Howarth–Dorodnitsyn transformation

In fluid dynamics, Howarth–Dorodnitsyn transformation (or Dorodnitsyn-Howarth transformation) is a density-weighted coordinate transformation, which reduces variable-density flow conservation equations to simpler form (in most cases, to incompressible form). The transformation was first used by Anatoly Dorodnitsyn in 1942 and later by Leslie Howarth in 1948. The transformation of ${\displaystyle y}$ coordinate (usually taken as the coordinate normal to the predominant flow direction) to ${\displaystyle \eta }$ is given by

${\displaystyle \eta =\int _{0}^{y}{\frac {\rho }{\rho _{\infty }}}\ dy,}$

where ${\displaystyle \rho }$ is the density and ${\displaystyle \rho _{\infty }}$ is the density at infinity. The transformation is extensively used in boundary layer theory and other gas dynamics problems.