science

Von Kármán constant

Von Kármán constant is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Von Kármán constant rather than just read about it. In short: In fluid dynamics, the von Kármán constant (or Kármán's constant), named for Theodore von Kármán, is a dimensionless constant involved in the logarithmic law describing the distribution of the longitudinal velocity in the wall-normal direction of a turbulent fluid flow near a boundary with a no-slip condition. The equation for such boundary layer flow profiles is: u = u ⋆ κ ln ⁡ z z 0 , {\displaystyle u={\frac {u_{\…

Key takeaways

Von Kármán constant belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Von Kármán constant to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Von Kármán constant from memory before moving on to harder problems.

Reference excerpt

In fluid dynamics, the von Kármán constant (or Kármán's constant), named for Theodore von Kármán, is a dimensionless constant involved in the logarithmic law describing the distribution of the longitudinal velocity in the wall-normal direction of a turbulent fluid flow near a boundary with a no-slip condition. The equation for such boundary layer flow profiles is:

u = u ⋆ κ ln ⁡ z z 0 , {\displaystyle u={\frac {u_{\star }}{\kappa }}\ln {\frac {z}{z_{0}}},}

where u is the mean flow velocity at height z above the boundary. The roughness height (also known as roughness length) z0 is where u {\displaystyle u} appears to go to zero. Further κ is the von Kármán constant being typically 0.41, and u ⋆ {\displaystyle u_{\star }} is the friction velocity which depends on the shear stress τw at the boundary of the flow:

u ⋆ = τ w ρ , {\displaystyle u_{\star }={\sqrt {\frac {\tau _{w}}{\rho }}},}

with ρ the fluid density. The Kármán constant is often used in turbulence modeling, for instance in boundary-layer meteorology to calculate fluxes of momentum, heat and moisture from the atmosphere to the land surface. It is considered to be a universal (κ ≈ 0.40). Gaudio, Miglio and Dey argued that the Kármán constant is however nonuniversal in flows over mobile sediment beds. In recent years the von Kármán constant has been subject to periodic scrutiny. Reviews (Foken, 2006; Hogstrom, 1988; Hogstrom, 1996) report values of κ between 0.35 and 0.42. The overall conclusion of over 18 studies is that κ is constant, close to 0.40. For incompressible and frictionless ("ideal") fluids, Baumert (2013) used Kolmogorov's classical ideas on turbulence to derive ideal values of a number of relevant constants of turbulent motions, among them von Kármán's constant as κ = 1 / 2 π ≈ 0.399 {\displaystyle \kappa =1/{\sqrt {2\pi }}\approx 0.399} .

See also Law of the wall Log wind profile

References Baumert, H. Z. (2013). "Universal equations and constants of turbulent motion" Physica Scripta T155 (2013) 014001 (12pp). Online at stacks.iop.org/PhysScr/T155/014001 Baumert H. Z., Wessling B. (2016). "On turbulence in dilatant dispersions". Physica Scripta 91(7):074003. DOI:10.1088/0031-8949/91/7/074003 Bonan, G. B. (2005). "Land Surface Model (LSM 1.0) for Ecological, Hydrological, Atmospheric Studies. Model product". Available on-line [1] from Oak Ridge National Laboratory Distributed Active Archive Center, Oak Ridge, Tennessee, U.S.A. Foken T. (2006). "50 years of the Monin-Obukhov similarity theory". Boundary-Layer Meteorology, Vol. 119, 431-447. Gaudio, R. Miglio, R. and Dey, S. (2010). "Nonuniversality of von Kármán’s κ in fluvial streams". Journal of Hydraulic Research, International Association for Hydraulic Research (IAHR), Vol. 48, No. 5, 658-663 Hogstrom U (1996). "Review of some basic characteristics of the atmospheric surface layer". Boundary-Layer Meteorology, Vol. 78, 215-246. Hogstrom U (1988). "Non-dimensional wind and temperature profiles in the atmospheric surface layer-a re-evaluation". Boundary Layer Meteorology, Vol. 42, 55-78.

External links http://www.ccsm.ucar.edu/models/ccsm3.0/cpl6/users_guide/node21.html Archived 2008-08-21 at the Wayback Machine a list of physical constants used in the NCAR Community Climate System Model

Worked examples

Example 1 — a first encounter with Von Kármán constant

Start with the simplest possible case. Write down what Von Kármán constant claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Von Kármán constant before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Von Kármán constant ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Von Kármán constant

In research: Von Kármán constant appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Von Kármán constant in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Von Kármán constant is common in secondary-school and first-year university syllabi. It links to neighbouring topics Boundary layer meteorology, Turbulence, so understanding it makes those chapters shorter.
In everyday life: Look for Von Kármán constant outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Von Kármán constant” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Von Kármán constant in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Von Kármán constant means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Von Kármán constant out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Von Kármán constant in simple terms?

Why does Von Kármán constant matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Von Kármán constant?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Von Kármán constant.