Application of Local Gauge Theory to Fluid Mechanics - Part 2 Example: Basic Model of Tollmien-Schlichting Waves and Analytical Solution

Thomas Merz

doi:10.20944/preprints202210.0156.v2

Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 10 October 2022 / Approved: 11 October 2022 / Online: 11 October 2022 (15:28:43 CEST)
Version 2 : Received: 11 October 2022 / Approved: 12 October 2022 / Online: 12 October 2022 (10:32:00 CEST)

The gauge field equation for fluid mechanics established in Part 1 is developed into a first-order scattering theory in the simplified case of a two-dimensional incompressible flow over a flat plate. This is used to present a model for the origin of Tollmien-Schlichting (TS) waves based on scattering between fluid particles. As a result, analytical formulae for the maximum amplification factor and the transition point from laminar to turbulent flow in the boundary layer are obtained. The mathematical transformations from the stationary field equations in Part 1 to a scattering theory with time evolution along the flow axis using Wick rotation are elaborated in detail.

boundary layers; transition to turbulence; Navier–Stokes equations; local gauge

Physical Sciences, Condensed Matter Physics

Comment 1

Received: 12 October 2022
Commenter: Thomas Merz
Commenter's Conflict of Interests: Author

Comment: Only the title and abstract were adjusted such that the numbering of the parts is better formatted.

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Application of Local Gauge Theory to Fluid Mechanics - Part 2 Example: Basic Model of Tollmien-Schlichting Waves and Analytical Solution

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