What is the physics of crosswind landings for large airplanes?
When the wind acts on the tall fin upon touchdown, is there a yaw effect, or does the wind push the airplane downwind? And what is the rudder correction to be anticipated?


Let's assume a strong crosswind at 90° from the right with a 747 on a dry, uncontaminated runway for illustration purposes.

Once the airplane is firmly on the runway, the wind is acting on the whole airplane, with the crosswind pushing it downwind, and given the greater side force aft of the c.g. (especially because of the tailplane) than the side force forward of the c.g., there is at the same time a net yaw effect wanting to rotate the airplane about the c.g. into the wind.

Perhaps its best to think of the rudder pedal displacement not just as where you want the rudder, but also what you want the nose gear to do. While there were some 747s that had no connection between the nose gear steering and the rudder pedals, most did (at least the ones I flew). Now think of what you have to do to get the airplane where you want it, pointed in the direction you want, and actually traveling in the direction you want.

What you want to wind up with is the airplane's longitudinal axis on the runway center line, nose pointed straight down the center line, and the airplane actually moving straight down the center line. Let's say you've succeeded in getting the airplane to that state. To keep it, in our strong 90° right crosswind,you would use right aileron to keep the wind from getting under the upwind wing so to speak, and some left rudder. How much would depend on whether you had rudder pedals that connected to the nose gear steering, your speed, your weight and when you started using the tiller for steering. I forget the details of the connection between the nose gear steering and the rudder pedals, but it's not linear, and as I remember you can have the nose gear tracking straight ahead even though you are using some rudder.

On a 747, once you've slowed down to tiller speed, you would use it, and on a dry, uncontaminated runway, the main and wing gear will keep you from moving sideways and the nosegear will control your direction of movement, at least in the strongest of winds I operated in, say 40-45 knots or so.

Chances are, once you are firmly on the runway after touchdown, you will not be exactly on the center line nor pointed precisely down the runway. Your first and second illustrations are dealing with getting there from a less than ideal touchdown, and if I understand them, they are correct. If to the right of the center line, you can allow a drift leftward. If to the left, you don't have a lot of room to spare so you need positive action to get to the center line.