@wikipedia


Given velocity vector  the streaklines is a bunch of curves , parametrized by the stem points  at zero-time , and solving the following equation:

\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}