xdotool lets you send keyboard keys too so all the standard stuff like:

xdotool key Page_Down

xdotool key Down Down Down  # presses down three times with a 12ms delay

xdotool key --delay 2 Down Down Down  # as above but 2ms

With respect to the "deeper command", there's no one such thing. A window is sent an event (like a mousewheel) and it (the program or —more commonly— its toolkit) decides how to interpret that.

The scrolling isn't directly controllable (unless you're using an application or framework that provides an interface for doing just that). I've explained this a little bit more in your last question.