Fluid dynamical equations

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Fluid dynamical equations (Navier-Stokes
equations)
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Fluid dynamical equations (Navier-Stokes
equations) Dimensional reduction from QM to
Boltzmann eq. to the fluid equations Continuum
hypothesis
T
d
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Mass conservation (continuity equation)
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Mass conservation (continuity equation)
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Incompressible fluid
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Conservation of linear momentum (Navier-Stokes
equations)
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stress tensor for surface forces
The stress tensor is symmetric!
commons.wikimedia.org/ wiki/FileStress_tensor.png
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constitutive equation (relationship between
stress and strain) for a Newtonian fluid (with
the Stokes assumption)
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Conservation of linear momentum (Navier-Stokes
equations)
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Thermodynamic equation first principle of
Thermodynamics
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Till now
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Equations of state
Perfect gas (e.g., dry air)
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Perfect gas (e.g., dry air)
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Fluid dynamical eqns. for a perfect gas
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The static solution
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Adiabatic processes
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Static stability of a perfect gas (adiabatic
processes)
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Neutral stability of a perfect gas (adiabatic
processes)
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For a general, non adiabatic process
Relationship between potential temperature and
entropy
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Fluid dynamical eqns. for a perfect gas
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Fluid dynamical eqns. for a perfect gas
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The Boussinesq approximation (adiabatic process,
ideal fluid)
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The Boussinesq approximation (adiabatic process,
ideal fluid)
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The Boussinesq approximation
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The Boussinesq approximation (adiabatic process,
ideal fluid)
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The Boussinesq approximation (real fluid)
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The Boussinesq approximation (real fluid)
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The Boussinesq approximation (real fluid)
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The Boussinesq approximation (real fluid)