  The field of active matter explores the behaviors of self propelled agents
out of equilibrium, with active suspensions, such as swimming bacteria in
solutions, serving as impactful models. These systems exhibit spatio-temporal
patterns akin to active turbulence, driven by internal energy injection. While
bacterial turbulence in dense suspensions is well studied, the dynamics in
growing bacterial suspensions are less understood. This work presents a
phenomenological coarse-grained model for growing bacterial suspensions,
incorporating hydrodynamic equations for bacterial density, orientation, and
fluid velocity, with birth and death terms for colony growth. Starting with low
density and random orientations, the model shows the development of local
ordering as bacterial density increases. As density continues to rise, the
model captures four distinct phases; dilute, clustered, turbulent, and trapped
based on structural patterns and dynamics, with the turbulent phase
characterized by spatio-temporal vortex structures, aligning with observations
in dense bacterial suspensions.
