Bioluminescence in turbulence: intermittent straining lights up dinoflagellates

Abstract

Dinoflagellates are marine phytoplankton that emit flashes of light in response to flow-induced deformation; they are responsible for illuminating breaking-waves, wakes of ships, and other intensely turbulent spots of the upper ocean. Here, we ask how bioluminescence is affected by the fluctuating nature of turbulence -- a question motivated by the dependence of emitted flashes on both the extent and rate of deformation. Introducing a light-emitting dumbbell as a minimal model, we study the Lagrangian dynamics of flashing in a homogeneous isotropic turbulent flow, and contrast it with that in an extensional flow and a Gaussian random flow. We show that turbulent fluctuations strongly enhance bioluminescence, while introducing a Poisson-like stochasticity in the flashing dynamics. Furthermore, the intermittent fluctuations of the velocity-gradient subjects the dinoflagellate to bursts of extreme straining and produces bright flashes -- more intense, though less frequent, than what would result from Gaussian fluctuations. Our results suggest that radiant displays of marine bioluminescence are strongly promoted by turbulence and its dissipation-scale intermittency.

Figures (4)

• Figure 1: Illustration of the light-emission model in Eq. \ref{['eq:light']}. (a) Strain profile ${\delta}(t)$, with rate of change of strain $\dot \delta = \tau_s^{-1} \approx 5 \,\tau_h^{-1}$ during deformation and relaxation. (b) Evolution of $s$, $h$, and $I$. (c) Intensity of light $I^*$ obtained by replacing negative values of $I$ with zero (no light emission).
• Figure 2: Comparison of the PDFs of (a) strain-rates experienced by the dumbbell $|\nabla \bm{v} \cdot \hat{\bm{R}}|\lambda^{-1}$ (where $\hat{\bm R} = \bm R/R$), (b) dumbbell extension $R$, and (c) rate of change of strain $\dot \delta = \dot {R}/R_{eq}$, in the turbulent DNS and in the Gaussian gradient (GG) model. Here $\mathrm{Wi} = 0.3$; analogous results are obtained for $\mathrm{Wi} = 1.0$supplement.
• Figure 3: Evolution of (a) the magnitude of the strain-rate experienced by the dumbbell $|\nabla \bm{v} \cdot \hat{\bm R}|$ (where $\hat{\bm R} = {\bm R}/R$), (b) the end-to-end extension $R$, and (c) the light intensity $I^*$ (for $\mathrm{Wi}_L = 0.5$ and $2.0$), in the turbulent flow. These repeated flashes may be contrasted with the single, much weaker, flash in an extension flow (see Fig S1 in the SM supplement). Here $\mathrm{Wi} = 0.3$.
• Figure 4: (a) Variation of the mean light intensity $\langle I^* \rangle$ with $\mathrm{Wi}_L$, in the turbulent DNS and the Gaussian-gradient (GG) flow. (b) PDF of the light intensity $I^\star$, for $\mathrm{Wi}_L = 0.5$ and $2.0$, in the two fluctuating flows. (c) Variation of the mean waiting-time between flashes $\langle t_f\rangle$ with $\mathrm{Wi}_L$. Here, $\mathrm{Wi} = 0.3$; analogous results are obtained for $\mathrm{Wi} = 1.0$supplement.