Reminder of fluids mechanics and introduction to turbulence

Objectives

Reminder on local balances in fluids mechanics (mass and momentum balances)

Description of the transition to turbulence.

Write Navier-Stokes equations with Reynolds averaging.

Obtain the profile mean velocity in a turbulent channel

Description

Differential operators and calculation with matrices

Navier-Stokes equations in cartesian, cylindrical, spherical coordinates

Couette and Poiseuille laminar flows

Transition to turbulence

Navier-Stokes equations with Reynolds averaging

Turbulent channel flow and Prandtl model

Targeted skills

Writing and simplification of Navier-Stokes equations

Description of turbulence and instabilities of flows

Solutions of Navier-Stokes equations for simplified geometries

Pre-requisites

Basic knowledge on differential operators and matrices

Mass and momentum balances in fluids mechanics