Rotations and accumulation of ellipsoidal microswimmers in isotropic turbulence

2018 ◽  
Vol 838 ◽  
pp. 356-368 ◽  
Author(s):  
N. Pujara ◽  
M. A. R. Koehl ◽  
E. A. Variano
Keyword(s):  
Isotropic Turbulence ◽  
Swimming Velocity ◽  
Triaxial Ellipsoid ◽  
Local Flow ◽  
Equal Distribution ◽  
Ellipsoidal Particles ◽  
Velocity Gradients ◽  
Lower Fluid ◽  
Micro Organisms ◽  
Particle Shapes

Aquatic micro-organisms and artificial microswimmers locomoting in turbulent flow encounter velocity gradients that rotate them, thereby changing their swimming direction and possibly providing cues about the local flow environment. Using numerical simulations of ellipsoidal particles in isotropic turbulence, we investigate the effects of body shape and swimming velocity on particle motion. Four particle shapes (sphere, rod, disc and triaxial ellipsoid) are investigated at five different swimming velocities in the range $0\leqslant V_{s}\leqslant 5u_{\unicode[STIX]{x1D702}}$, where $V_{s}$ is the swimming velocity and $u_{\unicode[STIX]{x1D702}}$ is the Kolmogorov velocity scale. We find that anisotropic, swimming particles preferentially sample regions of lower fluid vorticity than passive particles do, and hence they accumulate in these regions. While this effect is monotonic with swimming velocity, the particle enstrophy (variance of particle angular velocity) varies non-monotonically with swimming velocity. In contrast to passive particles, the particle enstrophy is a function of shape for swimming particles. The particle enstrophy is largest for triaxial ellipsoids swimming at a velocity smaller than $u_{\unicode[STIX]{x1D702}}$. We also observe that the average alignment of particles with the directions of the velocity gradient tensor are altered by swimming leading to a more equal distribution of rotation about different particle axes.

On the time scales and structure of Lagrangian intermittency in homogeneous isotropic turbulence

2019 ◽  
Vol 867 ◽  
pp. 438-481 ◽  
Author(s):  
R. Watteaux ◽  
G. Sardina ◽  
L. Brandt ◽  
D. Iudicone
Keyword(s):  
Time Scales ◽  
Isotropic Turbulence ◽  
Flow Characteristics ◽  
Residence Times ◽  
Particle Trajectories ◽  
Local Flow ◽  
Available Energy ◽  
Homogeneous And Isotropic Turbulence ◽  
History Of ◽  
Optimum Manner

We present a study of Lagrangian intermittency and its characteristic time scales. Using the concepts of flying and diving residence times above and below a given threshold in the magnitude of turbulence quantities, we infer the time spectra of the Lagrangian temporal fluctuations of dissipation, acceleration and enstrophy by means of a direct numerical simulation in homogeneous and isotropic turbulence. We then relate these time scales, first, to the presence of extreme events in turbulence and, second, to the local flow characteristics. Analyses confirm the existence in turbulent quantities of holes mirroring bursts, both of which are at the core of what constitutes Lagrangian intermittency. It is shown that holes are associated with quiescent laminar regions of the flow. Moreover, Lagrangian holes occur over few Kolmogorov time scales while Lagrangian bursts happen over longer periods scaling with the global decorrelation time scale, hence showing that loss of the history of the turbulence quantities along particle trajectories in turbulence is not continuous. Such a characteristic partially explains why current Lagrangian stochastic models fail at reproducing our results. More generally, the Lagrangian dataset of residence times shown here represents another manner for qualifying the accuracy of models. We also deliver a theoretical approximation of mean residence times, which highlights the importance of the correlation between turbulence quantities and their time derivatives in setting temporal statistics. Finally, whether in a hole or a burst, the straining structure along particle trajectories always evolves self-similarly (in a statistical sense) from shearless two-dimensional to shear bi-axial configurations. We speculate that this latter configuration represents the optimum manner to dissipate locally the available energy.

scholarly journals A neutrally stable shell in a Stokes flow: a rotational Taylor's sheet

2019 ◽  
Vol 475 (2227) ◽  
pp. 20190178 ◽  
Author(s):  
G. Corsi ◽  
A. De Simone ◽  
C. Maurini ◽  
S. Vidoli
Keyword(s):  
Viscous Fluid ◽  
Phase Speed ◽  
Travelling Wave ◽  
Viscous Fluids ◽  
Swimming Velocity ◽  
Active Materials ◽  
Seminal Paper ◽  
Transversal Displacement ◽  
Stable Equilibria ◽  
Micro Organisms

In a seminal paper published in 1951, Taylor studied the interactions between a viscous fluid and an immersed flat sheet which is subjected to a travelling wave of transversal displacement. The net reaction of the fluid over the sheet turned out to be a force in the direction of the wave phase-speed. This effect is a key mechanism for the swimming of micro-organisms in viscous fluids. Here, we study the interaction between a viscous fluid and a special class of nonlinear morphing shells. We consider pre-stressed shells showing a one-dimensional set of neutrally stable equilibria with almost cylindrical configurations. Their shape can be effectively controlled through embedded active materials, generating a large-amplitude shape-wave associated with precession of the axis of maximal curvature. We show that this shape-wave constitutes the rotational analogue of a Taylor's sheet, where the translational swimming velocity is replaced by an angular velocity. Despite the net force acting on the shell vanishes, the resultant torque does not. A similar mechanism can be used to manoeuver in viscous fluids.

scholarly journals Swimming mediated by ciliary beating: comparison with a squirmer model

2019 ◽  
Vol 874 ◽  
pp. 774-796 ◽  
Author(s):  
Hiroaki Ito ◽  
Toshihiro Omori ◽  
Takuji Ishikawa
Keyword(s):  
Cell Body ◽  
Hydrodynamic Interactions ◽  
Swimming Velocity ◽  
Energy Costs ◽  
Theoretical Studies ◽  
Free Swimming ◽  
Ciliary Beating ◽  
Aspect Ratios ◽  
Swimming Efficiency ◽  
Micro Organisms

The squirmer model of Lighthill and Blake has been widely used to analyse swimming ciliates. However, real ciliates are covered by hair-like organelles, called cilia; the differences between the squirmer model and real ciliates remain unclear. Here, we developed a ciliate model incorporating the distinct ciliary apparatus, and analysed motion using a boundary element–slender-body coupling method. This methodology allows us to accurately calculate hydrodynamic interactions between cilia and the cell body under free-swimming conditions. Results showed that an antiplectic metachronal wave was optimal in the swimming speed with various cell-body aspect ratios, which is consistent with former theoretical studies. Exploiting oblique wave propagation, we reproduced a helical trajectory, like Paramecium, although the cell body was spherical. We confirmed that the swimming velocity of model ciliates was well represented by the squirmer model. However, squirmer modelling outside the envelope failed to estimate the energy costs of swimming; over 90 % of energy was dissipated inside the ciliary envelope. The optimal swimming efficiency was given by the antiplectic wave; the value was 6.7 times larger than in-phase beating. Our findings provide a fundamental basis for modelling swimming micro-organisms.

Algebraic probability density tails in decaying isotropic two-dimensional turbulence

1996 ◽  
Vol 313 ◽  
pp. 223-240 ◽  
Author(s):  
Javier Jiménez
Keyword(s):  
Isotropic Turbulence ◽  
Cauchy Distribution ◽  
Two Dimensional ◽  
Scaling Properties ◽  
Velocity Gradients ◽  
Random Arrangement ◽  
Coherent Vortices ◽  
Statistical Argument ◽  
Decaying Turbulence ◽  
The One

The p.d.f. of the velocity gradients in two-dimensional decaying isotropic turbulence is shown to approach a Cauchy distribution, with algebraic s−2 tails, as the flow becomes dominated by a large number of compact coherent vortices. The statistical argument is independent of the vortex structure, and depends only on general scaling properties. The same argument predicts a Gaussian p.d.f. for the velocity components. The convergence to these limits as a function of the number of vortices is analysed. It is found to be fast in the former case, but slow (logarithmic) in the latter, resulting in residual u−3 tails in all practical cases. The influence of a spread Gaussian vorticity distribution in the cores is estimated, and the relevant dimensionless parameter is identified as the area fraction covered by the cores. A comparison is made with the result of numerical simulations of two-dimensional decaying turbulence. The agreement of the p.d.f.s is excellent in the case of the gradients, and adequate in the case of the velocities. In the latter case the ratio between energy and enstrophy is computed, and agrees with the simulations. All the one-point statistics considered in this paper are consistent with a random arrangement of the vortex cores, with no evidence of energy screening.

Distribution of gyrotactic micro-organisms in complex three-dimensional flows. Part 1. Horizontal shear flow past a vertical circular cylinder

2018 ◽  
Vol 852 ◽  
pp. 358-397 ◽  
Author(s):  
L. Zeng ◽  
T. J. Pedley
Keyword(s):  
Circular Cylinder ◽  
Shear Flow ◽  
Vortex Shedding ◽  
Water Surface ◽  
Concentration Distribution ◽  
Three Dimensional ◽  
Swimming Velocity ◽  
Horizontal Shear ◽  
Active Particles ◽  
Micro Organisms

As a first step towards understanding the distribution of swimming micro-organisms in flowing shallow water containing vegetation, we formulate a continuum model for dilute suspensions in horizontal shear flow, with a maximum Reynolds number of 100, past a single, rigid, vertical, circular cylinder that extends from a flat horizontal bed and penetrates the free water surface. A numerical platform was developed to solve this problem, in four stages: first, a scheme for computation of the flow field; second, a solver for the Fokker–Planck equation governing the probability distribution of the swimming direction of gyrotactic cells under the combined action of gravity, ambient vorticity and rotational diffusion; third, the construction of a database for the mean swimming velocity and the translational diffusivity tensor as functions of the three vorticity components, using parameters appropriate for the swimming alga, Chlamydomonas nivalis; fourth, a solver for the three-dimensional concentration distribution of the gyrotactic micro-organisms. Upstream of the cylinder, the cells are confined to a vertical strip of width equal to the cylinder diameter, which enables us to visualise mixing in the wake. The flow downstream of the cylinder is divided into three zones: parallel vortex shedding in the top zone near the water surface, oblique vortex shedding in the middle zone and quasi-steady flow in the bottom zone. Secondary (vertical) flow occurs just upstream and downstream of the cylinder. Frequency spectra of the velocity components in the wake of the cylinder show two dominant frequencies of vortex shedding, in the parallel- and oblique-shedding zones respectively, together with a low frequency, equal to the difference between those two frequencies, that corresponds to a beating modulation. The concentration distribution is calculated for both active particles and passive, non-swimming, particles for comparison. The concentration distribution is very similar for both active and passive particles, except near the top surface, where upswimming causes the concentration of active particles to reach values greater than in the upstream strip, and in a thin boundary layer on the downstream surface of the cylinder, where a high concentration of active particles occurs as a result of radial swimming.

The spatial distribution of gyrotactic swimming micro-organisms in laminar flow fields

2011 ◽  
Vol 680 ◽  
pp. 602-635 ◽  
Author(s):  
R. N. BEARON ◽  
A. L. HAZEL ◽  
G. J. THORN
Keyword(s):  
Random Walk ◽  
Diffusion Model ◽  
Diffusion Models ◽  
Random Walk Model ◽  
Two Dimensional ◽  
Local Flow ◽  
Spatial And Temporal Scales ◽  
Advection Diffusion ◽  
Micro Organisms ◽  
Good Agreement

We compare the results of two-dimensional, biased random walk models of individual swimming micro-organisms with advection–diffusion models for the whole population. In particular, we consider the influence of the local flow environment (gyrotaxis) on the resulting motion. In unidirectional flows, the results of the individual and population models are generally in good agreement, even in flows in which the cells can experience a range of shear environments, and both models successfully predict the phenomena of gravitactic focusing. Numerical results are also compared with asymptotic expressions for weak and strong shear. Discrepancies between the models arise in two cases: (i) when reflective boundary conditions change the orientation distribution in the random walk model from that predicted by the long-term asymptotics used to derive the advection–diffusion model; (ii) when the spatial and temporal scales are not large enough for the advection–diffusion model to apply. We also use a simple two-dimensional flow containing a variety of flow regimes to explore what happens when there are localized regions in which the generalized Taylor dispersion theory used in the derivation of the population model does not apply. For spherical cells, we find good agreement between the models outside the ‘break-down’ regions, but comparison of the results within these regions is complicated by the presence of nearby boundaries and their influence on the random walk model. In contrast, for rod-shaped cells which are reorientated by both vorticity and strain, we see qualitatively different spatial patterns between individual and advection–diffusion models even in the absence of gyrotaxis, because cells are advected between regions of differing rates of strain.

Influence of flow topology and dilatation on scalar mixing in compressible turbulence

2016 ◽  
Vol 793 ◽  
pp. 633-655 ◽  
Author(s):  
Mohammad Danish ◽  
Sawan Suman ◽  
Sharath S. Girimaji
Keyword(s):  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Compressible Turbulence ◽  
Scalar Dissipation ◽  
Stable Node ◽  
Scalar Mixing ◽  
Flow Topology ◽  
Local Flow ◽  
Amplification Mechanism ◽  
Almost All

The kinematics of passive scalar mixing and its relation to local flow topology and dilatation in compressible turbulence are examined using direct numerical simulations (DNS) of decaying isotropic turbulence. The main objective of this work is to characterize the dependence of various evolution mechanisms of scalar dissipation on local streamline topology and normalized dilatation. The DNS results indicate that the topology has a stronger influence on the nonlinear amplification mechanism than the dilatation level of a fluid element. In its appropriately normalized form, the amplification mechanism is found to be fairly independent of the Mach and Reynolds numbers. Non-focal topologies (the so called unstable-node/saddle/saddle and stable-node/saddle/saddle) are found to be associated with more intense mixing than the focal topologies at almost all dilatation levels. Alignment tendencies (jointly conditioned upon topology and dilatation) between the scalar-gradient vector and the strain-rate eigenvectors are shown to play a key role in shaping the observed behaviour in compressible turbulence. Finally, some modelling implications of these findings are discussed.

scholarly journals The scaling of straining motions in homogeneous isotropic turbulence

2017 ◽  
Vol 829 ◽  
pp. 31-64 ◽  
Author(s):  
G. E. Elsinga ◽  
T. Ishihara ◽  
M. V. Goudar ◽  
C. B. da Silva ◽  
J. C. R. Hunt
Keyword(s):  
Reynolds Number ◽  
Shear Layer ◽  
Spatial Organization ◽  
Isotropic Turbulence ◽  
Local Strain ◽  
Scale Structure ◽  
Small Scale ◽  
Length Scale ◽  
Local Flow ◽  
Small Scale Structure

The scaling of turbulent motions is investigated by considering the flow in the eigenframe of the local strain-rate tensor. The flow patterns in this frame of reference are evaluated using existing direct numerical simulations of homogeneous isotropic turbulence over a Reynolds number range from $Re_{\unicode[STIX]{x1D706}}=34.6$ up to 1131, and also with reference to data for inhomogeneous, anisotropic wall turbulence. The average flow in the eigenframe reveals a shear layer structure containing tube-like vortices and a dissipation sheet, whose dimensions scale with the Kolmogorov length scale, $\unicode[STIX]{x1D702}$. The vorticity stretching motions scale with the Taylor length scale, $\unicode[STIX]{x1D706}_{T}$, while the flow outside the shear layer scales with the integral length scale, $L$. Furthermore, the spatial organization of the vortices and the dissipation sheet defines a characteristic small-scale structure. The overall size of this characteristic small-scale structure is $120\unicode[STIX]{x1D702}$ in all directions based on the coherence length of the vorticity. This is considerably larger than the typical size of individual vortices, and reflects the importance of spatial organization at the small scales. Comparing the overall size of the characteristic small-scale structure with the largest flow scales and the vorticity stretching motions on the scale of $4\unicode[STIX]{x1D706}_{T}$ shows that transitions in flow structure occur where $Re_{\unicode[STIX]{x1D706}}\approx 45$ and 250. Below these respective transitional Reynolds numbers, the small-scale motions and the vorticity stretching motions are progressively less well developed. Scale interactions are examined by decomposing the average shear layer into a local flow, which is induced by the shear layer vorticity, and a non-local flow, which represents the environment of the characteristic small-scale structure. The non-local strain is $4\unicode[STIX]{x1D706}_{T}$ in width and height, which is consistent with observations in high Reynolds number flow of a $4\unicode[STIX]{x1D706}_{T}$ wide instantaneous shear layer with many $\unicode[STIX]{x1D702}$-scale vortical structures inside (Ishihara et al., Flow Turbul. Combust., vol. 91, 2013, pp. 895–929). In the average shear layer, vorticity aligns with the intermediate principal strain at small scales, while it aligns with the most stretching principal strain at larger scales, consistent with instantaneous turbulence. The length scale at which the alignment changes depends on the Reynolds number. When conditioning the flow in the eigenframe on extreme dissipation, the velocity is strongly affected over large distances. Moreover, the associated peak velocity remains Reynolds number dependent when normalized by the Kolmogorov velocity scale. It signifies that extreme dissipation is not simply a small-scale property, but is associated with large scales at the same time.

Collision statistics of inertial particles in two-dimensional homogeneous isotropic turbulence with an inverse cascade

2014 ◽  
Vol 745 ◽  
pp. 279-299 ◽  
Author(s):  
Ryo Onishi ◽  
J. C. Vassilicos
Keyword(s):  
Reynolds Number ◽  
Isotropic Turbulence ◽  
Particle System ◽  
Stochastic Simulations ◽  
Collision Kernel ◽  
Inertial Particles ◽  
Two Dimensional ◽  
Homogeneous Isotropic Turbulence ◽  
Local Flow ◽  
Reynolds Number Dependence

AbstractThis study investigates the collision statistics of inertial particles in inverse-cascading two-dimensional (2D) homogeneous isotropic turbulence by means of a direct numerical simulation (DNS). A collision kernel model for particles with small Stokes number ($\mathit{St}$) in 2D flows is proposed based on the model of Saffman & Turner (J. Fluid Mech., vol. 1, 1956, pp. 16–30) (ST56 model). The DNS results agree with this 2D version of the ST56 model for $\mathit{St}\lesssim 0.1$. It is then confirmed that our DNS results satisfy the 2D version of the spherical formulation of the collision kernel. The fact that the flatness factor stays around 3 in our 2D flow confirms that the present 2D turbulent flow is nearly intermittency-free. Collision statistics for $\mathit{St}= 0.1$, 0.4 and 0.6, i.e. for $\mathit{St}<1$, are obtained from the present 2D DNS and compared with those obtained from the three-dimensional (3D) DNS of Onishi et al. (J. Comput. Phys., vol. 242, 2013, pp. 809–827). We have observed that the 3D radial distribution function at contact ($g(R)$, the so-called clustering effect) decreases for $\mathit{St}= 0.4$ and 0.6 with increasing Reynolds number, while the 2D $g(R)$ does not show a significant dependence on Reynolds number. This observation supports the view that the Reynolds-number dependence of $g(R)$ observed in three dimensions is due to internal intermittency of the 3D turbulence. We have further investigated the local $\mathit{St}$, which is a function of the local flow strain rates, and proposed a plausible mechanism that can explain the Reynolds-number dependence of $g(R)$. Meanwhile, 2D stochastic simulations based on the Smoluchowski equations for $\mathit{St}\ll 1$ show that the collision growth can be predicted by the 2D ST56 model and that rare but strong events do not play a significant role in such a small-$\mathit{St}$ particle system. However, the probability density function of local $\mathit{St}$ at the sites of colliding particle pairs supports the view that powerful rare events can be important for particle growth even in the absence of internal intermittency when $\mathit{St}$ is not much smaller than unity.

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