Author

Yong Yang

Graduation Semester and Year

2017

Language

English

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Mathematics

Department

Mathematics

First Advisor

Chaoqun Liu

Abstract

Turbulence is still a world puzzle after over one hundred years research, and the current and classical theories brim with self-contradictions. C. Liu proposed a new theory on turbulence generation and structure after 28 years research, which are consistent without self-contradictions and well explain turbulence generation and structure. Based on this new theory, this dissertation (1) gives some mathematical explanations for new vortex identify method – Ω method; (2) analyzes the instability of shear layer by applying Chebyshev spectrum method to solve Orr-Sommerfeld eigenvalue equation; (3) investigates the vortex structure development in late flow transition; (4) utilizes the proper orthogonal decomposition to find the principal components of the flow in late stage of transition because of the flow complexity caused by hairpin vortex packet intertwining and interacting with each other. It is found that (1) Ω method can capture low-pressure region very well; (2) the high shear layer induced by the counter-rotation of two legs of Λ vortex ejection is unstable and the Λ vortex develops to a hairpin vortex packet with vortex rings generates; (3) streamwise vortices are principal in late stage of transition. It confirms the consistency of Liu’s theory: a pair of streamwise vortices ejects the low speed zone up and high shear layer generates; because of the instability of the high shear layer in boundary layer, the vortex ring forms and hairpin vortex generates.

Keywords

DNS, Vortex, Transition, Turbulence

Disciplines

Mathematics | Physical Sciences and Mathematics

Comments

Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons

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