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Effect of density maximum of water on the stability of gravitactic convective motions in biothermal convection

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Abstract

Microorganisms inhabit various natural environments and thrive in diverse ecosystems, including freshwater and marine bodies. Many of these microorganisms can swim and have a higher density than water, generating a vertical stratification of cell concentration that may lead to instability due to the buoyancy force. Biothermal convection refers to the convective motion that arises due to the combined effect of up-swimming microorganism and thermal gradients in a fluid medium. In the present work we investigate the onset of biothermal convection in a horizontal layer of cold water in the presence of the density inversion. This previously unexplored issue holds significance due to its potential applications in both natural and industrial contexts. We applied linear stability analysis to determine the critical thresholds at which instability initiates. To confirm these stability findings, we conducted numerical simulations using the finite volume method and compared them with the available experimental results in the case of penetrative convection. The critical threshold is shown to depend essentially upon the value of the density inversion parameter and the thermal Rayleigh number. Additionally, the linear stability analysis suggests the possible occurrence of Hopf bifurcations at the onset of motion.

Article Highlights

  • Biothermal convection stability depends on both the thermal Rayleigh number and the density inversion parameter.

  • The temperature stratification can either stabilize or destabilize, depending on the density inversion parameter.

  • An increase in the thermal Rayleigh number can introduces wave number transitions.

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The data that support the findings of this study are available on request from the corresponding author.

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Funding

No funding was received for conducting this study.

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Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Applied Sciences, University of Kasdi Merbah Ouargla, 30000, Ouargla, Algeria

    Imane Alloui

  2. LESEI Laboratory, Mechanical Engineering Department, University of Batna 2, Batna, Algeria

    Riadh Ouzani

  3. Engineering Department, Faculty of Agriculture, Dalhousie University, Truro, Canada

    Tri Nguyen-Quang

  4. LICEGS Laboratory, Mechanical Engineering Department, University of Batna 2, Batna, Algeria

    Zineddine Alloui

Authors
  1. Imane Alloui
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  2. Riadh Ouzani
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  3. Tri Nguyen-Quang
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  4. Zineddine Alloui
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Contributions

Study conception and design: I.A. and R.O. Stability analysis and numerical simulations: I.A., R.O. and Z.A. Analysis and interpretation of results: I.A., R.O.,T.N.G. and Z.A. Revision of the manuscript: I.A., R.O.,T.N.G. and Z.A.

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Correspondence to Zineddine Alloui.

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Alloui, I., Ouzani, R., Nguyen-Quang, T. et al. Effect of density maximum of water on the stability of gravitactic convective motions in biothermal convection. Environ Fluid Mech (2024). https://doi.org/10.1007/s10652-024-09981-1

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