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

Using DNS-based Eulerian-Lagrangian simulations, we investigate the dynamics of small gyrotactic swimmers in free-surface turbulence. We consider open channel flow turbulence in which bottom-heavy swimmers are dispersed. Swimmers are characterized by different vertical stability, so that some realign to swim upward with a characteristic time smaller than the Kolmogorov time scale, while others possess a re-orientation time longer than the Kolmogorov time scale. We cover one order of magnitude in the flow Reynolds number, and two orders of magnitude in the stability number, which is a measure of bottom heaviness. We observe that large-scale advection dominates vertical motion when the stability number, scaled on the local Kolmogorov time scale of the flow, is larger than unity: This condition is associated to enhanced migration towards the surface, particularly at low Reynolds number, when swimmers can rise through surface renewal motions that originate directly from the bottom-boundary turbulent bursts. Conversely, small-scale effects become more important when the Kolmogorov-based stability number is below unity: Under this condition, migration towards the surface is hindered, particularly at high Reynolds, when bottom-boundary bursts are less effective in bringing bulk fluid to the surface. In an effort to provide scaling arguments to improve predictions of models for motile micro-organisms in turbulent water bodies, we demonstrate that a Kolmogorov-based stability number around unity represents a threshold beyond which swimmer capability to reach the free surface and form clusters saturates.