In fluid dynamics, Batchelor vortices, first described by George Batchelor in a 1964 article, have been found useful in analyses of airplane vortex wake hazard problems.
[1][2] The Batchelor vortex is an approximate solution to the Navier–Stokes equations obtained using a boundary layer approximation.
The physical reasoning behind this approximation is the assumption that the axial gradient of the flow field of interest is of much smaller magnitude than the radial gradient.
The axial, radial and azimuthal velocity components of the vortex are denoted
We now write the system above in dimensionless form by scaling time by a factor
Using the same symbols for the dimensionless variables, the Batchelor vortex can be expressed in terms of the dimensionless variables as
denotes the free stream axial velocity and
and considers an infinitely large swirl number then the Batchelor vortex simplifies to the Lamb–Oseen vortex for the azimuthal velocity: where