Orientation Dynamics of Gyrotactic Microswimmers in Turbulent Flows

We study the dynamics of gyrotactic microswimmers suspended in homogeneous and isotropic turbulence by using direct numerical simulations (DNS). The swimmers are characterized by three non-dimensional parameters: their aspect ratio ($γ$), a dimensionless swimming speed ($φ$), and a dimensionless reorientation time ($ψ$). Strong gyrotaxis (smaller $ψ$) promotes vertical alignment of the swimmers, while weak gyrotaxis leads to nearly isotropic orientations. At low swimming numbers, the orientation distribution is largely shape-independent with spheres and spheroids showing marginally greater vertical alignment than rods, whereas at higher activity the peaks of the distributions exhibit largely shape-independent behavior and the tails show a clear dependence on particle shape. However, at large $ψ$ rods exhibit a stronger alignment along the vertical. We observe that at small $ψ$ the rod-shaped swimmers respond to shear by aligning with the stretching direction of the strain-rate tensor, while at large $ψ$ the alignment with the vorticity vector is preferred. The orientation autocorrelation is found to decay exponentially, with a decay rate that scales as $1/(2ψ)$. Analysis of the mean-squared displacement (MSD) reveals a transition from a ballistic motion at short times to a diffusive regime at longer times. To assess the efficiency of vertical migration, we compute the probability distributions of vertical displacement over a fixed time interval and the time taken to migrate a specific vertical distance. Furthermore, we use a simplified two-dimensional model for spherical swimmers that qualitatively reproduces the key trends observed in the full three-dimensional (3D) simulations.