THERMOTAXIS PATTERN IN FLUID MEDIum
Taxis is a natural response that a living organism has towards stimuli such as gravity (gravitaxis), light (phototaxis), or chemical substances (chemotaxis), etc. Thermotaxis is the motion of a microorganism towards or away from a thermal stimulus, which generates a thermotactic pattern in nature. Examples include the motion of Dictyostelium slugs , the thermoregulation of honeybees, the behavior of roundworms (specifically Caenorhabditis elegans ), the behavior of human and animal sperm, and how colloidal particles act. Multiple mathematical models were suggested to deal with thermotaxis. The main goal of this paper is to predict the onset of thermotactic convection in fluid medium by using the linear stability analysis. Biological systems are known as the most common systems, where thermotactic patterns generated by living organisms could happen. This category of taxis takes place in a variety of directional motion of microorganisms, having the common sense of motion under the gradient-stimuli and can be generalized mathematically under the form of gradient-based taxis. The results from linear stability analysis show that the thermotactic convection is analogous to the classical thermal convection created by a constant temperature, when the Peclet number is small, and there exists an important overstability condition, when the microorganism cell diffusivity is greater than the thermal diffusivity. The promising future study from this analysis will rely on the application to the harmful algal blossoming.