June 2025 – Present · with Alexander Morozov
Modelling Bacterial Turbulence with Finite Tumbling
In this work, we investigate how introducing a finite tumbling duration into models of bacterial swimmers affects the onset of hydrodynamic instabilities, as revealed through changes in the system’s dispersion relations. We treat the population as consisting of runners and tumblers, with stochastic switching between the two states at prescribed rates. This leads to a coupled pair of Smoluchowski equations for the distribution functions of each population, incorporating both translational and rotational dynamics.
Unlike the instantaneous reorientation assumed in classic run-and-tumble models, tumblers here undergo active reorientation at a finite angular velocity, while also experiencing the same hydrodynamic couplings as runners. We identify the uniform, isotropic steady state of the system and perform a linear stability analysis about this base state. By projecting perturbations onto monopole, dipole, and quadrupole spherical harmonics, the governing equations reduce to a tractable eigenvalue problem.
This formulation allows us to quantify how finite tumbling modifies the critical parameters for instability onset, alters the growth rates of unstable modes, and changes the relative contributions of hydrodynamic and reorientation mechanisms. The results provide a systematic route to connect microscopic swimmer dynamics with emergent large-scale flow patterns in active suspensions.