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 is extensively used in boundary layer theory and other gas dynamics problems.
Keith Stewartson and C. R. Illingworth, independently introduced in 1949,[6][7] a transformation that extends the Howarth–Dorodnitsyn transformation to compressible flows.
denotes the sound speed and
For ideal gas, the transformation is defined as where
is the specific heat ratio.