The waves set up parallel to the barrier (not perpendicular to the wind) - the inversion allows the wave to 'bounce' back up on the downwind side of the barrier.
Wave orientation is roughly perpendicular to the prevailing wind, but modified by the obstacle causing the wave (and it need not be a mountain). A solitary mountain will have a crescent shaped wave pattern roughly akin to the mountain shape layed down facing downwind...it will curve and be lower in magnitude and closer to the mountain at the lower ends of the mountain, and be farthest with the greatest magnitidue, downwind at a point corresponding roughly with the highest point in the mountain.
Because a mountain isn't a continuous, even obstacle with even neight and gradient, neither are it's effects downwind. Additionally, most of the time multiple mountains exist, and the wave form isn't solitary or a singular repeating wave, but a series of mixed waves more akin the the swells and wave pattens one might see in the surf. Amid these waves can be turbulent rotors which may or may not coincide with the crests and/or troughs of each wave.
Of course to have massive sink and turbulence downwind of a ridge does not require wave...
Quite correct.
You'll find wave is extremely smooth.
In some cases this is true, in some cases it's not. A wave can form a distinct shear which can produce severe clear air turbulence.
They are also geographically static - they do not blow downwind.
If wind magnitude remains constant, this is true, unless atmospheric properties change (airmass change, frontal passage, etc); the waves do move then. If the magnitude of the wind changes, so do the positions of the waves.
In August I was flying westwards approaching the Rockies just north of Salt lake City when I hit mounatain wave. I was 2,000ft above the highest peak and approaching at the recommended 45 degree angle, my VSI maxed out downwards and I turned tail and fled to my alternate airport on the east side of the range. It was a clear day and there were no clouds to provide warning, my alternate airport was reporting calm winds.
It's common to have calm winds near the surface and strong winds aloft, particularly near or above the peaks, in the Rockies. Also strong winds in and around passes or gaps between mountains or saddles...these act as venturis where you'll find a pressure drop and a wind velocity increase.
Very often the best place to be is near the peak; get on the upwind side and enjoy the lift it provides.
I did a lot of fire flying around SLC, much of it in single engine air tankers. We were often maxed out in load, meaning minimal performance...airplanes capability of doing only one or two hundred feet per minute climb. Less than the Skyhawk. What I did to get to altitude, on my way to a fire, was hug the hill, usually with about half a wingspan's distance from the surface or less, and let the rising air carry me to altitude. Approaches to drops are planned the same way; knowing where the rising air is and where the descending air will be found is a key to coming out the other side of the drop alive.
Same thing in the Grand Canyon. When flying from some of the canyon airstrips in heavy loads, often the airplane didn't have the capability to do better than maintain altitude, initially. Takeoffs would be made which lead to flight over a drop-off of one to three thousand feet, and the rising air at the drop off was then used as the lift necessary to climb out of the canyon. Many of those flights were made in 172's, often from dirt strips in high density altitude situations; successfully operating there was all about finding and using the available orographic lift.
Sometimes if you find yourself approaching the lee or downwind side of a ridge and sinking, you can tuck in closer to the ridge to avoid the sink. This places you into rotors, and you have to know where you're going to go and always have a generous escape path...this is something to try after you've got some training and experience in the mountains...but a wave with descending air is a sure sign that somewhere not too far away is rising air of the same value or better...if you can find it you can really boost your performance, reduce your fuel burn, and even enjoy a quieter ride.
Again, waves or even rotors don't trap you. There's no cage there. If you don't like the performance where you are, fly to a different location and see what you get. Find the lift...it's all about looking for lift.