<p>A linear stability analysis of oxytactic bioconvection in a fluid-saturated porous medium subjected to thermal gradients and high-frequency, low-amplitude vertical vibrations is presented. A time-averaging approach is employed to derive effective governing equations that describe the system’s averaged dynamics. The main novelty of this work is the developmenst of a unified analytical framework for vibrated oxytactic bioconvection in porous media, enabling a systematic description of vibration-modified stability characteristics. The governing equations are analyzed using the Galerkin method to derive the secular equation for the critical thermal Rayleigh number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$R_a$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mi>a</mi> </msub> </math></EquationSource> </InlineEquation> in terms of the bioconvection Rayleigh–Darcy number <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$R_b$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mi>b</mi> </msub> </math></EquationSource> </InlineEquation>, vibrational Rayleigh–Darcy number <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$R_v$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mi>v</mi> </msub> </math></EquationSource> </InlineEquation>, thermovibrational parameter <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$R_t$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mi>t</mi> </msub> </math></EquationSource> </InlineEquation>, microorganism-to-oxygen diffusivity ratio <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\delta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>δ</mi> </math></EquationSource> </InlineEquation>, depth parameter <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$\widehat{\omega } = P_e\beta _1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mi>ω</mi> <mo stretchy="true">^</mo> </mover> <mo>=</mo> <msub> <mi>P</mi> <mi>e</mi> </msub> <msub> <mi>β</mi> <mn>1</mn> </msub> </mrow> </math></EquationSource> </InlineEquation>, and vibrational parameter <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\eta $</EquationSource> <EquationSource Format="MATHML"><math> <mi>η</mi> </math></EquationSource> </InlineEquation>. The results indicate that thermal gradients destabilize the system and promote the onset of bioconvection, whereas vertical vibrations significantly modify the evolution of convective instability. Both the thermovibrational parameter and the vibrational modulation parameter exert a destabilizing influence on the system. Moreover, the depth parameter significantly affects pattern selection, with more considerable depths favoring shorter-wavelength convective modes. These findings underscore the intricate coupling between thermal, vibrational, and bioconvective agencies in porous microbial systems and offer valuable insight into the control of instability onset and convective pattern formation.</p>

Impact of thermal vibrations on oxytactic bioconvection in a porous medium

期刊论文
发表日期：

2026年7月27日

查看全文

K. Srikanth,
Virendra Kumar

摘要

A linear stability analysis of oxytactic bioconvection in a fluid-saturated porous medium subjected to thermal gradients and high-frequency, low-amplitude vertical vibrations is presented. A time-averaging approach is employed to derive effective governing equations that describe the system’s averaged dynamics. The main novelty of this work is the developmenst of a unified analytical framework for vibrated oxytactic bioconvection in porous media, enabling a systematic description of vibration-modified stability characteristics. The governing equations are analyzed using the Galerkin method to derive the secular equation for the critical thermal Rayleigh number $R_a$ $R_{a}$ in terms of the bioconvection Rayleigh–Darcy number $R_b$ $R_{b}$ , vibrational Rayleigh–Darcy number $R_v$ $R_{v}$ , thermovibrational parameter $R_t$ $R_{t}$ , microorganism-to-oxygen diffusivity ratio $\delta $ $δ$ , depth parameter $\widehat{\omega } = P_e\beta _1$ $\hat{ω} = P_{e} β_{1}$ , and vibrational parameter $\eta $ $η$ . The results indicate that thermal gradients destabilize the system and promote the onset of bioconvection, whereas vertical vibrations significantly modify the evolution of convective instability. Both the thermovibrational parameter and the vibrational modulation parameter exert a destabilizing influence on the system. Moreover, the depth parameter significantly affects pattern selection, with more considerable depths favoring shorter-wavelength convective modes. These findings underscore the intricate coupling between thermal, vibrational, and bioconvective agencies in porous microbial systems and offer valuable insight into the control of instability onset and convective pattern formation.