  A rational theory is proposed to describe the large-scale motion in
turbulence. The fluid element with inner orientational structures is proposed
to be the building block of fluid dynamics. The variance of the orientational
structures then constitutes new fields suitable to describe the vortex state in
turbulence. When the fluid element is assumed to be an open subsystem, the
differentiable manifold description of turbulence ought to be set up, and the
complete fluid dynamics can be deduced from a variational calculus on the
constructed Lagrangian dissipation energy density. The derived dynamical
equations indicate that the vortex evolution is naturally related with the
angular momentum balance.
