Version 1
: Received: 20 December 2023 / Approved: 21 December 2023 / Online: 21 December 2023 (16:01:59 CET)
How to cite:
Godwin, L.E.; Trevelyan, P.M.; Akinaga, T.; Generalis, S. Energy Budget Characterisation of the Optimal Disturbance in Stratified Shear Flow. Preprints2023, 2023121670. https://doi.org/10.20944/preprints202312.1670.v1
Godwin, L.E.; Trevelyan, P.M.; Akinaga, T.; Generalis, S. Energy Budget Characterisation of the Optimal Disturbance in Stratified Shear Flow. Preprints 2023, 2023121670. https://doi.org/10.20944/preprints202312.1670.v1
Godwin, L.E.; Trevelyan, P.M.; Akinaga, T.; Generalis, S. Energy Budget Characterisation of the Optimal Disturbance in Stratified Shear Flow. Preprints2023, 2023121670. https://doi.org/10.20944/preprints202312.1670.v1
APA Style
Godwin, L.E., Trevelyan, P.M., Akinaga, T., & Generalis, S. (2023). Energy Budget Characterisation of the Optimal Disturbance in Stratified Shear Flow. Preprints. https://doi.org/10.20944/preprints202312.1670.v1
Chicago/Turabian Style
Godwin, L.E., Takeshi Akinaga and Sotirios Generalis. 2023 "Energy Budget Characterisation of the Optimal Disturbance in Stratified Shear Flow" Preprints. https://doi.org/10.20944/preprints202312.1670.v1
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. It is reported that as Gr increases, the maximum amplification factor ($G_0$) initially decays before it eventually starts growing after reaching a certain critical value Gr$_{c}$. Assuming other parameters of the model are kept constant, the value Gr$_{c}$ changes with respect to different speed ratios of the cylinders. The observed decay/growth pattern of $G_0$ is attributed to the interplay between the induced shear and buoyancy. In this study, the mechanism that triggers this observed pattern is investigated. The kinetic budget of the optimal transient perturbation is analysed numerically to simulate the interaction of the shear production (SP), buoyancy production (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 $G_0$ 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 Gr.
Computer Science and Mathematics, Computational Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
