Applied Turbulence Modeling - Lecture 1
14 October 2026, Sebastian Spring
Course Organisation
Objectives:
- physical and mathematical foundations of turbulence modeling
- understand how closure models are built, calibrated and where they fail
- orientation in a growing literature - selected models, not an encyclopedia
- link to industrial cfd
Lectures: theory, derivations, examples
Exercises: hands-on experience in OpenFOAM - variation of turbulence models for selected benchmark cases
Study with the OpenFOAM book at home!
Likely oral exam: three or four dates can be selected throughout the semester break
Not as many equations in the exam, general understanding more important
Some kind of teamwork required - not clear yet
Generation of turbulent motion
- related to the non-linear character of the navier stokes (momentum) equations
- at high reynolds numbers, any random perurbation grows and produces a chaotic random motion: flow instability and non-linearity
- For turbulence, three things are needed:
- Re much larger than 1: inertia dominates viscous damping
- Disturbance to trigger non-linear convective term
- Transition: instability - non-linear growth - turbulence
The Energy Cascade
\ skizze folie 25
energy transfer to smaller scales at rate $\varepsilon$
viscosity is determining the size of the smallest structures $\ell$ inside the turbulence
direct numerical simulation: no model: cover the full lifespan of the eddies (grid needs to be smaller than smallest structure) - very very expensive computationally
slide 26: large eddies on the left side, small eddies on the right side\
Large and Small Scales
| large scales ($\ell \propto L$) | small scales ($\ell \propto \eta$ |
|---|---|
| generated by the meaen flow | generated by larger eddies |
| depend on geometry and boundary conditions | universal, independent of the geometry |
| anisotropic and inhomogeneous, clear structure | statistically isotropic and homogeneous |
| carry most of the kinetic energy, long-lived | little energy, short-lived, dissipative |
| hard to model - no universal model | easier to model - universal models plausible |
- the dissipation rate is set by the large scales, it does not depend on the viscosity
- viscosity only determines the scale at which the energy is finally dissipated
- lower viscosity means smaller dissipative eddies, same dissipation rate
next lecture: Kolmogorov‘s theory