u/SatanGoku

My previous video derived the full TKE transport equation and this one explains it more physically.

Link: https://www.youtube.com/watch?v=VVqos9V-BAA

It explains why the transport term neither creates nor destroys k, integrates to zero for a closed system, what production really represents in terms of energy exchange between the mean flow and the turbulent fluctuations, why dissipation is structurally always a sink while production can in principle act as either, and what viscous diffusion's role is compared to turbulent transport.

The second half introduces the Richardson energy cascade and talks briefly about Kolmogorov microscale. I also talk about why the cascade direction is downscale in 3D turbulence and what that implies for what sets the smallest eddy size.

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.

Video 4 of my turbulence course a short detour from the physics to introduce a mathematical tool: index notation and the Einstein summation convention.

The motivation is simple. The full Navier-Stokes momentum equation, written out component by component, takes up most of a whiteboard. Written in index notation, it's one line!! Every term you've already seen can be just compressed into a form that scales to far more complex expressions without becoming unreadable.

This video covers free vs. dummy indices, the summation convention itself, the Kronecker delta and its substitution property, a brief look at the permutation symbol, and rewrites the continuity and momentum equations as a worked example. It's setup for deriving the turbulent kinetic energy transport equation next, the point where component-form algebra genuinely becomes unmanageable.

Link: https://www.youtube.com/watch?v=TdfMawfDr_0

PDF notes on Patreon if useful as a reference.

Hi all,

I have just posted the third video of my ongoing series on turbulence covering everything from Reynolds number through to its modeling.

Link: https://www.youtube.com/watch?v=3lSf_ctJheM

This video explains why ⟨u′v′⟩ can be non-zero even though each fluctuation averages to zero. It builds up using the Moody diagram and the gap in drag between laminar and turbulent friction factor at the same Reynolds number, which turns out to be the macroscopic impression of this mechanism.

From there it builds the full Reynolds stress tensor, and provide a first look into the turbulent kinetic energy.

Consider subscribing to the channel if you would like to be updated. Please provide your feedback if you end up watching. Cheers!

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A few weeks ago, I posted an overview of a turbulence course I'm putting together. The first lecture is now up: https://www.youtube.com/watch?v=myI2dymuUHM

It covers briefly how the flow transitions from a laminar to a turbulent state and highlight the role of Reynolds number which is derived properly from scaling arguments on the momentum equation. Alongside, the limiting cases (Stokes and Euler), what the characteristic scales actually mean for pipe flow and flat plate boundary layers, and a look at the Kelvin-Helmholtz instability is discussed.

It's aimed at senior undergrad, postgrad students and engineers who want a deeper understanding, not just the results. Notes are shared in the comments of the video. Feedback (both positive and constructive) is welcomed and appreciated.

Hi everyone! I've been invested in fluid mechanics research for a while now, and I've wanted to put together an introductory course on turbulence for some time. One that connects the physics directly to the equations that are derived from first principles. I've just posted an overview video kicking off that series. It's aimed at senior undergrads, postgrad students, and engineers who use turbulence models in solvers like ANSYS or OpenFOAM and want to understand what's actually going on under the hood.

The course covers two halves: the first on flow physics (Reynolds decomposition, RANS derivation, TKE budget, Kolmogorov theory, wall-bounded and free shear flows), and the second on modelling and computation (k-ε, k-ω SST, LES, solver implementation and data analysis). Lecture notes will be shared alongside each video.

If that sounds like something useful, the overview is here: https://www.youtube.com/watch?v=436HwwfMH4A

Happy to hear any thoughts on the structure or topics, always useful to know what gaps people feel are missing in existing resources.