djnks, you might have a different species of willow than mine but when my willows flooded, all died except those at or near the bank and waterline. The deeper the water, the quicker they died - over a span of one to four years. If you cut those near the bank and they have access to dirt, they'll continue to grow, putting up new growth all along the tree. You'll have to herbicide that new growth with glyphosate or 2,4-D or both, unless you want a thicket of willows. I had one large tree standing alone in about three feet of water that took around six years to give up.