I asked the question because the OP is concerned about the board 'bowing' - apparently since it was plain sawn. He continues by mentioning he does 'not want to cut the plank'. This confuses things, because he proposes that cutting the plank will somehow prevent bowing. Not a good linkage of cause and effect. His OP in fact has two statements that utilize defective cause and effect. This is the reason for all the confusion that follows. His statements presuppose conditions that are faulty, or at least unclear, and the conclusions are based on that, as well as many of the responses.
I asked why he is concerned about it bowing (whatever is meant by that could be another discussion...). Does plain sawing affect its proclivity to bow? -- as an attempt to explore the faulty (in my opinion) connection.
>> Answer: Why does wood move (assumed to include 'bowing')? Wood moves in response to changes in Moisture Content (MC). This is normally caused by changes in the Relative Humidity (RH) in the environment of the board. A reading of Hoadley or any basic book on wood technology, or even here on Woodweb, will get that basic bit of info.
So, is the piece going to be in an area where MC is likely to change from changes in RH? What will be the parameters of that change in RH > MC?
Then, how will that affect the board? "Bowing" is one response. Cupping, twisting, cracking, moving, winding, splitting, or more are other responses.
Battens, assumed to be cross grain, can prevent cupping. I'm unsure about preventing bowing since I don't know what is meant by that term. The battens (cleats, sticks, things) placed cross grain will do nothing to prevent most of the other defects that can happen.
Natural curiosity is good thing, but must be countered by logical and rational thought, generating a sound line of reasoning. Without those simple basics, we would have a planet full of religious wars and hatred.