Where does a flock of starlings end and the sky begin?

This shows a flock, also called a murmuration, of starlings at sunset. The hundreds or thousands of starlings are moving almost as if they are a single body, and mostly there is a pretty clear edge to the flock. It is pretty obvious where the flock ends and the rest of the sky begins. As the flock is a three-dimensional object, this should mean that the flock has a well defined surface, which separates the volume of sky occupied by the starling flock, from the surrounding sky where there are no starlings.

The starlings have kind of condensed into the murmuration, in the sense that the starlings have come together to form a volume where the density of starlings is high, surrounded by a volume where there no starlings. Now we know that water molecules condense into a water droplet, in the sense that they come together to form a volume where the density of water molecules is high, surrounded by a volume (the surrounding air) where there are almost no water molecules.

Maybe there are analogies between a murmuration and a droplet. If so we could steal ideas used to understand water droplets and apply them to murmurations. For example, a water droplet has a well defined surface, between the liquid and the surrounding air. We mostly understand the surface of a water droplet, in particular we know that associated with that surface is a tension. This surface tension acts to shrink the surface and it is this that tends to makes water droplets round up into spheres. It behaves a bit like an elastic sheet around the droplet.

If I look at flock turning and swirling across the sky, I can believe that it can be modelled as a set of moving objects inside an invisible elastic surface that keeps them together. But as far as I know no one has modelled a flock like this (I talk a bit about some work by a group in Italy in an earlier post). To do that, you would have to work out some properties of this surface. I don’t know if doing that would be useful, but it might be an interesting way of thinking about this amazing behaviour.