I am pleased to share some of the results of my research over the past few years. These just appeared as a review article in the Proceedings of the Royal Society A and you can download it from here (and the cool thing about the Royal Society – besides its very professional reviewers – review articles are free access to everyone!)
I hope that you will enjoy reading this manuscript as it includes many classical ideas with a novel twist as well as some original derivations and solutions for flows at large Reynolds numbers.
The heart of this research resides in the fact that we were able to capture solutions that range from purely irrotational to highly rotational fields using a single formulation. These have different energy signatures and morph according to the energy level they are at. The second law of thermodynamics is then used to identify which of those solutions is the most likely to occur in practice based on the entropy maximization principle. Finally, Kelvin’s minimum energy theorem is extended to open regions thus granting it applicability to a wider class of problems. It is used here to prove that the solution with minimum kinetic energy corresponds indeed to the irrotational motion.
Working on this article is one of the main reasons that I have not been posting recently,