Editing Boundary layer (section)

===Crocco's transformation===
For steady two-dimensional compressible boundary layer, [[Luigi Crocco]]<ref>Crocco, L. "A characteristic transformation of the equations of the boundary layer in gases." ARC 4582 (1939): 1940.</ref> introduced a transformation which takes <math>x</math> and <math>u</math> as independent variables instead of <math>x</math> and <math>y</math> and uses a dependent variable <math>\tau=\mu\partial u/\partial y</math>(shear stress) instead of <math>u</math>. The boundary layer equation then becomes

: <math>
\begin{align}
& \mu \rho u \frac{\partial}{\partial x}\left(\frac{1}{\tau}\right)  + \frac{\partial^2 \tau}{\partial u^2} -\mu \frac{dp}{dx} \frac{\partial }{\partial u}\left(\frac{1}{\tau}\right) =0, \\[5pt]
& \text{if } \frac{dp}{dx}=0, \text{ then } \frac{\mu\rho}{\tau^2} \frac{\partial \tau}{\partial x} = \frac{1}{u}\frac{\partial^2 \tau}{\partial u^2}.
\end{align}
</math>

The original coordinate is recovered from

:<math> y = \mu \int \frac{du} \tau .</math>