Bio‐thermal convection caused by combined effects of swimming of oxytactic bacteria and inclined temperature gradient in a shallow fluid layer

Abstract

PurposeThe aim of this paper is to investigate the onset of bio‐thermal convection in a shallow fluid layer; the convection is thus driven by the combined effect of swimming of oxytactic microorganisms and inclined temperature gradient.Design/methodology/approachLinear stability analysis of the basic state is performed; the numerical problem is solved using the collocation method.FindingsThe most interesting outcome of this analysis is the correlation between three Rayleigh numbers, two traditional, “thermal” Rayleigh numbers, which are associated with the vertical and horizontal temperature gradients in the fluid layer, and the bioconvection Rayleigh number, which is associated with the density variation induced by the upswimming of microorganisms.Research limitations/implicationsFurther research should address the application of weakly nonlinear analysis to this problem.Practical implicationsThe increase of the horizontal thermal Rayleigh number stabilizes the basic flow. The effect of increasing the horizontal thermal Rayleigh number is to distort the basic temperature profile away from the linear one. The increase of the Schmidt number stabilizes the basic flow. The increase of the Prandtl number first causes the bioconvection Rayleigh number to decrease and then to increase.Originality/valueTo the best of the authors’ knowledge, this is the first research dealing with the effect of inclined temperature gradient on the stability of bioconvection.