I don't know if the application that I'm going to refer is well-known. I've read it from a book, Wikipedia has an article dedicated to the author [*E. O. Wilson*](https://en.wikipedia.org/wiki/E._O._Wilson), that refers in chapter 14 of the book [1] (I know the Spanish edition of the book Editorial Planeta, Crítica 2022); the chapter is potentially interesting for mathematicians.

Wikipedia has an article including the section [*In engineering applications*](https://en.wikipedia.org/wiki/Logarithmic_spiral#In_engineering_applications) from the Wikipedia article dedicated to *Logarithmic spiral.*

If I understad well whirls don't fit with your question/post, but I include the following references as general reference in case that you or the readers want to know these notes that I consider interesting, in fact these aren't applications, if I remember well [2] include notes about whirls, and [3] seems interesting for me (is a note in Spanish language).

Please let me to know (you or your colleagues) if my post isn't a good answer that I can to delete it in next few hours, many thanks.

References:
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[1] Edward O. Wilson, *Tales from the Ant World*, Published by Liveright (2020).

[2] Leo Zippin, *Uses of Infinity*, Dover Publications (2000).

[3] Juan Luis Varona, $\zeta(2k)$ *versus* $zeta(k)$: *una relación geométrica en una espiral*, Miniaturas matemáticas, La Gaceta de la RSME 
Vol. 18 (2015), Núm. 2, Pág. 352.