  An elegant quaternionic formulation is given for the Lagrangian advection
equation for velocity vector potential in fluid dynamics. At first we study the
topological significance of a restricted conserved quantity viz.,
stream-helicity and later more realistic configuration of open streamlines is
figured out. Also, using Clebsch parameterisation of the velocity vector
potential yet another physical significance for the stream-helicity is
provided. Finally we give a Nambu-Poisson formalism of the Lagrangian advection
equation for velocity vector potential.
