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Effects of phase boundary and shear on diffusive instability

Published online by Cambridge University Press:  22 May 2023

Cailei Lu ,
Mengqi Zhang Open the ORCID record for Mengqi Zhang [Opens in a new window] ,
Xuerao He ,
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]
Cailei Lu
Affiliation:
School of Energy Science and Engineering, Harbin Institute of Technology, Harbin 150001, PR China Key Laboratory of Aerospace Thermophysics, Harbin Institute of Technology, Harbin 150001, PR China
Mengqi Zhang
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575 Singapore, Republic of Singapore
Xuerao He
Affiliation:
Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575 Singapore, 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 Key Laboratory of Aerospace Thermophysics, Harbin Institute of Technology, Harbin 150001, PR China
*
†Email addresses for correspondence: luokang@hit.edu.cn, yihongliang@hit.edu.cn
†Email addresses for correspondence: luokang@hit.edu.cn, yihongliang@hit.edu.cn
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Abstract

We study the diffusive instability subject to a solid–liquid interface and a Kolmogorov flow using modal, non-modal analyses and energy analysis. It is found that the phase boundary has different effects on the threshold of diffusive convection for weak and strong salinity stratification. In the context of oceanography where the salinity Rayleigh number RS is very high, the ice–water interface has negligible influence on the onset of diffusive convection. In the presence of shear, the diffusive convection for RS < 106 tends to be inhibited and with the increase of shear intensity, the oscillatory, steady convective and Kelvin–Helmholtz instabilities will be successively dominant. For RS > 106, the shear has a destabilizing effect on the diffusive convection, due to the generation of thermohaline-sheared instability found by Radko (J. Fluid Mech., vol. 805, 2016, pp. 147–170). Non-modal analysis indicates that for realistic parameters of high-latitude oceans, with the transition of the ultimate energy source of instability from the density gradient to background current, the thermohaline-shear instability is expected to transition from oscillatory to steady instability. The initial transient amplification due to double diffusion has also been studied, which is due to the generation of overstable instability at the initial phase. For RS < 106, the optimal initial condition to achieve the maximum transient growth favours longitudinal rolls. For thermohaline-shear instability, however, it favours transverse rolls and specifically, in oscillatory thermohaline-shear instability, the transient amplification can be enhanced by the shear by one order of magnitude, thus having important influence on the stability of the system.

JFM classification

Convection: Double diffusive convection Phase change: Solidification/melting
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 963 , 25 May 2023 , A38
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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Footnotes

The online version of this article has been updated since original publication. A notice detailing the change has also been published.

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