The subject of fluid mechanics is a rich, vibrant, and rapidly developing branch of applied mathematics. Historically, it has developed hand-in-hand with the elegant subject of complex variable theory. The Westmont College NSF-sponsored workshop on the revitalization of complex variable theory in the undergraduate curriculum focused partly on identifying scientific areas where complex variables plays an active role. The author presented a lecture on this topic and here we highlight parts of that presentation and follow-up discussion.