While reading this document on Coriolis effect http://empslocal.ex.ac.uk/people/staff/gv219/classics.d/Persson98.pdf, I saw the followig sentence
Two kinematic effects each contribute half of the Coriolis acceleration: relative velocity and the turning of the frame of reference.
And this is the reason why Coriolis term has that factor $2$. Unfortunately it does not specify anything about this two causes. Does anyone have some further explanation for how "relative velocity" and "turning of the frame" actually give rise to the Coriolis term?