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Turbulence is difficult because many interacting spatial and time scales must be resolved or modeled. Useful mean predictions are possible, but they require validation and quantified uncertainty.
By Matan · Updated
Small viscosity can create a large scale range
In a three-dimensional turbulent cascade, energy passes through interacting motions and is eventually dissipated by viscosity at small scales. Under ideal high-Reynolds-number scaling, the large-to-small length ratio can grow roughly as Re^(3/4). This is a scaling estimate, not a universal grid prescription. [1]
Worked resolution scaling
If a representative Reynolds number increases from 10⁴ to 10⁶, the estimated length-scale ratio grows from 1000 to about 31,623. Resolving comparable detail in three dimensions would increase a simple grid-count estimate by (31.623)³ ≈ 31,623, before accounting for shorter time steps. Geometry and numerical method affect actual cost.
DNS, LES and RANS answer different questions
Direct numerical simulation resolves the relevant turbulent scales. Large-eddy simulation resolves larger motions and models unresolved effects. Reynolds-averaged equations predict statistical fields using closure models. More computation does not automatically correct a bad boundary condition or an inappropriate closure. [1], [2]
Chaos does not make every statistic unknowable
An individual instantaneous trajectory can be sensitive to initial conditions while average pressure drop or mixing rate remains predictably constrained. Check mesh sensitivity, statistical convergence and comparison with measurements. A good result for one flow is not blanket validation for separated, compressible or multiphase cases.
Continue learning
- Navier-Stokes equations
- Three fluid instabilities: shear, gravity and capillary breakup
- Boundary layers: laminar, transitional, turbulent and separated flow
How this article was checked
Sources checked; calculations checked where shown. Main claims and model assumptions were checked against the references below. Example arithmetic and units were checked separately. Numerical examples are illustrative calculations, not experimental measurements.
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Sources and further reading
- MIT: Classical Mechanics III, turbulence and scaling
- NASA: Turbulence Modeling Resource and validation cases
Cite this article
Matan. “Why does turbulence remain a challenge in fluid dynamics.” Your Physicist. Originally published 2023-05-17; updated 2026-09-10. https://your-physicist.com/why-does-turbulence-remain-a-challenge-in-fluid-dynamics/
Revision history
10 September 2026: Completed the interrupted explanation and added a scale-cost calculation plus distinctions among simulation approaches. Added references and a transparent verification record.
