Efficient survival strategy for zooplankton in turbulence

TL;DR

A simple, robust, and highly efficient strategy, that relies on measuring the sign of gradients of squared strain, is found that has the potential to reconcile competing fitness pressures.

Abstract

Zooplankton in a quiescent environment can detect predators by hydrodynamic sensing, triggering powerful escape responses. Since turbulent strain tends to mask the hydrodynamic signal, the organisms should avoid such regions, but it is not known how they accomplish this. We found a simple, robust, and highly efficient strategy, that relies on measuring the sign of gradients of squared strain. Plankton following this strategy show very strong spatial clustering, and align against the local flow velocity, facilitating mate finding and feeding. The strategy has the potential to reconcile competing fitness pressures.

Figures (6)

• Figure 1: ( a) Snapshot showing five spatial slices with positions of swimmers (green points) following the optimal strategy (\ref{['eq:optimal_policy']}) in the stochastic model (see text). Flow strain ${{\mathcal{S}}^2}$ is color-coded. ( b) Zoom, including flow streamlines and swimmer direction projected onto the image plane. ( c) Steady-state probability distributions of ${{\mathcal{S}}^2}$ evaluated along swimmer trajectories (green) and for tracer particles (black). Parameters $\lambda=2$, $v^{({\rm s})}=20mm\per\s$, $\omega^{({\rm s})}=5rad\per\s$, $\nu=1mm\squared\per\s$ and $\varepsilon=1mm\squared\per\s\cubed$ (${u_{\rm rms}}=10mm\per\s$ and $\tau_{\eta}=1\s$).
• Figure 2: Probability distributions of ( a) ${\hat{\boldsymbol{n}}}^*\cdot{\hat{\boldsymbol{n}}}$ and ( b) $\hat{\boldsymbol{u}}\cdot{\hat{\boldsymbol{n}}}$ for the parameters in Fig. \ref{['fig:positions']}. ( c) Example trajectory (green) with color coded $\hat{\boldsymbol{u}}\cdot{\hat{\boldsymbol{n}}}$ (small markers) for duration $\sqrt{5}\tau_{\eta}$. Large markers denote start (blue), midpoint (pink), and end (orange). The black trajectory shows the location of the only local strain minimum in the displayed region.
• Figure 3: Strain avoidance and counter-current alignment against the turbulent dissipation rate $\varepsilon$. ( a) Average strain $\langle{{\mathcal{S}}^2}\rangle$ in the stochastic model (filled markers) and DNS with ${\rm Re}_\lambda\approx 60$ (empty markers). Solid line shows model results for the simplified dynamics (\ref{['eq:eqm_simplified']}). Horizontal dashed line shows value for tracer particles. Vertical dashed lines show where $v^{({\rm s})}/{u_{\rm rms}}=1$ and ${{\nabla\mathcal{S}}^2_{\rm th}}{u_{\rm rms}}\tau_{\eta}^3=1$. The dimensionless rotational swimming speed is $\omega^{({\rm s})}\tau_{\eta}=2.5v^{({\rm s})}/{u_{\rm rms}}$. ( b) Same as panel ( a), but for the average counter-current alignment, $\langle\hat{\boldsymbol{u}}\cdot{\hat{\boldsymbol{n}}}\rangle$. Parameters $\lambda=2$, $v^{({\rm s})}=20mm\per\s$, $\omega^{({\rm s})}=5rad\per\s$, ${{\nabla\mathcal{S}}^2_{\rm th}}=1\per m\per\s\squared$ and $\nu=1mm\squared\per\s$.
• Figure 4: Strain rate distributions for the optimal strategy (\ref{['eq:optimal_policy']}) (green), the simplified signal $\tilde{\mathcal{S}}$ (blue), the simplified signal with $\omega^{({\rm s})}_{p,{\rm opt}}(t)$ put to zero (magenta), and tracer particles (black) in DNS of homogeneous isotropic turbulence with ( a) ${\rm Re}_\lambda\approx 60$, and ( b) ${\rm Re}_\lambda\approx 418$, and channel flow turbulence with friction Reynolds number ${\rm Re}_\tau=180$ ( c). Parameters as in Fig. \ref{['fig:positions']}( c).
• Figure 5: Distribution of ${{\mathcal{S}}^2}$ in the turbulence model for ( a) different levels of the sensing threshold ${{\nabla\mathcal{S}}^2_{\rm th}}$, ( b) swimming speed $v^{({\rm s})}$, and ( c) angular swimming speed $\omega^{({\rm s})}$. Parameters $\lambda=2$, $\nu=1mm\squared\per\s$ and $\varepsilon=0.64mm\squared\per\s\cubed$. Unless otherwise stated, $v^{({\rm s})}=20mm\per\s$, $\omega^{({\rm s})}=5rad\per\s$, ${{\nabla\mathcal{S}}^2_{\rm th}}=0$.