The swirl sign refers to the non-contrast CT appearance of acute extravasation of blood into a hematoma, for example an extradural hematoma or subdural hematoma. It represents unclotted fresh blood which is of lower attenuation than the clotted blood which surrounds it 1).
Black curved arrow
It is the corollary of the spot sign on CTA which represents the same phenomenon, but in that case caused by contrast extravasation 2).
see Gupta VK, Seth A. “Swirl Sign” in Extradural Hematoma. World Neurosurg. 2018 Oct 10. pii: S1878-8750(18)32302-7. doi: 10.1016/j.wneu.2018.10.010. [Epub ahead of print] PubMed PMID: 30315986.