Wakes and Turbulence

What is it about?

Very few problems are comparable in other fields to turbulence and the Navier-Stokes problem in physics and mathematics respectively. However, a parallel to them can be drawn in the decipherment of the ancient Egyptian scripts or hieroglyphs. Prior to the discovery of the Rosetta stone in 1799, understanding the hieroglyphs was believed by many to be impossible. This was because of the loss in the generational connection with any modern language. The beauty of the Rosetta stone is that the Egyptian priestly writers under the Greek ruler of Egypt, Ptolemy V, inscribed what is now called the decree of Memphis firstly in the hieroglyphs, then in the Egyptian Coptic script, and lastly in the ancient Greek letters on the stone. The hieroglyphs are ancestral to the Egyptian Coptic (or Demotic) scripts, and the Demotic had some connections to the spoken Coptic language at the time of the stone’s discovery. There are also firm connections between ancient Greek and modern European languages. Thus, starting from the translation of the ancient Greek account of the decree and identification of the mentioned Greek names in the Demotic account, expert researchers including Thomas Young and Jean-Francois Champollion employed their expertise on the grammatical structures of languages to decipher the hieroglyphs. Champollion was French but read Coptic, Ancient Greek, Latin, Hebrew, and Arabic as a young man. Young was British but had an entry in Encyclopedia Britannica that compared the grammar and vocabulary of 400 languages. In fact, Young was a polymath who made significant contributions to physics as well. Perhaps, Young also wondered what ‘language’ moving fluid particles ‘speak’ as did the Frenchman Claude-Louis Navier and the Irishman George Gabriel Stokes who independently codified the ‘grammatical structure of the language’ of viscous fluid motion in what are now known as the Navier-Stokes equations in mathematics. Much as the hieroglyphs are both phonetic and ideographic, the language of viscous flows can have both laminar and turbulent manifestations. To speak this language so to say, scientists and engineers try to solve the Navier-Stokes equations that govern its grammar. Depending on the laminar or turbulent manifestations, present solution methods currently offer varying proficiencies in the language. The language is so rich, dynamic, and diverse in its ‘vocabulary’ that it is not known whether with an understanding of ‘a document written in it at an instant’ (like the circular cylinder flow), an analytical solution of the governing equations of its ‘grammatical structure’ exits that can offer theoretical analyses of future manifestations of the same ‘document’. This is the Navier-Stokes problem. However, the published literature is somewhat of a ‘Rosetta stone’ on which a ‘decree of Memphis’ (flow over a circular cylinder) is ‘inscribed’ in ‘hieroglyphs’ (experimentally observed cylinder flow), ‘Demotic’ (computationally observed cylinder flow), and ‘ancient Greek’ (analytically described cylinder flow in classical potential flow theory) with the streamlines of the flow. The issue is that the description in classical potential flow theory is incomplete (e.g. does not include viscous effects, three-dimensional effects, and turbulence) even though it satisfies the Navier-Stokes equations. Much like a dead clock that is at least correct twice a day, it only matches the experimental and computational descriptions at some instant and/or specific Reynolds numbers. These identified instances are very crucial and akin to identification of Greek names in the hieroglyphs. With these, my yearslong work was to develop a refined potential flow theory that deciphers the experimentally observed cylinder flow, attempts to augment the incomplete classical potential flow theory for viscous effects, three-dimensional effects, and turbulence, and adheres to the sacrosanct ‘grammatical structure’ of the flow (Navier-Stokes Equations).

Featured Image

Photo by CHUTTERSNAP on Unsplash

Photo by CHUTTERSNAP on Unsplash

Why is it important?

Refined Potential Flow Theory introduces an unsteady viscous incompressible quasi-irrotational three-dimensional stream function that satisfies the governing equations and offers an analytical enquiry into the temporal evolution of the wake flow with both laminar and turbulent manifestations. It is the hope that it will be extensible and useful to more complex configurations.

Perspectives