Physics Question

The equation is based on a cylinder, but an actual cylinder has valve reliefs in the pistons, domes, dishes, quench areas, etc... so I tried to simplify the original question. Realistically, any ICE cylinder is a chaotic mosh pit during the compression stroke due to those variables.

In the example, I'm referencing a 2-valve engine with offset intake valve and port creating a swirl (parallel to cylinder) in the cylinder. A pent roof chamber (modern 4-valve DOHC) will tend to create what's called a tumble (perpendicular).
 
Can make some assumptions, but the orientation of the spin is a pretty important clarifying question. Rotation which axis makes a difference here.

The first "fact" is ( no assumption) is that there is no "spin" of this "mixture" ( atomized fuel and air with 2 different densities, mass etc.)- this is basic CFD

What "momentary deflections" ( giving the "illusion" of rotation) there would be during entry is a series of angular deflections ( remember, energy cannot turn a corner) that would be "facets' or "chords" of a circle.

Each impact would create a nano second stop, angular change then movement ( no different than loss in a pipe elbow)- then its pushing against the additional mass already accumulating.

This "velocity" ( moving energy) of the mixture entering ( once the valve closed to start a compression) would be consumed almost instantaneously and move toward fluid equilibrium and then start being compressed.
 
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