Howarth–Dorodnitsyn transformation

In fluid dynamics, Howarth–Dorodnitsyn transformation (or Dorodnitsyn-Howarth transformation) is a density-weighted coordinate transformation, which reduces compressible flow conservation equations to simpler form (in most cases, to incompressible form). The transformation was first used by Anatoli A. Dorodnitsyn in 1942 and later by Leslie Howarth in 1948.[1][2][3][4][5] The transformation of ${\displaystyle y}$ coordinate 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.

References

1. Dorodnitsyn, A. A. (1942). Boundary layer in a compressible gas. Prikl. Mat. Mekh, 6(6), 449-486.
2. Howarth, L. (1948). Concerning the effect of compressibility on lam inar boundary layers and their separation. Proc. R. Soc. Lond. A, 194(1036), 16-42.
3. Stewartson, K. (1964). The theory of laminar boundary layers in compressible fluids. Oxford: Clarendon Press.
4. Rosenhead, L. (Ed.). (1963). Laminar boundary layers. Clarendon Press.
5. Lagerstrom, P. A. (1996). Laminar flow theory. Princeton University Press.