Putting fog in the sides?

I would like to place a cloud of fog to the west and one to the east in my scene.

I have learned from the API that I cannot use exponential fog, since that kind is always relative to the camera, whereas I need localized fog.

So, I use linear fog, which has nice functions like setLinearRange.
Now it is easy to create those clouds to the north and south (in front and in back) - along the forward-axis (Y).

This is all good, except that I want this fog rotated 90 degrees.
That is, I want it to the east and west (along the X-axis).

Can anyone tell me how to offset the fog along the X-axis, please?

Or perhaps guide me on how to rotate the fog (node?)
My problem is that I think I need to set the fog on render:
and I really cannot go around rotating render.

Then I tried introducing some dummy nodes, but I failed.

Any hints please?