> FWIW the words pull and push are used in sailing training to emphasize the importance of keeping the leeward flow attached when going to weather.

Ding ding ding! Sailing is a practical matter, for nearly all sailors. It's nearly a folk activity. The models that are used to transmit and retain that information have more to do with achieving results than with achieving theoretical understanding. The trouble only really comes in when we try to use these pragmatic models as scientific models!

> Assuming the flow is attached on the leeward side, does that side also turn flow and generate force?

Notionally, yes. To be theoretical, attached flow on the leeward side is going to exert less pressure than detached flow would, due to irreversibilities in the detached turbulent flow. To be even stricter, because the equations of subsonic flow are elliptical and not hyperbolic, a mess of detached flow on the leeward side is going to jam up the whole works, even upstream and to windward.

The difficulty comes in when we try to mentally divide the flow between the windward and leeward sides of the sail. (Additional difficulty comes in because the "adverse pressure gradient" is essential to understanding this, but is tricky enough that it would probably do more harm than good to talk about it to sailing students. The first rule of Sailing Club is that you do not talk about the adverse pressure gradient. The second rule of....)

In practice, "[k]eeping the leeward flow attached" really amounts to "not stalling the sail." This is probably more important when sailing to windward because you're running as close to a stall as you can (at as high an angle of attack as you can) in order to point as high as you can. Also, with the sheets reefed in and with the higher apparent wind, the sail is more likely to be distorted. This can result in one part of the sail being stalled. Once one part stalls, the increased pressure in that area is likely to inject turbulent flow into neighboring areas that might otherwise not be stalled.

Another thing to consider is that there's something filling in that area of detached flow. Guess where it comes from? The windward side of the sail via the trailing edge. While the flow has to come off the leech in the direction of the leech, nature is a bit lest strict about what it does right after; It can get turned completely around, in short order, to fill that void behind the sail. The only thing it requires is that its turning radius not be unreasonably small. Congratulations! You've just (1) injected higher-pressure air into the lee, and equivalently (2) stopped turning the flow on the windward side. Because of (2), you can bet that there's an equivalent drop in pressure on the windward side as well.

That was the pragmatic way of understanding things. Now, I'm going to break the first rule of Sailing Club. When a flow is adjacent to a surface, the flow stops at the surface. That is, a 10 knot breeze blowing over your sail comes to a halt at the part of the breeze that contacts the sail. Because the adjacent flow hasn't touched the surface, it tries to maintain its 10 knots. However, nature is sticky. Any time there are adjacent regions of flow traveling at different velocities--any time there is a velocity gradient--viscosity tries to average things out: The flow right next to the sail is nearly stopped; The bit next to that is traveling a bit faster; And so on. (Incidentally, on a larger scale, this is why the wind is stronger aloft than on the deck. You're in the boundary layer, as it's called.) All of this viscous transfer is doing work on the flow. Doing work raises pressure. Because this happens as the flow moves downstream, more work is done on the flow the farther you get from the luff, and the higher the pressure gets. I don't think I need to convince you that fluids like to go away from high pressure to lower pressure. That is, fluids like to follow pressure gradients. And adverse pressure gradient can stop, and even reverse a flow. Note that this is likely to happen at the surface in question. Typically, the flow on the windward side has a stronger favorable pressure gradient to start with, and so can tolerate the adverse contributions of the viscous boundary layer without becoming detached. Because the point of a sail is to have lower pressure on the leeward side, there's less total pressure available to start with to overcome the adverse pressure gradient, and the flow can become detached on the back side of the sail.

This detached condition is called, in aeronautical terms, a "stall".

Just sheet in until the telltales flutter, and then back off until they don't. If that doesn't work, play with the vang until it does. ;)