I specifically remember as a kid playing in the bathtub, and interrupting or splashing around with the little cyclone that would form by the drain. I could get it to go away but it would always reform fairly quickly.
So I suspect on a larger scale, you could probably disrupt a tornado with a big enough of "boom" but if the surrounding weather conditions were conducive to a tornado forming, it would probably come back reasonably quickly.
Unless you made a big enough "boom" to disrupt local weather patterns. But for that you'd need, like, a MOAB or something at least.
A cyclone or hurricane, however, would probably be too big even for nukes. Those are hundreds of miles across.