remark 31.83 The closure problem, stated exactly

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:2809 · p. 1073

remark -- no derivation owed by its kind

Rests on

depends_on theorem 31.82 The Reynolds-averaged equations ¶
- 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-41 ¶

Supports

depends_on remark 31.87 What a theory of turbulence would have to do ¶

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`	→	The Reynolds-averaged equations	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2837
`depends_on`	←	What a theory of turbulence would have to do	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:3012