As per your reply, I understand the rule from CII as follow:

Local +x = wave direction
Local +z = element From-To direction
Local +y = right hand rule = transverse force direction

Is this rule mentioned in any text book?

In real world, 2D wave, at phase 0 (wave crest) I image the transverse foce should always be up even if the wave direction forward or backward. This conflict with CII rule. Do I have any misunderstanding?