Create Fog using Arnold in Maya 2018 – YouTube
Render setting – Arnold Renderer – Environment – aiFog
Distance: Distance of the point of origin of the fog from the camera.
Height: Height of the fog.
Ground Normal: The direction of the fog along the x, y, z axis.
Ground Point: The position of the fog along the x, y, z axis.
And we can k animation in these options.
Here is a simulation I tried to make: