Weakly non-linear analysis of phototaxis-induced bioconvection in an isotropic scattering algal suspension under normal and oblique collimated irradiation
Abstract
We investigate the weakly nonlinear evolution of phototaxis-induced bioconvection in an absorbing and isotropically scattering algal suspension subjected to oblique and normal collimated irradiation. Two hydrodynamic configurations are considered, a rigid lower boundary with either a stress-free or a rigid upper surface. A multiple-scales expansion is carried to third order, and the Fredholm solvability condition yields a Stuart--Landau equation for the amplitude of the critical mode. Oblique irradiation affects the onset threshold in opposite ways in the two configurations. It progressively lowers the critical Rayleigh number beneath a stress-free surface and progressively raises it beneath a rigid surface. Beneath a stress-free surface the onset remains stationary, but the pitchfork bifurcation changes from supercritical to subcritical and becomes strongly subcritical at large incidence angles, where the preferred pattern wavelength also increases markedly. Beneath a rigid surface the critical mode changes from stationary to oscillatory at moderate obliquity, giving a supercritical Hopf bifurcation, and returns to stationary at large obliquity, where the pitchfork bifurcation becomes subcritical.
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BibTeX
@misc{rajput2026weakly,
title = {{Weakly non-linear analysis of phototaxis-induced bioconvection in an isotropic scattering algal suspension under normal and oblique collimated irradiation}},
author = {S. K. Rajput and A. Rathi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03299},
eprint = {2610.03299},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03299},
}
RIS
TY - UNPB
TI - Weakly non-linear analysis of phototaxis-induced bioconvection in an isotropic scattering algal suspension under normal and oblique collimated irradiation
AU - S. K. Rajput
AU - A. Rathi
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03299
UR - https://arxiv.org/abs/2610.03299
AB - We investigate the weakly nonlinear evolution of phototaxis-induced bioconvection in an absorbing and isotropically scattering algal suspension subjected to oblique and normal collimated irradiation. Two hydrodynamic configurations are considered, a rigid lower boundary with either a stress-free or a rigid upper surface. A multiple-scales expansion is carried to third order, and the Fredholm solvability condition yields a Stuart--Landau equation for the amplitude of the critical mode. Oblique irradiation affects the onset threshold in opposite ways in the two configurations. It progressively lowers the critical Rayleigh number beneath a stress-free surface and progressively raises it beneath a rigid surface. Beneath a stress-free surface the onset remains stationary, but the pitchfork bifurcation changes from supercritical to subcritical and becomes strongly subcritical at large incidence angles, where the preferred pattern wavelength also increases markedly. Beneath a rigid surface the critical mode changes from stationary to oscillatory at moderate obliquity, giving a supercritical Hopf bifurcation, and returns to stationary at large obliquity, where the pitchfork bifurcation becomes subcritical.
ER -