Can black hole experiences Coriolis effect? The weather here are thanks to Earth's rotation, so would there be any coriolis effect however tiny occurs when black hole rotates?
 A: Calculations have shown a coriolis term.  Example:

In this work, we consider the fluid/gravity correspondence for general rotating black holes. By using the Petrov-like boundary condition in near horizon limit, we study the correspondence between gravitational perturbation and fluid equation. We find that the dual fluid equation for rotating black holes contains a Coriolis force term, which is closely related to the angular velocity of the black hole horizon. This can be seen as a dual effect for the frame-dragging effect of rotating black hole under the holographic picture.

A: Yes, there is a Coriolis-like effect due to frame-dragging. A radially infalling geodesic in the Lense-Thirring spacetime will satisfy the equation $$0 = r\frac{d^2\phi}{dt^2}+2\frac{GJ}{c^2r^3}\frac{dr}{dt}$$ which can be compared to motion subject to the Coriolis force $$0=r\frac{d\phi}{dt^2}+2\omega\frac{dr}{dt}.$$ (see also Lämmerzahl &  Neugebauer 2001, who derive it with more rigour and an extra term; see equation 70 and 79).
One can also think about it using gravitoelectromagnetism, the formal analogy between electromagnetism and the weak field approximation of GR. In this case the Coriolis-like force is due to the analogy to magnetism: massive objects in motion feel a force at a right angle to their velocity just like charged objects feel a magnetic force at a right angle to their velocity. 
