Transient Dynamics in Counter-Rotating Stratified Taylor–Couette Flow

Sotos Generalis; Takeshi Akinaga; Philip Trevelyan; Larry Godwin

doi:10.3390/math11143250

Transient Dynamics in Counter-Rotating Stratified Taylor–Couette Flow

Sotos Generalis^*, Takeshi Akinaga, Philip Trevelyan, Larry Godwin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	3250
Pages (from-to)	3250-3265
Number of pages	15
Journal	Mathematics
Volume	11
Issue number	14
Early online date	23 Jul 2023
DOIs	https://doi.org/10.3390/math11143250
Publication status	Published - 24 Jul 2023

Bibliographical note

Copyright:© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution( CCBY) license
(https:// creativecommons.org/licenses/by/ 4.0/).

Funding Information:
This research was funded by RISE Horizon 2020 ATM2BT, Atomistic to Molecular Turbulence, grant no. 824022, TETFUND scholarship and DTI EPSRC grant, Aston University sponsorship.

Publisher Copyright:
© 2023 by the authors.

Keywords

Taylor–Couette flow
bifurcation
buoyancy
convection
nonlinear dynamics
stability
thermal diffusivity

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10.3390/math11143250Licence: CC BY 4.0

mathematics-11-03250-v2
Copyright:© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution( CCBY) license (https:// creativecommons.org/licenses/by/ 4.0/).
Final published version, 855 KBLicence: CC BY 4.0

Cite this

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title = "Transient Dynamics in Counter-Rotating Stratified Taylor–Couette Flow",

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 = "Taylor–Couette flow, bifurcation, buoyancy, convection, nonlinear dynamics, stability, thermal diffusivity",

author = "Sotos Generalis and Takeshi Akinaga and Philip Trevelyan and Larry Godwin",

note = "Copyright:{\textcopyright} 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution( CCBY) license (https:// creativecommons.org/licenses/by/ 4.0/). Funding Information: This research was funded by RISE Horizon 2020 ATM2BT, Atomistic to Molecular Turbulence, grant no. 824022, TETFUND scholarship and DTI EPSRC grant, Aston University sponsorship. Publisher Copyright: {\textcopyright} 2023 by the authors.",

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AU - Akinaga, Takeshi

AU - Trevelyan, Philip

AU - Godwin, Larry

N1 - Copyright:© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution( CCBY) license (https:// creativecommons.org/licenses/by/ 4.0/). Funding Information: This research was funded by RISE Horizon 2020 ATM2BT, Atomistic to Molecular Turbulence, grant no. 824022, TETFUND scholarship and DTI EPSRC grant, Aston University sponsorship. Publisher Copyright: © 2023 by the authors.

PY - 2023/7/24

Y1 - 2023/7/24

N2 - 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.

AB - 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.

KW - Taylor–Couette flow

KW - bifurcation

KW - buoyancy

KW - convection

KW - nonlinear dynamics

KW - stability

KW - thermal diffusivity

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DO - 10.3390/math11143250

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VL - 11

SP - 3250

EP - 3265

JO - Mathematics

JF - Mathematics

IS - 14

M1 - 3250

ER -

Transient Dynamics in Counter-Rotating Stratified Taylor–Couette Flow

Abstract

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Keywords

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Pattern Competition for the Sequential Bifurcations Approach (SBA) to Turbulence in the Co-Rotating Taylor–Couette System: Quinary States

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