What causes a high pitch humming noise similar to blowing across the top of an empty beer bottle when turning right on a 05 Grand Caravan especially accellerating through the turn?

my 2003 g/c sport 3.3 makes a whinning noise similar to your "high pitch humming" and both may be the alternator whirring. It seems worse when cold, but there are no other associated problems, although the sound comes and goes. could be low Power Steering fluid or air in steering system, check fluid level if full turn steering wheel all the way to stop in both directions(do not hold at stop)this should push air back to reservoir