Transient Dynamics in Counter-Rotating Stratified Taylor–Couette Flow

Larry E. Godwin, Philip M. J. Trevelyan, Takeshi Akinaga and Sotos C. Generalis ()
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Larry E. Godwin: Department of Applied Mathematics and Data Science, School of Engineering and Applied Science, Aston University, Birmingham B4 7ET, UK
Philip M. J. Trevelyan: Department of Applied Mathematics and Data Science, School of Engineering and Applied Science, Aston University, Birmingham B4 7ET, UK
Takeshi Akinaga: Faculty of Engineering Science, Akita University, 1-1 Tegatagakuen-machi, Akita 010-8502, Japan
Sotos C. Generalis: Department of Applied Mathematics and Data Science, School of Engineering and Applied Science, Aston University, Birmingham B4 7ET, UK

Mathematics, 2023, vol. 11, issue 14, 1-15

Abstract: This study focuses on the investigation of stratified Taylor–Couette flow (STCF) using non-modal analysis, which has received relatively limited attention compared to other shear flows. The dynamics of perturbations under different temperature conditions are explored, and their patterns of amplification are analyzed. The study highlights the correlation between flow configurations, emphasizing the similarity in transient dynamics despite different speed ratios. The subcritical effects of thermal stratification on disturbance dynamics are examined, considering the interplay between viscous and buoyancy effects counteracted by strong centrifugal forces. It is found that increasing the wall temperature beyond a critical value leads to buoyancy forces dominating, resulting in a linear increase in the amplification factor. The research reveals significant deviations from previous results, indicating the significant role of temperature stratification.

Keywords: bifurcation; stability; nonlinear dynamics; Taylor–Couette flow; convection; buoyancy; thermal diffusivity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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