I don't know if the application that I'm going to refer is well-known (an invention of the author of [1]). I've read it from a book, Wikipedia has an article dedicated to the author E. O. Wilson, that refers the application 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, and are included the related articles in the bibliography of this book.
Wikipedia has an article including the section 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, if I remember well [2] include notes about whirls, and [3] seems interesting for me (is a note in Spanish language).
Other instances are the following, 1) this time is an historical example, is from the book [4], see Figure 2.8 and the preceding subsection of Chapter 2; and 2) the meaning of article [5] (I don't know what's the revelance of this article published from a journal of the American Chemical Society, but I believe that sure it is interesting).
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:
[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.
[4] Michio Kaku, Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and The Tenth Dimension, Oxford University Press (1994).
[5] Audrey R. Sulkanen, Minyuan Wang, Logan A. Swartz, Jaeuk Sung, Gang Sun, Jeffrey S. Moore, Nancy R. Sottos and Gang-yu Liu, Production of Organizational Chiral Structures by Design, J. Am. Chem. Soc. 144, 2 (2022), pages 824–831.