<p><em>K</em> is in fact just an empirical proportionality value without any significant meaning. In fact each of the tracers (such as temperature, humidity and ...) should have had their own <em>K</em> <strong>BUT</strong> we dump that coefficient into the (star)* version of that tracer, for example T* (near surface temperature) or Hum* (near surface humidity), so we can still use <em>K</em> in their respective formulation.</p>

<p>Monin-Obukhov length has <em>K</em> in it because that length is related to u*. That length comes from dividing the Shear production and buoyancy procution/dissipation term in turbulence kinetic energy (TKE) equation. As you know Shear production is a function of momentum transfer and u*. Since there is a u* there is a <em>k</em> in there too. </p>

<p>Unlike other stuff in turbulence, the story of <em>K</em> is unfortunately boring.</p>

CC BY-SA 3.0
2018-02-03T07:47:58.760Z
2018-02-03T07:47:58.760Z
Arash Bigdeli
<p>I know that the von Kármán constant ($k\approx0.4$) is useful in turbulence modeling. Something that bothers me is my lack of understanding where $k$ comes from or the physical meaning behind it. If $k$ is mainly used as a proportionality in the log-wind profile, why is it within the formulation of the Monin-Obukhov length? What is the physical meaning behind $k$? Is it a universal value (i.e. valid on extraterrestrial planets)? Why is $k$ considered important enough to be eponymous, while I see $\frac{1}{k}$ more often in formulations than $k$?</p>

<turbulence>
What is the physical meaning of the von Kármán constant?
BarocliniCplusplus
# What is the physical meaning of the von Kármán constant?

(Asked by: username_0 on 2017-03-27)

I know that the von Kármán constant ($k\approx0.4$) is useful in turbulence modeling. Something that bothers me is my lack of understanding where $k$ comes from or the physical meaning behind it. If $k$ is mainly used as a proportionality in the log-wind profile, why is it within the formulation of the Monin-Obukhov length? What is the physical meaning behind $k$? Is it a universal value (i.e. valid on extraterrestrial planets)? Why is $k$ considered important enough to be eponymous, while I see $\frac{1}{k}$ more often in formulations than $k$?

**Tags:** turbulence


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## 1 answers

### Answer by username_1 on 2018-02-03. Score: 1 | Accepted answer

*K* is in fact just an empirical proportionality value without any significant meaning. In fact each of the tracers (such as temperature, humidity and ...) should have had their own *K* **BUT** we dump that coefficient into the (star)\* version of that tracer, for example T\* (near surface temperature) or Hum\* (near surface humidity), so we can still use *K* in their respective formulation.

Monin-Obukhov length has *K* in it because that length is related to u\*. That length comes from dividing the Shear production and buoyancy procution/dissipation term in turbulence kinetic energy (TKE) equation. As you know Shear production is a function of momentum transfer and u\*. Since there is a u\* there is a *k* in there too.

Unlike other stuff in turbulence, the story of *K* is unfortunately boring.


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