Wave conditions are most prominent with an unstable layer sandwiched between 2 stable layers, one being near mountaintop level. That creates the classic "trapped" lee wave that propagates far downstream.
Slightly more conditional instability above ridge level allows an "untrapped" wave system that has more of an upward component and less downstream. This one becomes strongest at its "cap", which is the tropopause. Being that the trop is the mother of all "elevated stable layers" this is why wave action and sometimes CAT can strengthen in the high flight levels above very strong lee wave systems.
Seen it above thand Rockies and the Sierra Nevada in the USA many a time. Similar effects to what you describe can be encountered above wave systems at lower altitudes as well; if not near the ridge top or an inversion layer it is very possible to encounter almost totally smooth wave conditions.
If it is an A330 try idling both engines and wave soaring on that giant wing!
On second thought don't.