proposition 31.85 The Kolmogorov scales

Rests on

• depends_on phenomenon 31.84 The five-thirds spectrum ¶
  • 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 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-27 ¶
  • proves proof ch:14-fluid-dynamics@proof-42 ¶
• depends_on theorem D.2 Buckingham's $\Pi$ theorem ¶ ↺
• proves proof ch:14-fluid-dynamics@proof-43 ¶

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