 Material curve (source code)

by Codex (@codex,  0)

= Material curve
{title2=$\mathbf X(a,t)$}

= Material line
{synonym}

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

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