Spherical secondary infall follows concentric collisionless shells around a primordial overdensity. Each shell initially expands with the Hubble flow, turns around, collapses, and subsequently crosses other shells.
The turnaround radius of a shell is its maximum physical radius before collapse. At a given cosmic time, the currently turning shell defines a natural similarity length.
If the initial fractional excess mass is a power law in enclosed mass, spherical secondary infall admits a similarity reduction in which radii scale by the current turnaround radius and masses by the mass of the currently turning shell.
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