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@wikipedia


Given velocity vector 

LaTeX Math Inline
body{\vec {u}}=(u_x,u_y,u_z)
 the streaklines is a bunch of curves 
LaTeX Math Inline
body{\vec {r}}_s = \big( \, x_s, \, y_s, \, z_s \, \big) \in \mathbb{R}^3
, parametrized by the stem points 
LaTeX Math Inline
body{\vec {r}}_{s0}
 at zero-time 
LaTeX Math Inline
bodyt_0
, and solving the following equation:

LaTeX Math Block
alignmentleft
\begin{cases}

\displaystyle 

{\frac {d{\vec {r}}_s(t)}{dt}}={\vec {u}}_s({\vec {r}}_s,t)
\\[1.2ex]

{\vec {r}}_s(t = \tau_s)={\vec {r}}_{s0}

\end{cases}