Material curve ($\mathbf{X}(a,t)$)

A material curve consists of the same fluid elements at all times. Differentiating their flow map gives $D\mathbf{\ell }/Dt=(\mathbf{\ell }\cdot \nabla )\mathbf{u}$ for its tangent. In ideal magnetohydrodynamics a magnetic-field tangent obeys this same transport law after division by mass density.