The onset of bio‐thermal convection in a suspension of gyrotactic microorganisms in a fluid layer with an inclined temperature gradient

Abstract

Purpose

The purpose of this paper is to investigate a combined bioconvection and thermal instability problem in a horizontal layer of finite depth with a basic temperature gradient inclined to the vertical. The basic flow, driven by the horizontal component of temperature gradient, is the Hadley circulation, which becomes unstable when the vertical temperature difference and density stratification induced by upswimming of microorganisms that are heavier than water become sufficiently large.

Design/methodology/approach

Linear stability analysis of the basic state is performed; the numerical problem is solved using the collocation method.

Findings

The steady‐state solution of this problem is obtained. Linear stability analysis of this steady‐state solution for the case of three‐dimensional disturbances is performed; the numerical problem is solved using the collocation method. The stability problem is governed by three Rayleigh numbers: the bioconvection Rayleigh number and two thermal Rayleigh numbers characterizing temperature gradients in the vertical and horizontal directions, respectively.

Research limitations/implications

Further research should address the application of weakly non‐linear analysis to this problem.

Practical implications

The dependence of the critical bioconvection Rayleigh number on the two thermal Rayleigh numbers and other relevant parameters is investigated.

Originality/value

This paper presents what is believed to be the first research dealing with the effect of inclined temperature gradient on the stability of bioconvection in a suspension of gyrotactic microorganisms.

Citation

Avramenko, A.A. and Kuznetsov, A.V. (2010), "The onset of bio‐thermal convection in a suspension of gyrotactic microorganisms in a fluid layer with an inclined temperature gradient", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 20 No. 1, pp. 111-129. https://doi.org/10.1108/09615531011008154