In a real lottery bowl, the balls are blown up from a stream of air that is quite thin in diameter. If you are using the Wind object with default settings, it blows evenly across the whole area.
So you should set the Falloff to Tube, then you have to adjust Max Distance and for the diameter change Radial > Max Distance. The values depend a lot on the size of your objects and the look you want to achieve.
To help blow the balls to the outside I've added a Force object above with limited Max Distance to affect the balls as soon as the wind decreases. I've also set the weight of the balls quite low. The result looks like this: