definition 31.8 Rate of strain and vorticity

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:209 · p. 1043

ground object -- no derivation owed

Rests on

depends_on definition 13.91 Symmetric and antisymmetric parts ¶
depends_on equation 7.126 eq:ana-nabla-curl ¶

Supports

depends_on definition 31.63 Circulation ¶
- depends_on theorem 31.64 Kelvin's circulation theorem ¶
  - depends_on corollary 31.65 Lagrange: an irrotational flow stays irrotational ¶
    - depends_on remark 31.69 The Kutta condition, and where the circulation comes from ¶
  - depends_on remark 31.66 Only three things make circulation ¶
  - depends_on theorem 31.59 Helmholtz's vortex theorems ¶
    - depends_on corollary 31.65 Lagrange: an irrotational flow stays irrotational ¶ ↺
    - depends_on example 31.60 Vortex rings ¶
depends_on definition 31.32 Newtonian fluid; dynamic and kinematic viscosity ¶
- depends_on remark 31.35 Non-Newtonian fluids are out of scope ¶
- depends_on remark 31.33 Reading the two viscosities ¶
- depends_on theorem 31.36 The Newtonian constitutive relation ¶
  - depends_on theorem A.718 Stokes' drag law with its coefficient ¶
  - depends_on theorem 31.37 The Navier–Stokes equations ¶
    - depends_on definition A.741 The statistical setting ¶
    - depends_on definition A.760 The convecting layer ¶
      - depends_on proposition A.761 The Boussinesq equations ¶
    - depends_on definition 31.43 Creeping flow ¶
      - depends_on lemma A.716 The creeping-flow equation for $\psi$ ¶
      - depends_on proposition 31.44 Kinematic reversibility ¶
    - 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 phenomenon 31.41 The fourth-power law of pipe flow ¶
      - depends_on phenomenon 31.53 Transition to turbulence in a pipe ¶
      - depends_on remark 31.42 The entry length ¶
    - depends_on phenomenon 31.49 Dynamical similarity ¶
      - depends_on definition 31.51 The other similarity groups ¶
      - depends_on phenomenon 31.53 Transition to turbulence in a pipe ¶ ↺
      - depends_on remark 31.50 Reading the Reynolds number ¶
      - depends_on remark 31.52 Similarity is only as good as the control of the data ¶
      - depends_on remark 31.62 What the spacing calculation settles, and what it does not ¶
    - depends_on proposition A.761 The Boussinesq equations ¶ ↺
    - depends_on proposition 31.40 Circular Couette flow ¶
      - depends_on proposition 31.80 Rayleigh's circulation criterion ¶
      - depends_on remark 31.79 Bénard's own cells, and Taylor's cylinders ¶ ↺
    - depends_on proposition 31.39 Plane Couette flow ¶
      - depends_on proposition 31.40 Circular Couette flow ¶ ↺
    - depends_on remark 31.48 What is actually proved ¶
      - depends_on remark 31.87 What a theory of turbulence would have to do ¶
    - depends_on remark 31.38 Whose equations, and the Stokes hypothesis ¶
    - depends_on theorem A.745 Kármán–Howarth–Monin relation ¶
      - depends_on proposition A.746 The Kármán–Howarth equation in classical form ¶
      - depends_on theorem A.749 Kolmogorov's equation and the four-fifths law ¶
    - … 3 more
depends_on proposition 31.9 Cauchy–Stokes decomposition ¶
- depends_on remark 31.10 Vorticity is local rotation, not curvature of the path ¶
- depends_on theorem 31.36 The Newtonian constitutive relation ¶ ↺

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`	→	Symmetric and antisymmetric parts	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:219
`depends_on`	→	eq:ana-nabla-curl	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:219
`depends_on`	←	Circulation	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:2009
`depends_on`	←	Newtonian fluid; dynamic and kinematic viscosity	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:920
`depends_on`	←	Cauchy–Stokes decomposition	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:233