Motility and phototaxis of Gonium, the simplest differentiated colonial alga.

Green algae of the Volvocine lineage, spanning from unicellular Chlamydomonas to vastly larger Volvox, are models for the study of the evolution of multicellularity, flagellar dynamics, and developmental processes. Phototactic steering in these organisms occurs without a central nervous system, driven solely by the response of individual cells. All such algae spin about a body-fixed axis as they swim; directional photosensors on each cell thus receive periodic signals when that axis is not aligned with the light. The flagella of Chlamydomonas and Volvox both exhibit an adaptive response to such signals in a manner that allows for accurate phototaxis, but in the former the two flagella have distinct responses, while the thousands of flagella on the surface of spherical Volvox colonies have essentially identical behavior. The planar 16-cell species Gonium pectorale thus presents a conundrum, for its central 4 cells have a Chlamydomonas-like beat that provide propulsion normal to the plane, while its 12 peripheral cells generate rotation around the normal through a Volvox-like beat. Here we combine experiment, theory, and computations to reveal how Gonium, perhaps the simplest differentiated colonial organism, achieves phototaxis. High-resolution cell tracking, particle image velocimetry of flagellar driven flows, and high-speed imaging of flagella on micropipette-held colonies show how, in the context of a recently introduced model for Chlamydomonas phototaxis, an adaptive response of the peripheral cells alone leads to photoreorientation of the entire colony. The analysis also highlights the importance of local variations in flagellar beat dynamics within a given colony, which can lead to enhanced reorientation dynamics.

Disentangling inertial waves from eddy turbulence in a forced rotating-turbulence experiment.

We present a spatiotemporal analysis of a statistically stationary rotating-turbulence experiment, aiming to extract a signature of inertial waves and to determine the scales and frequencies at which they can be detected. The analysis uses two-point spatial correlations of the temporal Fourier transform of velocity fields obtained from time-resolved stereoscopic particle image velocimetry measurements in the rotating frame. We quantify the degree of anisotropy of turbulence as a function of frequency and spatial scale. We show that this space-time-dependent anisotropy is well described by the dispersion relation of linear inertial waves at large scale, while smaller scales are dominated by the sweeping of the waves by fluid motion at larger scales. This sweeping effect is mostly due to the low-frequency quasi-two-dimensional component of the turbulent flow, a prominent feature of our experiment that is not accounted for by wave-turbulence theory. These results question the relevance of this theory for rotating turbulence at the moderate Rossby numbers accessible in laboratory experiments, which are relevant to most geophysical and astrophysical flows.

Mach-like capillary-gravity wakes.

We determine experimentally the angle α of maximum wave amplitude in the far-field wake behind a vertical surface-piercing cylinder translated at constant velocity U for Bond numbers Bo(D)=D/λ(c) ranging between 0.1 and 4.2, where D is the cylinder diameter and λ(c) the capillary length. In all cases the wake angle is found to follow a Mach-like law at large velocity, α∼U(-1), but with different prefactors depending on the value of Bo(D). For small Bo(D) (large capillary effects), the wake angle approximately follows the law α≃c(g,min)/U, where c(g,min) is the minimum group velocity of capillary-gravity waves. For larger Bo(D) (weak capillary effects), we recover a law α∼√[gD]/U similar to that found for ship wakes at large velocity [Rabaud and Moisy, Phys. Rev. Lett. 110, 214503 (2013)]. Using the general property of dispersive waves that the characteristic wavelength of the wave packet emitted by a disturbance is of order of the disturbance size, we propose a simple model that describes the transition between these two Mach-like regimes as the Bond number is varied. We show that the new capillary law α≃c(g,min)/U originates from the presence of a capillary cusp angle (distinct from the usual gravity cusp angle), along which the energy radiated by the disturbance accumulates for Bond numbers of order of unity. This model, complemented by numerical simulations of the surface elevation induced by a moving Gaussian pressure disturbance, is in qualitative agreement with experimental measurements.

Ship wakes: Kelvin or Mach angle?

From the analysis of a set of airborne images of ship wakes, we show that the wake angles decrease as U(-1) at large velocities, in a way similar to the Mach cone for supersonic airplanes. This previously unnoticed Mach-like regime is in contradiction with the celebrated Kelvin prediction of a constant angle of 19.47° independent of the ship's speed. We propose here a model, confirmed by numerical simulations, in which the finite size of the disturbance explains this transition between the Kelvin and Mach regimes at a Froude number Fr=U/√[gL]~/=0.5, where L is the hull ship length.

Laminar-turbulent cycles in inclined lock-exchange flows.

We consider strongly confined, stably stratified shear flows generated as a lock exchange in a tube inclined at an angle of θ=45(∘). This paper focuses on a transitional regime, in which the flow alternates between two distinct states: laminar, parallel shear flow and intense transverse motion characteristic of turbulence. Laminar-turbulent cycles were captured at Atwood numbers At≡(ρ(2)-ρ(1))/(ρ(1)+ρ(2)) ranging from 2.45×10(-3) to 4.0×10(-3), where (ρ(1),ρ(2)) are the initial densities of the two fluids, with multiple cycles observed at At=2.55×10(-3). The evolution of the density and velocity fields in these flows was measured simultaneously using laser-induced fluorescence and particle image velocimetry. During each laminar-turbulent cycle, the axial velocity exhibits a distinctive ramp-cliff pattern, indicating that the flow accelerates as it relaminarizes, then decelerates rapidly as the Kelvin-Helmholtz billows break down. Within the range of experimental conditions, transverse stratification does not directly determine the onset of instability. Instead, the data suggest that a necessary criterion for the onset of instability is for the local Reynolds number to exceed 2200, with only a weak dependence on the Richardson number.

Direct measurements of anisotropic energy transfers in a rotating turbulence experiment.

We investigate experimentally the influence of a background rotation on the energy transfers in decaying grid turbulence. The anisotropic energy flux density F(r) = <δu(δu)²>, where δu is the vector velocity increment over separation r, is determined for the first time by using particle image velocimetry. We show that rotation induces an anisotropy of the energy flux ∇·F, which leads to an anisotropy growth of the energy distribution E(r) = <(δu)²>, in agreement with the von Kármán-Howarth-Monin equation. Surprisingly, our results prove that this anisotropy growth is essentially driven by a nearly radial, but orientation-dependent, energy flux density F(r).