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# Log Law of the Wall

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Use the slider to choose varying values of $$R_m$$; the values of $$R_\tau$$, $$n$$, and $$s$$ will simultaneously update.

The panel below will plot the same flow expressed in inner wall variables $$y^+$$ and $$u^+$$. The inner wall variable serves to magnify the three distinct regimes in a wall bounded turbulent flow.

Superimposed on the panel are two functions $$u^+ = y^+$$ (in red) and $$u^+ = \frac{1}{\kappa}\ln y^+ + c$$ (in green) where $$\kappa = 0.41$$ and $$c = 5.5$$ are empirical constants (e.g. [10]).

The first relationship which holds in the range $$0 < y^+ < 5$$ is called the "viscous sublayer region" and the second relationship which holds in the range $$30 < y^+ < 100$$ is called the "logarithmic law of the wall". Beyond $$y^+ > 100$$ is the "velocity defect region" where $$\frac{u_m - \bar{u}}{u_\tau} = F\left(\eta\right)$$ where $$F$$ is an empirical function (e.g. [11]).

$$R_\tau =$$ ,
$$n =$$ ,
$$s =$$