Two-dimensional potential flow expressed by means of
the complex potential function uses Euler
coordinates, i.e. a fixed point approach. However,
there are many cases where the identical particle
time is required, for example the settling time of
suspended particles, heat convection (because in
incompressible potential flow the heat and flow
equations are uncoupled), and dispersion of fluid
particles due to distortion.
In real variables the differential equation for the
Lagrange time is generally too complicated because
it involves two coordinates as functions of time. In
the following a differential equation of single
complex variable is derived.