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Non-modal analysis of Rayleigh–Bénard convection with and without bounded shear flows in viscoelastic fluids

Published online by Cambridge University Press:  14 May 2025

Zhenze Yao ,
Cailei Lu ,
Mengqi Zhang Open the ORCID record for Mengqi Zhang [Opens in a new window] ,
Kang Luo Open the ORCID record for Kang Luo [Opens in a new window]  and
Hongliang Yi Open the ORCID record for Hongliang Yi [Opens in a new window]
Zhenze Yao
Affiliation:
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China
Cailei Lu
Affiliation:
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China
Mengqi Zhang
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, Singapore 117575, Republic of Singapore
Kang Luo*
Affiliation:
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China
Hongliang Yi
Affiliation:
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China
*
Corresponding author: Kang Luo, luokang@hit.edu.cn
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Abstract

We perform a comprehensive linear non-modal stability analysis of the Rayleigh–Bénard convection with and without a Poiseuille/Couette flow in Oldroyd-B fluids. In the absence of shear flow, unlike the Newtonian case in which the perturbation energy decays monotonically with time, the interaction between temperature gradient and polymeric stresses can surprisingly cause a transient growth up to 104. This transient growth is maximized at the Hopf bifurcation when the stationary instability dominant in the weakly elastic regime transitions to the oscillatory instability dominant in the strongly elastic regime. In the presence of a Poiseuille/Couette flow, the streamwise-uniform disturbances may achieve the greatest energy amplification, and similar to the pure bounded shear flows, Gmax ∝ Re2 and tmax ∝ Re, where Gmax is the maximum energy growth, tmax the time to attain Gmax, Re the Reynolds number. It is noteworthy that there exist two peaks during the transient energy growth at high-Re cases. Different from the first one which is less affected by the temperature gradient and elasticity, the second peak, at which the disturbance energy is the largest, is simultaneously determined by the temperature gradient, elasticity and shear intensity. Specifically, the polymeric stresses field absorbs energy from the temperature field and base flow, which is partially transferred into the perturbed hydrodynamic field eventually, driving the transient amplification of the perturbed wall-normal vorticity.

JFM classification

Instability: Shear-flow instability Non-Newtonian Flows: Viscoelasticity

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JFM Papers
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Journal of Fluid Mechanics , Volume 1011 , 25 May 2025 , A37
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© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

†

Zhenze Yao and Cailei Lu contributed equally to this work.

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