Numerical study of plume patterns in a chemotaxis–diffusion–convection coupling system

Abstract A chemotaxis–diffusion– convectioncoupling system for describing a form of buoyant convectionin which the fluid develops convection cellsand plumepatterns will be investigated numerically in this study. Based on the two-dimensional convective chemotaxis-fluid model proposed in the literature, we developed an upwind finite element method to investigate the pattern formationand the hydrodynamical stabilityof the system. The numerical simulations illustrate different predicted physical regimes in the system. In the convectiveregime, the predicted plumesresemble Benard instabilities. Our numerical results show how structured layers of bacteria are formed before bacterium rich plumesfall in the fluid. The plumeshave a well defined spectrum of wavelengths and have an exponential growth rate, yet their positions can only be predicted in very simple examples. In the chemotactic and diffusive regimes, the effects of chemotaxisare investigated. Our results indicate that the chemotaxiscan stabilize the overall system. A time scale analysis has been performed to demonstrate that the critical taxis Rayleigh numberfor which instabilities set in depends on the chemotaxishead and sensitivity. In addition, the comparison of the differential systems of chemotaxis–diffusion– convection, double diffusive convection, and Rayleigh–Benard convectionestablishes a set of evidences that even if the physical mechanisms are different at the same time the PDE systems share similarities.