发表机构
Indian Institute of Technology Bombay（印度理工学院孟买分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过弱非线性稳定性分析，探讨热浮力对光趋性生物对流的影响，发现热瑞利数接近临界值时对流由光趋性主导转为热驱动，并预测了超临界分岔行为。
AI 中文摘要
本文进行了弱非线性稳定性分析，以研究热浮力对水平边界之间受限的游动微生物悬浮液中光趋性生物对流的影响，并施加底部加热或冷却。目标是考察热强迫如何通过其对分岔行为和有限振幅对流的影响来改变生物对流不稳定性的临界后演化。首先采用线性稳定性理论来确定对流起始的临界条件。然后数值求解相应的直接和伴随特征值问题，以及二阶预解系统，以推导控制扰动非线性演化的Stuart-Landau振幅方程。针对不同的热瑞利数进行了系统分析。结果表明，随着热瑞利数接近经典的瑞利-贝纳德临界值，临界生物对流瑞利数降至零，表明从光趋性主导的对流逐渐过渡到热驱动对流。计算得到的正朗道系数分别预测了静止和振荡不稳定性的超临界叉形分岔和Hopf分岔。在振荡起始的参数区域中，增加热瑞利数驱动了从超临界Hopf分岔到超临界叉形分岔的转变。非线性动力学进一步通过振幅演化、相图、势函数和有限振幅流动结构来表征。
英文摘要
A weakly nonlinear stability analysis is performed to investigate the influence of thermal buoyancy on phototactic bioconvection in a suspension of swimming microorganisms confined between horizontal boundaries and subjected to bottom heating or cooling. The objective is to examine how thermal forcing modifies the post-critical evolution of bioconvective instability through its influence on bifurcation behaviour and finite-amplitude convection. Linear stability theory is first employed to determine the critical conditions for the onset of convection. The corresponding direct and adjoint eigenvalue problems, together with the second-order resolvent system, are then solved numerically to derive the Stuart-Landau amplitude equation governing the nonlinear evolution of disturbances. A systematic analysis is carried out for varying thermal Rayleigh numbers. The results show that, as the thermal Rayleigh number approaches the classical Rayleigh-Benard critical value, the critical bioconvection Rayleigh number decreases to zero, indicating a gradual transition from phototaxis-dominated to thermally driven convection. The computed positive Landau coefficient predicts supercritical pitchfork and Hopf bifurcations for stationary and oscillatory instabilities, respectively. In parameter regimes with oscillatory onset, increasing the thermal Rayleigh number drives a transition from a supercritical Hopf bifurcation to a supercritical pitchfork bifurcation. The nonlinear dynamics are further characterized through amplitude evolution, phase portraits, potential functions, and finite-amplitude flow structures.
