Numerical study of plume patterns in the chemotaxis-diffusion-convection\n coupling system

Abstract

A chemotaxis-diffusion-convection coupling system for describing a form of\nbuoyant convection in which the fluid develops convection cells and plume\npatterns will be investigated numerically in this study. Based on the\ntwo-dimensional convective chemotaxis-fluid model proposed in the literature,\nwe developed an upwind finite element method to investigate the pattern\nformation and the hydrodynamical stability of the system. The numerical\nsimulations illustrate different predicted physical regimes in the system. In\nthe convective regime, the predicted plumes resemble B\\'enard instabilities.\nOur numerical results show how structured layers of bacteria are formed before\nbacterium rich plumes fall in the fluid. The plumes have a well defined\nspectrum of wavelengths and have an exponential growth rate, yet their position\ncan only be predicted in very simple examples. In the chemotactic and diffusive\nregimes, the effects of chemotaxis are investigated. Our results indicate that\nthe chemotaxis can stabilize the overall system. A time scale analysis has been\nperformed to demonstrate that the critical taxis Rayleigh number for which\ninstabilities set in depends on the chemotaxis head and sensitivity. In\naddition, the comparison of the differential systems of\nchemotaxis-diffusion-convection, double diffusive convection, and\nRayleigh-B\\'enard convection establishes a set of evidences that even if the\nphysical mechanisms are different at the same time the dimensionless systems\nare strongly related to each other.\n