I think it decreases the energy level of the whole wave. If you think of the way a wavebox works when there's no overflow to deal with, it goes back and forth like a seesaw. If you cut off the top of the cycle, you lose out on all the extra energy that would be gained on the "downstroke". Real waves seem to be less about current and more about momentum, if that makes any sense. A center overflow is ideal because the wave in the middle of the tank doesn't really move up and down, almost like it's a fulcrum point.
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