  Vorticity dynamics of the three-dimensional incompressible Euler equations is
cast into a quaternionic representation governed by the Lagrangian evolution of
the tetrad consisting of the growth rate and rotation rate of the vorticity. In
turn, the Lagrangian evolution of this tetrad is governed by another that
depends on the pressure Hessian. Together these form the basis for a direction
of vorticity theorem. Moreover, in this representation, fluid particles carry
ortho-normal frames whose Lagrangian evolution in time are shown to be directly
related to the Frenet-Serret equations for a vortex line. The frame dynamics
suggest an elegant Lagrangian relation regarding the pressure Hessian tetrad.
The equations for ideal MHD are similarly considered.
