Why is there very little water in the washer tub during a cycle?

This is normal operation for a High Efficiency (HE) low-water washer. The washer automatically senses the load size and adds only the correct amount of water needed for optimal cleaning, so the load will not be completely submerged. You should not add more water to the washer, as added water lifts laundry off the washplate and results in less effective cleaning. (Page 12)