Not your typical power steering whining noise.

The car listed above is a 7th gen. So, I have a whine noise but only after turning and accelerating. I know what a power steering pump normally sounds like, but this is different and does not get louder the more I turn nor when parked and turning the wheel. The only thing I can compare it to is the noise of friction motor in a toy car after you push it forward a few times. It does not change when putting it in neutral. After it is triggered, the noise continues until I turn it off or drive for about 10 minutes without any speedy turning. Fluids are topped. The car is high miles. 186,000 on card, 118,000 on motor. If I make a turn and let off the accelerated, and do not heavy-brake, and ease into my turn, it prevents the flare up. Thanks in advance!