The beauty and the complexity of turbulence

Joris Coddé

In 1920, Lewis F. Richardson wrote

“Big whorls have little whorls
That feed on their velocity,
And little whorls have lesser whorls
And so on to viscosity.”

This blog post discusses the topic of turbulence, which is excellently captured in the poem of L.F. Richardson above. The picture displays the behavior very well. It is an inherently complex subject though. For Coldstream users, understanding the basics of turbulence and turbulence modeling will help reach more accurate results.

Figure 1: Turbulent vortex at the tip of an air plane wing. Source NASA Langley Research Center (NASA-LaRC)

Turbulent flows are common in real life, think for example of the blood flow in your veins, the air flow over the wing of a plane, breaking waves at the beach, ….

The beauty of turbulent motions inspired artists such as Van Gogh:

Figure 2: Starry Night, Van Gogh. The eddies in the painting are remarkably close to the concept of “Kolmogorov scaling”.

Its complexity still appalls scientists though. The Nobel Prize Werner Heisenberg said in 1932 that if he were allowed to ask God two questions, they would be, “Why quantum mechanics? And why turbulence?”. He was pretty sure God would be able to answer the first question! We’re still on to the turbulence question, as one of the millennium prizes is on the solution of the Navier-Stokes equations, the equations which describe the motion of the fluid flow.

Nevertheless, we have learned a great deal about turbulent phenomena. Especially the modeling of turbulent flow has made big steps forward - for example, nowadays one can include turbulence in industrial simulations, as we do in ColdStream.

How to distinguish between laminar and turbulent flow?

In fluid dynamics, flow can either be considered laminar or turbulent. In the first case, the fluid particles follow a smooth path with almost no mixing or disruption between adjacent paths. On the other hand, in turbulent flow, the flow becomes very irregular and the fluid particles follow a chaotic path, full of eddies, swirls, and flow instabilities. The picture below displays both regimes.

Figure 3: The plume from this candle flame goes fromlaminar to turbulent. The Reynolds number can be used to predict where this transition will take place (Gary Settles)

The characterization of laminar and turbulent flow regimes is quantitatively captured by the Reynolds number:

\[Re = \frac{\rho\space \upsilon \space L}{\mu}\]

Where ρ is the density, v the velocity, L the reference length scale, and μ the viscosity. It’s the dimensionless ratio between inertial and viscous forces. For instance, when the Reynolds number is smaller than 2300 in circular tubes, a laminar flow regime will occur. If the Reynolds number is higher than 4000, the flow will be turbulent. Everything in between is called the transitional regime.

A typical heat transfer application has internal flow, meaning the flow is confined to channels (as opposed to external flow, where there is free-stream flow around an object). For this application, the Reynolds number is the easiest to calculate at the inlet, with L being the hydraulic diameter of the inlet and v being the velocity at the inlet.

How do we include turbulence in ColdStream?

When running simulations with turbulent flow, the turbulence needs to be resolved or an appropriate model needs to be selected. Turbulence models are simplified constitutive equations that predict the evolution of the turbulent flow.

For the industrial problems that are solved on ColdStream, flow is either considered laminar – meaning no turbulent equations are solved – or turbulent, modeled through “RANS”-type equations. RANS stands for “Reynolds-averaged Navier-Stokes” equations, which model the time-averaged effect of turbulence on flow. It is considered sufficiently accurate for industrial use, provided a suitable model is chosen [1]. Coldstream proposes the kOmegaSST turbulence model – in general, it is more able to capture flow phenomena than other RANS models. However, you can change the model based on the following flow chart:

Figure 4: Flow chart for the correct turbulence modelfor a case

First, the Reynolds number of the flow should be estimated, to determine whether or not your case is turbulent. It is acceptable to make assumptions and simplifications regarding the geometry or parameters for this. If the Reynolds model is larger than 4000, the phase of the fluid is taken into account. Then, for gasses (generally air), it is distinguished between internal and external flow. For more detailed information on the different models, please refer to our documentation.

Figure 5: Turbulent flow as displayed in ColdStream.


Turbulence is still an interesting research topic and will remain so in the upcoming years. While theoretical advancement has been slow, we can still enjoy the benefits of turbulence modeling in CFD – being accurate enough for industrial use. For a more in-depth explanation, as well as advice on which turbulence model is the best to use, visit this page.

[1] J. Gorman, S.Bhattacharyya, L. Cheng, and J. Abraham, "Turbulence Models Commonly Usedin CFD", in Computational Fluid Dynamics [Working Title]. London, UnitedKingdom: IntechOpen, 2021 [Online]. Available: doi: 10.5772/intechopen.99784

Continue reading