definition 31.51 The other similarity groups

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:1540 · p. 1059

ground object -- no derivation owed

Rests on

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 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-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 ¶

Supports

depends_on definition A.760 The convecting layer ¶
- 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 proposition A.765 The roll equations ¶ ↺
depends_on phenomenon 31.78 Convective onset at a computed threshold ¶
- depends_on proposition A.761 The Boussinesq 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 ¶
  - 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 proposition A.766 Nondimensionalisation ¶ ↺
depends_on remark 31.89 The Mach number and the regimes it separates ¶
- depends_on phenomenon 31.93 The Mach cone ¶

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`	→	Dynamical similarity	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:1563
`depends_on`	→	Buckingham's $\Pi$ theorem	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:1563
`depends_on`	←	The convecting layer	declared	appendices/A-long-proofs.tex:37085
`depends_on`	←	Convective onset at a computed threshold	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2608
`depends_on`	←	Nondimensionalisation	declared	appendices/A-long-proofs.tex:37289
`depends_on`	←	The Mach number and the regimes it separates	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:3093