definition 31.21 Ideal fluid

open in the book · parts/03-classical-mechanics/14-fluid-dynamics.tex:577 · p. 1047

ground object -- no derivation owed

Rests on

depends_on definition 31.1 Fluid ¶
- depends_on theorem 30.18 Cauchy: the stress tensor exists ¶
  - depends_on definition 30.17 Traction ¶
    - depends_on definition 7.126 Line and surface integrals ¶
      - depends_on definition 7.98 Functions of class $C^{1}$ ¶
      - depends_on definition 7.125 Multiple integral ¶
    - depends_on definition 30.2 Representative volume element; continuum field ¶
      - depends_on definition 7.97 Partial derivative; gradient ¶
  - depends_on definition 13.5 Tensor under orthogonal transformations ¶
    - depends_on definition 13.4 Orthogonal coordinate transformation ¶
      - depends_on definition 13.3 Orthogonal coordinate system ¶
  - proves proof ch:13-continuum-elasticity@proof-7 ¶

Supports

depends_on theorem 31.22 Euler's equations of motion ¶
- depends_on lemma A.712 The force is a far-field integral ¶
- depends_on phenomenon 31.88 Sound travels at the adiabatic speed ¶
  - depends_on remark 31.89 The Mach number and the regimes it separates ¶
    - depends_on phenomenon 31.93 The Mach cone ¶
  - depends_on remark 31.90 Why a compression wave must steepen ¶
- depends_on proposition A.797 The outer limit loses a boundary condition ¶
- depends_on proposition 31.80 Rayleigh's circulation criterion ¶
  - depends_on remark 31.81 Where the threshold comes from, and what it costs ¶
- depends_on proposition 52.24 The p-mode cavity ¶
  - depends_on phenomenon 52.25 The Sun rings, and its interior can be inverted ¶
    - depends_on phenomenon 52.22 The solar-neutrino deficit, and its resolution ¶
- depends_on remark 31.23 Boundary conditions, and what the ideal model omits ¶
- depends_on theorem 31.24 Bernoulli ¶
  - depends_on corollary A.799 The impressed pressure gradient ¶
  - depends_on lemma 31.67 Blasius' force formula ¶
    - depends_on theorem 31.68 Kutta–Joukowski ¶
      - depends_on proposition 31.70 The lift-curve slope of a thin aerofoil ¶
      - depends_on remark 31.69 The Kutta condition, and where the circulation comes from ¶
      - depends_on theorem A.737 The lift-curve slope of the flat plate ¶
  - depends_on phenomenon 31.25 Pressure falls where the flow speeds up ¶
    - depends_on example 31.26 The Venturi meter ¶
    - depends_on remark 31.27 What the 1738 source contains ¶
  - depends_on theorem A.707 D'Alembert's paradox ¶
  - depends_on theorem 31.74 The interface dispersion relation ¶
    - depends_on corollary 31.76 Kelvin–Helmholtz instability ¶
    - depends_on corollary 31.75 Rayleigh–Taylor instability ¶
    - depends_on theorem 31.94 Gravity–capillary waves on a free surface ¶
      - depends_on phenomenon 31.96 The solitary wave ¶
      - depends_on phenomenon 31.95 The observed dispersion of water waves ¶
- 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 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 A.763 Two-dimensional rolls ¶
      - depends_on proposition A.765 The roll equations ¶
  - depends_on definition 31.43 Creeping flow ¶
    - depends_on lemma A.716 The creeping-flow equation for $\psi$ ¶
      - depends_on lemma A.717 The radial solution ¶
    - 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 remark A.768 Two conventions for the wavenumber ¶
      - depends_on theorem A.769 The Lorenz system ¶
  - 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 31.54 This one is not a gap in the writing ¶
    - 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 definition A.760 The convecting layer ¶ ↺
      - depends_on phenomenon 31.78 Convective onset at a computed threshold ¶ ↺
      - depends_on proposition A.766 Nondimensionalisation ¶
      - depends_on remark 31.89 The Mach number and the regimes it separates ¶ ↺
    - 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 theorem 31.91 Rankine–Hugoniot jump conditions ¶
  - depends_on phenomenon 31.93 The Mach cone ¶ ↺
  - depends_on remark 31.92 Entropy selects the physical branch ¶
- depends_on theorem 31.77 Rayleigh's inflexion-point criterion ¶

Neighborhood

Every logical edge within two steps of this node.

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partly declared
a check failed
not graded
declared in the source
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Edges

type	direction	node	provenance	where
`depends_on`	→	Fluid	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:582
`depends_on`	←	Euler's equations of motion	declared	parts/03-classical-mechanics/14-fluid-dynamics.tex:596