  We reanalyse an arbitrary-wavelength gyrokinetic formalism [A. M. Dimits,
Phys. Plasmas $\bf17$, 055901 (2010)], which orders only the vorticity to be
small and allows strong, time-varying flows on medium and long wavelengths. We
obtain a simpler gyrocentre Lagrangian up to second order. In addition, the
gyrokinetic Poisson equation, derived either via variation of the system
Lagrangian or explicit density calculation, is consistent with that of the
weak-flow gyrokinetic formalism [T. S. Hahm, Phys. Fluids $\bf31$, 2670 (1988)]
at all wavelengths in the weak flow limit. The reanalysed formalism has been
numerically implemented as a particle-in-cell code. An iterative scheme is
described which allows for numerical solution of this system of equations,
given the implicit dependence of the Euler-Lagrange equations on the time
derivative of the potential.
