Editing Boundary layer (section)

===Von Mises transformation===
For steady two-dimensional boundary layers, [[Richard von Mises|von Mises]]<ref>{{Cite book|doi=10.1007/978-3-662-11836-8_49|chapter=Bemerkungen zur Hydrodynamik|title=Ludwig Prandtl Gesammelte Abhandlungen|year=1961|last1=Tollmien|first1=Walter|last2=Schlichting|first2=Hermann|last3=Görtler|first3=Henry|last4=Riegels|first4=F. W.|pages=627–631|isbn=978-3-662-11837-5}}</ref> introduced a transformation which takes <math>x</math> and <math>\psi</math>([[stream function]]) as independent variables instead of <math>x</math> and <math>y</math> and uses a dependent variable <math>\chi = U^2-u^2</math> instead of <math>u</math>. The boundary layer equation then become

:<math>\frac{\partial \chi}{\partial x} = \nu \sqrt{U^2-\chi} \, \frac{\partial^2 \chi}{\partial \psi^2}</math>

The original variables are recovered from

:<math>y = \int \sqrt{U^2-\chi} \, d\psi, \quad u = \sqrt{U^2-\chi}, \quad v = u\int \frac{\partial}{\partial x} \left(\frac{1}{u}\right) \, d\psi.</math>

This transformation is later extended to compressible boundary layer by [[Theodore von Kármán|von Kármán]] and [[Qian Xuesen|HS Tsien]].<ref>{{Cite journal|doi=10.2514/8.591|title=Boundary Layer in Compressible Fluids|year=1938|last1=von Kármán|first1=T.|last2=Tsien|first2=H. S.|journal=Journal of the Aeronautical Sciences|volume=5|issue=6|pages=227–232}}</ref>