In tropical and subtropical ocean gyres, Trichodesmium colonies account for up to half of the total N2 fixation in the ocean, making it one of the most ecologically significant N2-fixing cyanobacteria. The processes whereby Trichodesmium colonies and large-scale surface blooms form have not been investigated thoroughly. In particular, the effects of fluid motion have not been included in previous studies. As the first step toward understanding the mechanical processes associated with Trichodesmium colony synthesis, we propose a shear-related flow-based growth model to enlighten how fluid dynamics affect bacteria colony formation and growth. To investigate the possibility that early growth characteristics are strongly dependent on the shear rate, a two-way coupled fluid-colony interaction is developed using the lattice Boltzmann method for a porous colony. This model captures the exponential growth trend during the colony formation phase found in experiments. Our results show that the flow field significantly impacts both the colony growth rate and shape. In pure shear conditions, colonies grow in circular shapes, whereas in uniform flow, they take filament-like forms. Additionally, the Reynolds number (Re) plays a crucial role in shaping the colonies, especially in uniform flow conditions where its effect is more profound.