Eulerian time derivative
= Eulerian time derivative
{c}
{title2=$\partial_t f|_{\mathbf x}$}
The <Eulerian time derivative> measures a continuum field's rate of change at a fixed <Eulerian coordinate>. For a <velocity field> $\mathbf u$, the <material derivative> instead follows a <fluid element> and satisfies $Df/Dt=\partial_t f+\mathbf u\cdot\nabla f$. A nonuniform <steady flow> has zero <Eulerian time derivative> of <velocity> but can have nonzero <material acceleration>.