theorem 31.22 Euler's equations of motion ¶
      - 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 theorem 31.37 The Navier–Stokes equations ¶ ↺
- proves proof ch:14-fluid-dynamics@proof-39 ¶
depends_on proposition A.766 Nondimensionalisation ¶
- depends_on definition 31.51 The other similarity groups ¶ ↺
- 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 phenomenon 31.78 Convective onset at a computed threshold ¶ ↺
      - 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 ¶
proves proof app:A-long-proofs@proof-446 ¶

Supports

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 ¶

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`	→	Convective onset at a computed threshold	declared	appendices/A-long-proofs.tex:37369
`depends_on`	→	Nondimensionalisation	declared	appendices/A-long-proofs.tex:37369
`depends_on`	←	Two conventions for the wavenumber	declared	appendices/A-long-proofs.tex:37442
`depends_on`	←	The Lorenz system	declared	appendices/A-long-proofs.tex:37487
`proves`	←	app:A-long-proofs@proof-446	declared	appendices/A-long-proofs.tex:37372