Hello. I'm the author of the original question and I'm having a deja vu now.
But I hope it will be easier for me to explain my position here, because I guess the readers of this forum have a better understanding of physics, because I have made my best to understand the problem, and because I have some experience explaining it now already.
So let me start.
First of all, in order to approach the problem clear-minded and without the need to fight your intuition, we start with two simple examples.
Take a bucket with water (or a plastic bottle) on a string (it is important, don't just hold it in your hand!), and start swinging the bucket. You may try swinging, rotating, performing curves by letting the rope go and pulling the rope towards you, making full turns around you and around your head. You will note that the water in the bucket will stay, amazingly, quite strictly parallel to the bottom. The explanation is simple (link)
, but I dare you to do the experiment to destroy some of your intuition that hinders the understanding of the airplane case.
You probably have seen paragliders in the air. If you haven't, just go to youtube and type "extreme paragliding". Note that no matter what the roll angle of the paraglider is, it is always hanging straight perpendicularly to the parachute. If you would give a cup of tea to a paraglider, which way, do you think, the tea would orient itself? Of course it will be parallel to the floor.
Now the main thing you need to understand, is that if gravity can act freely both on the container (i.e. an airplane, a bucket, a seat of the paragliderist) and the object inside it, the object "can not detect gravity", if the only thing it can observe is the container. In other words, it is not gravity that plays a role in water orientation
. And this is a crucial a-ha-revelation moment.
With this being clear and gravity out of the way, the intuitive question becomes different: how can water be not
parallel to the floor. In order for that to happen, there must be some force pushing "on the side" of the airplane. What could be the source of this force?
Although I have only flown a plane on a simulator, I've done some background studies and have some understanding of this point.
Reason number one - the rudder. Rudder can be used to change the yaw of an airplane, i.e. rotate it around its vertical axis. In physical terms this results in a side-force being applied to the hull, but interestingly, this force acts on one side in the front of the aircraft (before its center of mass) and in an opposite direction in the back. Therefore, when you turn the rudder to the left, say, the water will incline slightly to the right in the cabin of the airplane (similarly to the "ball" mentioned in the previous comment). However, in the back of the airplane the water will incline to the different side, and in the center of mass it will not incline (just rotate around its axis).
However, the rudder is a very sensitive way to control an aircraft, and is thus never used at the speed the commercial passenger airliners travel.
Reason number two - adverse yaw
. This is a weird effect related to the imperfect construction of the ailerons. That is, when an aircraft is turning using the ailerons, a momentarily rotating force is applied and this basically acts in the same way as the rudder. This is the force that must be counterbalanced during the turn via the rudder by "watching the ball" (mentioned above). The resulting turn is called "coordinated".
However, firstly, the side push of the adverse yaw only exists when the ailerons are not straight, that is, during the time when the airplane is rotating itself around its main axis, and this force is approximately proportional to the rate of rotation. Therefore, even if an uncoordinated turn is made, you could see water incline slightly in the period when the plane is going into the turn, but once the roll angle of the plane is established and the ailerons are straight again, adverse yaw disappears.
And when the turn is performed slowly, smoothly, without abrupt movements, adverse yaw is quite small and the water won't incline much, even if the airplane itself "slips".
Third reason - body lift. It is normal to assume that lift force is only applicable to the wings, not to the body of the airplane, and in most cases, when the airplane hull is oriented approximately along the path of its movement it is indeed the case. It is always the case for passenger flights and I guess the pilot must be a skilled aerobat or a suicidal to achieve significant body lift.
So how do you achieve it? Well, one way is to incline the airplane while avoiding the turn, i.e. keeping the orientation of the fuselage straight (I guess this can be done using tail ailerons).
As a result the airplane will start gliding downwards along the slope of its wings, with its falling speed increasing linearly at first. However, at some point the air resistance will prevail and the falling speed will become constant. The same effect happens to a human in free fall. If I'm not mistaken the free fall speed is about 60m/s, and I guess it must be even larger for an airplane. Clearly, most pilots will avoid letting the plane descend with such velocity.
Secondly, they say it is possible to modify the "falling" situation above slightly, by heading the nose slightly upwards. An airplane fly nearly on the side as long as it can keep the orientation of the hull inclined slightly upwards with respect to its travel direction and earth. The angle of attack of the body will then produce lift capable of holding the airplane in that position for some time.
However, clearly this kind of aerobatics is never performed on commercial airliners.
Therefore the answer to my question is rather 1 - the physics of the airplane, than 2 - the skill of the pilot.
And I'm happy that the first comment of a pilot confirms that.