phenomenon 31.78 Convective onset at a computed threshold

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:2588 · p. 1071

phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt

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 theorem 31.37 The Navier–Stokes equations ¶ ↺
proves proof ch:14-fluid-dynamics@proof-39 ¶

Supports

depends_on proposition A.761 The Boussinesq equations ¶
- depends_on definition A.763 Two-dimensional rolls ¶
  - depends_on proposition A.765 The roll equations ¶
    - depends_on proposition A.766 Nondimensionalisation ¶
      - depends_on theorem A.767 Marginal stability of the conducting state ¶
      - depends_on theorem A.769 The Lorenz system ¶
- depends_on proposition A.765 The roll equations ¶ ↺
depends_on remark 31.79 Bénard's own cells, and Taylor's cylinders ¶
depends_on remark 31.81 Where the threshold comes from, and what it costs ¶
depends_on theorem A.767 Marginal stability of the conducting state ¶ ↺

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
`cites` (evidence)	→	Étude expérimentale des courants de convection dans une nappe liquide. --- Régime permanent : tourbillons cellulaires	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:2594
`cites` (context)	→	Hydrodynamic and Hydromagnetic Stability	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:2606
`cites`	→	On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:2597
`depends_on`	→	The other similarity groups	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2608
`depends_on`	→	The Navier–Stokes equations	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2608
`depends_on`	←	The Boussinesq equations	declared	appendices/A-long-proofs.tex:37111
`depends_on`	←	Bénard's own cells, and Taylor's cylinders	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2658
`depends_on`	←	Where the threshold comes from, and what it costs	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2754
`depends_on`	←	Marginal stability of the conducting state	declared	appendices/A-long-proofs.tex:37369
`proves`	←	ch:14-fluid-dynamics@proof-39	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2611