Energy Budget Characterisation of the Optimal Disturbance in Stratified Shear Flow

Larry Godwin; Philip Trevelyan; Takeshi Akinaga; Sotos Generalis

doi:10.3390/fluids9050106

Energy Budget Characterisation of the Optimal Disturbance in Stratified Shear Flow

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

^*Corresponding author for this work

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

Abstract

Stratified Taylor–Couette flow (STCF) undergoes transient growth. Recent studies have shown that there exists transient amplification in the linear regime of counter-rotating STCF. The kinetic budget of the optimal transient perturbation is analysed numerically to simulate the interaction of the shear production (SP), buoyancy flux (BP), and other energy components that contributes to the total optimal transient kinetic energy. These contributions affect the total energy by influencing the perturbation to extract kinetic energy (KE) from the mean flow. The decay of the amplification factor resulted from the positive amplification of both BP and SP, while the growth is attributed to the negative and positive amplification of BP and SP, respectively. The optimal SP is positively amplified, implying that there is the possibility of constant linear growth. These findings agree with the linear growth rate for increasing values of Grashof number.

Original language	English
Article number	106
Number of pages	13
Journal	Fluids
Volume	9
Issue number	5
Early online date	29 Apr 2024
DOIs	https://doi.org/10.3390/fluids9050106
Publication status	Published - May 2024

Bibliographical note

Copyright © 2024 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 (CC BY) license (https://creativecommons.org/licenses/by/4.0/)

Data Access Statement

The Matlab sources codes used to generate the data in this study can be
made available upon request.

Keywords

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

Access to Document

10.3390/fluids9050106

Godwin et al Energy Budget Characterisation of the Optimal Disturbance in Stratified Shear Flow
Copyright © 2024 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 (CC BY) license (https://creativecommons.org/licenses/by/4.0/)
Final published version, 714 KBLicence: CC BY 4.0

Cite this

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title = "Energy Budget Characterisation of the Optimal Disturbance in Stratified Shear Flow",

abstract = "Stratified Taylor–Couette flow (STCF) undergoes transient growth. Recent studies have shown that there exists transient amplification in the linear regime of counter-rotating STCF. The kinetic budget of the optimal transient perturbation is analysed numerically to simulate the interaction of the shear production (SP), buoyancy flux (BP), and other energy components that contributes to the total optimal transient kinetic energy. These contributions affect the total energy by influencing the perturbation to extract kinetic energy (KE) from the mean flow. The decay of the amplification factor resulted from the positive amplification of both BP and SP, while the growth is attributed to the negative and positive amplification of BP and SP, respectively. The optimal SP is positively amplified, implying that there is the possibility of constant linear growth. These findings agree with the linear growth rate for increasing values of Grashof number.",

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

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

note = "Copyright {\textcopyright} 2024 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 (CC BY) license (https://creativecommons.org/licenses/by/4.0/)",

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doi = "10.3390/fluids9050106",

language = "English",

volume = "9",

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T1 - Energy Budget Characterisation of the Optimal Disturbance in Stratified Shear Flow

AU - Godwin, Larry

AU - Trevelyan, Philip

AU - Akinaga, Takeshi

AU - Generalis, Sotos

N1 - Copyright © 2024 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 (CC BY) license (https://creativecommons.org/licenses/by/4.0/)

PY - 2024/5

Y1 - 2024/5

N2 - Stratified Taylor–Couette flow (STCF) undergoes transient growth. Recent studies have shown that there exists transient amplification in the linear regime of counter-rotating STCF. The kinetic budget of the optimal transient perturbation is analysed numerically to simulate the interaction of the shear production (SP), buoyancy flux (BP), and other energy components that contributes to the total optimal transient kinetic energy. These contributions affect the total energy by influencing the perturbation to extract kinetic energy (KE) from the mean flow. The decay of the amplification factor resulted from the positive amplification of both BP and SP, while the growth is attributed to the negative and positive amplification of BP and SP, respectively. The optimal SP is positively amplified, implying that there is the possibility of constant linear growth. These findings agree with the linear growth rate for increasing values of Grashof number.

AB - Stratified Taylor–Couette flow (STCF) undergoes transient growth. Recent studies have shown that there exists transient amplification in the linear regime of counter-rotating STCF. The kinetic budget of the optimal transient perturbation is analysed numerically to simulate the interaction of the shear production (SP), buoyancy flux (BP), and other energy components that contributes to the total optimal transient kinetic energy. These contributions affect the total energy by influencing the perturbation to extract kinetic energy (KE) from the mean flow. The decay of the amplification factor resulted from the positive amplification of both BP and SP, while the growth is attributed to the negative and positive amplification of BP and SP, respectively. The optimal SP is positively amplified, implying that there is the possibility of constant linear growth. These findings agree with the linear growth rate for increasing values of Grashof number.

KW - bifurcation

KW - stability

KW - thermal diffusivity

KW - buoyancy

KW - convection

KW - Taylor–Couette flow

KW - nonlinear dynamics

UR - https://www.mdpi.com/2311-5521/9/5/106

U2 - 10.3390/fluids9050106

DO - 10.3390/fluids9050106

M3 - Article

SN - 2311-5521

VL - 9

JO - Fluids

JF - Fluids

IS - 5

M1 - 106

ER -

Energy Budget Characterisation of the Optimal Disturbance in Stratified Shear Flow

Abstract

Bibliographical note

Data Access Statement

Keywords

Access to Document

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