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Effect of oblique irradiation on the onset of thermal-phototactic-bioconvection in an isotropic scattering algal suspension

S. K. Rajput, M. K. Panda

Abstract

In this study, our focus is mainly to check the effect of light scattering on the onset of thermal-phototactic-bioconvection in an algal suspension where the suspension is illuminated by the collimated oblique irradiation from above while simultaneously applying heating or cooling from below. We conduct a numerical investigation into the linear stability of a suspension containing phototactic algae, focusing particularly on how the angle of incidence of oblique collimated irradiation influences the system. Our solutions reveal a transition of the most unstable mode from a stationary to an overstable state, or vice versa, under certain parameter configurations as the angle of incidence varies. Additionally, we frequently observe oscillatory instabilities in cases where the upper surface is rigid, particularly as the angle of incidence increases within the suspension.

Effect of oblique irradiation on the onset of thermal-phototactic-bioconvection in an isotropic scattering algal suspension

Abstract

In this study, our focus is mainly to check the effect of light scattering on the onset of thermal-phototactic-bioconvection in an algal suspension where the suspension is illuminated by the collimated oblique irradiation from above while simultaneously applying heating or cooling from below. We conduct a numerical investigation into the linear stability of a suspension containing phototactic algae, focusing particularly on how the angle of incidence of oblique collimated irradiation influences the system. Our solutions reveal a transition of the most unstable mode from a stationary to an overstable state, or vice versa, under certain parameter configurations as the angle of incidence varies. Additionally, we frequently observe oscillatory instabilities in cases where the upper surface is rigid, particularly as the angle of incidence increases within the suspension.
Paper Structure (11 sections, 89 equations, 4 figures)

This paper contains 11 sections, 89 equations, 4 figures.

Table of Contents

  1. INTRODUCTION
  2. GEOMETRY OF THE PROBLEM
  3. PHOTOTAXIS IN A SCATTERING SUSPENSION
  4. THE GOVERNING BIOCONVECTIVE SYSTEM
  5. THE EQUILIBRIUM STATE
  6. Linear stability of the problem
  7. SOLUTION PROCEDURE
  8. NUMERICAL RESULTS
  9. WHEN TOP SURFACE IS STRESS FREE
  10. WHEN TOP SURFACE IS RIGID
  11. Conclusion

Figures (4)

  • Figure 1: Formation of the sublayer within the suspension due to oblique collimated irradiation.
  • Figure 2: Oblique collimated irradiation on the upper surface of non-scattering algal suspension.
  • Figure 3: (a) The profiles formed at basic state and (b) the corresponding marginal stability curves as $\theta_i$ is increased.
  • Figure 4: (a) The profiles formed at basic state and (b) the corresponding marginal stability curves as $\theta_i$ is increased.