Role of large-scale advection and small-scale turbulence on the vertical migration of gyrotactic swimmers

We use DNS-based Eulerian-Lagrangian simulations to investigate the dynamics of small gyrotactic swimmers in free-surface turbulence. Swimmers are characterized by different vertical stability: some realign with a characteristic time smaller than the Kolmogorov time scale, $\tau_K$, while others possess a re-orientation time longer than $\tau_K$. We cover one order of magnitude in the flow Reynolds number, and two orders of magnitude in the stability number, which measures bottom heaviness. We observe that large-scale advection dominates vertical motion when the stability number, scaled on the local Kolmogorov time scale, is above unity: This leads to enhanced migration towards the surface, particularly at low Reynolds number, when swimmers can rise through surface renewal motions that originate from the bottom-boundary turbulent bursts. Small-scale effects become important when the Kolmogorov-based stability number is below unity: Migration towards the surface is hindered, particularly at high Reynolds, when bottom-boundary bursts are less effective in bringing bulk fluid to the surface. We demonstrate that a Kolmogorov-based stability number around unity represents a threshold beyond which swimmer capability to reach the surface and form clusters saturates.