Thank you so much. Actually, my first question came to my mind when I compared the input velocity way and moving wall way. Because in the moving wall, the given wall just move in the x direction and there is not any w velocity change?
So why we must use wvel=exp(0.4z)*cos(2t) ????????

You quoted this equation so you are in a better position than me to know.

But I suspect it is because water waves are caused by a circular motion of the water. This means it requires motion in the vertical direction as well as the wave propagation direction.