Fluid dynamical equations (Navier-Stokes equations)

Fluid dynamical equations (Navier-Stokes equations) Dimensional reduction: from QM to Boltzmann eq. to the fluid equations Continuum hypothesis: d T

Mass conservation (continuity equation)

Mass conservation (continuity equation)

Incompressible fluid

Conservation of linear momentum (Navier-Stokes equations)

stress tensor for surface forces commons.wikimedia.org/ wiki/File:Stress_tensor.png The stress tensor is symmetric!

constitutive equation (relationship between stress and strain) for a Newtonian fluid (with the Stokes assumption)

Conservation of linear momentum (Navier-Stokes equations)

Thermodynamic equation: first principle of Thermodynamics

Till now:

Equations of state: Perfect gas (e.g., dry air)

Fluid dynamical eqns. for a perfect gas

The static solution

Adiabatic processes

Static stability of a perfect gas (adiabatic processes)

Neutral stability of a perfect gas (adiabatic processes)

For a general, non adiabatic process Relationship between potential temperature and entropy

Fluid dynamical eqns. for a perfect gas

The Boussinesq approximation (adiabatic process, ideal fluid)

The Boussinesq approximation (adiabatic process, ideal fluid)

The Boussinesq approximation

(adiabatic process, ideal fluid)

The Boussinesq approximation (real fluid)

The Boussinesq approximation (real fluid)

The Boussinesq approximation (real fluid)

The Boussinesq approximation (real fluid)