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In fluid dynamics, the law of the wall (also known as the logarithmic law of the wall) states that the average velocity of a turbulent flow at a certain point is proportional to the logarithm of the distance from that point to the "wall", or the boundary of the fluid region.
I know that the von Kármán constant ( k ≈ 0.4 k ≈ 0.4) is useful in turbulence modeling. Something that bothers me is my lack of understanding where k k comes from or the physical meaning behind it.
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What is the von Kármán constant?
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Is the von Kármán constant a realistic uncertainty for wall turbulence?
When did von Kármán create a logarithmic velocity distribution?
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.
May 1, 2009 · The von Kármán constant k occurs throughout the mathematics that describe the atmospheric boundary layer. In particular, because k was originally included in the definition of the Obukhov length, its value has both explicit and implicit effects on the functions of Monin–Obukhov similarity theory.
- Edgar L. Andreas
- 2009
The wind shear associated with this stress is given by the derivative of eq. (18.14a): ∆M/∆z = u * /(k·z), where k = 0.4 is the von Kármán constant. At z = 10 m, the shear is ∆M/∆z = (0.5 m·s –1)/(0.4·10m) = 0.125 s –1.
Jul 17, 2023 · The log law for the mean velocity in wall-bounded turbulent flows goes back to the celebrated work of von Kármán (Reference von Kármán 1934) and Millikan (Reference Millikan 1938) and is firmly rooted in the framework of matched asymptotic expansions (MAE) (see for example Kevorkian & Cole (Reference Kevorkian and Cole 1981), Wilcox ...
Feb 1, 2013 · Abstract. In 1930, von Kármán presented an expression for the mean velocity distribution in channel and pipe flows that can be transformed into the today well-known logarithmic velocity distribution.
