I've only seen the term thermocline applied to water bodies, and it is the opposite of stratification.
Its not a matter of wiki being wrong, nor the construct of a cline in a non-liquid fluid. It's that the cline is the zone of high temperature differential between strata of much more uniform temperature. It is itself a strata, or layer, but its fundamental property is a temperature gradient with height. Because of water's unique characteristics, and their impact on both physical and biological systems, this stuff has been studied a lot (read up on "lake turnover" if interested). Air mixes more readily than water, and I'm not sure what the general temp profile in a house looks like other than warmer above cooler. I could measure it, but would need to build a manifold to hold the t-couple, bust out the data logger, and code in a measurement rgime. I'm not usre it's worth it (to me). If you read the logic behind counterclockwise-summer and clockwise-winter, it doesn't make complete sense from a heat transfer standpoint because summer is still forcing warmer air down. Both directions cause mixing; the winter arrangement pulls cooler air at low heights upward, and pushes warmer air downward by displacement around the boundary layer, effectively equalizing the temperature. The summer program forces air downward directly under the fan. Even though the air being forced down is warmer it is still is beneficial from convective cooling due to the air movement itself. If you are really warm, and slightly sweating, you get the added major bonus of vaporizing water off your skin and realizing the heat loss due to phase change.
. I know you already know this but thought it is interesting. As I have a 10,000 Koi pond and fish over winter. The properties of water are truly unique and somewhat amazing. It’s one of a few substances that can exist in all three phases, liquid, solid, gas. Water also expands when it freezes and it’s solid state is lighter than its liquid as we know ice floats. So water becomes more dense when it cools but as it becomes cooler at some point it becomes less dense again. This action also creates some heat. So water will only reach a certain temp I think @38-40 degrees at two to three feet deep below ice. Which allows wild life to survive etc. In any event, I just find this thermal process interesting. God new what he was doing. I also had a girlfriend who would drink her Starbucks throu a straw from the bottoms as she said it was cooler. LOL . In the winter I do run my fans on low pulling air up towards the ceiling and also forcing the warmer air down. I think it helps keep the room warmer. I have ten feet ceilings in one part of house and 12 feet in another. And as you pointed out I run the fans on a higher speed forcing air down just for air movement and evaporative cooling on body. The air isn’t any cooler but the movement helps.
No matter which direction you spin the blades hot air rises and cold air falls. The fan blowing down will always slightly increase the temp nearer the floor. Doesn't matter what time of year. Having the fan blow up has little to no effect on the temp nearer the floor. It is ineffective at "pulling" cool air up and all it will do is stir up the warm air near the ceiling and a little bit in the room. It's not going to suck cool air up from the floor. You would need a shroud going from the fan all the way to the floor to create enough vacuum to pull the air upward. Without a shroud it can't work effectively. Unless your ceiling is four feet tall. Having the fan blow down will always move warm air closer to the floor. But in winter you will actually feel colder because of the air moving across your skin. . So a low setting blowing down is the best compromise if you run the fan at all in winter.
I don’t want air blowing on me in the winter and the extra movement does move warmer air down to a lower level.
In the summer I’ll put a small fan blowing from the basement upstairs, amazing the amount of cool air it pushes up and with a good silent fan you don’t even know it’s there. Air movement is good for any house, I have no data to back that up but it just makes me feel better.
The convective forces caused by the spinning fan blades locally overcome the buoyancy of air at ambient residential temperatures by a couple orders of magnitude. So...at least locally, no. Garth: H20 max rho at 4C/39F.