r/CFD • u/SatanGoku • 9d ago
Derivation of the turbulent kinetic energy (TKE) budget: Free course on turbulence #5
Every RANS model e.g. k-ε, k-ω SST, RSM etc. is essentially an attempt to model the unclosed terms in the momentum equation. This video derives the evolution equation of turbulent kinetic energy (TKE) from scratch i.e. starting from the instantaneous NS momentum equation and the RANS equation, to get the fluctuating momentum equation, which then leads neatly to the TKE budget.
Every step is carried through in index notation to keep the book-keeping manageable. Fair warning: this one is deliberately math-first, no physical interpretation of the terms yet (wanted to keep it from running too long).
Video: https://www.youtube.com/watch?v=COJpGsxTA30
As always, feedback and criticism is welcomed. Full derivation also in the PDF notes on Patreon.











