We actually have a technique called "the other one"
@ Tim I mentioned earlier that usually the double strikes (redondos?) in shadow fighting look different when actually used to hit a bag or tire. I have noticed that some guys like Bobby Taboada do less of a circular motion and have more of a strike followed by a pulling back motion-folloed up with the second full power strike. The faster I go the more twirly the strike looks and thus less practical.
The Figure 8 or "Ocho" is also treated as multiple power strikes used to control center space and to smash anything that crosses attack line. I did a small workshop in September where I demonstrated the applications of the ocho. We treat these twirls as advanced applications of basic strikes.
I demonstrate this a few times in this clip:
Nice to see some more LSAI folks on here!
Generally in LESKAS/LSAI we refer to twirling as a general stickhandling/warmup exercise with no direct combat applicability.
Doblada strikes are how we refer to double strikes, as Basagulero noted. We'll do them from forehand or backhand, and can be used as a stick clear/strike, as a block/strike, or hand strike/head strike with with advancing footwork.
We'll also use verticals in a circular repeating manner occasionally. (LESKAS combination 11, etc). This can be from forehand or backhand. I particularly like the open side forehand vertical when entangled and somewhat head-on, as it's a good way to keep your weapon clear of a grab if you've already got your opponent's grabbed or you have him checked. The vertical allows of a tight retraction, but you can still get a lot of power on it.
Throwing a high diagonal once you're in close often just gives him a good grab opportunity. Just keep a left lead, maintain your check/grab, and if he reaches out to get the overwrap, just retract tight on the vertical and hit him on the tips of the fingers. Repeat as necessary.
In the system of Kombatan that I train in we do use a "twirling" strike as an application. We train against tires or heavy bags to practice the application of it with either the doblete, doblada and the redonda. It takes time to use it efficiently with power, simply doing it in the air is easy, but to hit a hard target over and over with power is tiring and if not trained you will lose power in any strike.
The twirling is also a way to keep your hand moving and not make it an easy target that can be focused on when fighting if it's just sitting in one general position. It's can also be used to feint when attacking and change the direction of a strike.