Groundcover under River Birch?
I have a large planter area surrounding a 20 yr. old River Birch. I am needing some suggestions on part-sun to shade groundcovers that can accomplish two things: 1.) tolerate some root/water competition from this very shallow-rooted, water-thirsty tree, and 2.)tolerate the deep soakings I have to give the tree to keep it alive in our Central Oklahoma heat.
Any ideas? I hate having areas that are just mulch (preferring to fill every spot with a lovely plant!), but I realize this may be the best option for the health of the River Birch. I appreciate your opinions!