phenomenon 31.84 The five-thirds spectrum

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:2853 · p. 1074

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

Rests on

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 31.58 The vorticity transport equation ¶
- depends_on equation 31.5 eq:fluid-curl-cross ¶
- 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-27 ¶
proves proof ch:14-fluid-dynamics@proof-42 ¶

Supports

depends_on proposition 31.85 The Kolmogorov scales ¶
depends_on remark 31.86 The one exact result, and the split attribution ¶

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)	→	Turbulence spectra from a tidal channel	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:2868
`cites`	→	The Local Structure of Turbulence in Incompressible Viscous Fluid for Very Large Reynolds Numbers	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:2866
`cites`	→	On the Distribution of Energy in the Spectrum of Turbulent Flow	derived	parts/03-classical-mechanics/14-fluid-dynamics.tex:2866
`depends_on`	→	Buckingham's $\Pi$ theorem	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2870
`depends_on`	→	The vorticity transport equation	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2870
`depends_on`	←	The Kolmogorov scales	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2931
`depends_on`	←	The one exact result, and the split attribution	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2993
`proves`	←	ch:14-fluid-dynamics@proof-42	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2873