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arXiv2013

Swimming near Deformable Membranes at Low Reynolds Number

Microorganisms are rarely found in Nature swimming freely in an unbounded fluid. Instead, they typically encounter other organisms, hard walls, or deformable boundaries such as free interfaces or membranes. Hydrodynamic interactions between the swimmer and nearby objects lead to many interesting phenomena, such as changes in swimming speed, tendencies to accumulate or turn, and coordinated flagellar beating. Inspired by this class of problems, we investigate locomotion of microorganisms near deformable boundaries. We calculate the speed of an infinitely long swimmer close to a flexible surface separating two fluids; we also calculate the deformation and swimming speed of the flexible surface. When the viscosities on either side of the flexible interface differ, we find that fluid is pumped along or against the swimming direction, depending on which viscosity is greater.

physics.flu-dyn↗

arXiv2014

Oscillatory instability and fluid patterns in low-Prandtl-number Rayleigh-Bénard convection with uniform rotation

We present the results of direct numerical simulations of flow patterns in a low-Prandtl-number ($Pr = 0.1$) fluid above the onset of oscillatory convection in a Rayleigh-Bénard system rotating uniformly about a vertical axis. Simulations were carried out in a periodic box with thermally conducting and stress-free top and bottom surfaces. We considered a rectangular box ($L_x \times L_y \times 1$) and a wide range of Taylor numbers ($750 \le Ta \le 5000$) for the purpose. The horizontal aspect ratio $η= L_y/L_x$ of the box was varied from $0.5$ to $10$. The primary instability appeared in the form of two-dimensional standing waves for shorter boxes ($0.5 \le η< 1$ and $1 < η< 2$). The flow patterns observed in boxes with $η= 1$ and $η= 2$ were different from those with $η< 1$ and $1 < η< 2$. We observed a competition between two sets of mutually perpendicular rolls at the primary instability in a square cell ($η= 1$) for $Ta < 2700$, but observed a set of parallel rolls in the form of standing waves for $Ta \geq 2700$. The three-dimensional convection was quasiperiodic or chaotic for $750 \le Ta < 2700$, and then bifurcated into a two-dimensional periodic flow for $Ta \ge 2700$. The convective structures consisted of the appearance and disappearance of straight rolls, rhombic patterns, and wavy rolls inclined at an angle $ϕ= \fracπ{2} - \arctan{(η^{-1})}$ with the straight rolls.

physics.flu-dyn↗

arXiv2013

Zonal Flow as Pattern Formation

Zonal flows are well known to arise spontaneously out of turbulence. We show that for statistically averaged equations of the stochastically forced generalized Hasegawa-Mima model, steady-state zonal flows and inhomogeneous turbulence fit into the framework of pattern formation. There are many implications. First, the wavelength of the zonal flows is not unique. Indeed, in an idealized, infinite system, any wavelength within a certain continuous band corresponds to a solution. Second, of these wavelengths, only those within a smaller subband are linearly stable. Unstable wavelengths must evolve to reach a stable wavelength; this process manifests as merging jets.

physics.ao-ph↗

arXiv2013

Direct Numerical Simulation of Electrokinetic Instability and Transition to Chaotic Motion

A new type of instability - electrokinetic instability - and an unusual transition to chaotic motion near a charge-selective surface was studied by numerical integration of the Nernst-Planck-Poisson-Stokes system and a weakly nonlinear analysis near the threshold of instability. Two kinds of initial conditions were considered: (a) white noise initial conditions to mimic "room disturbances" and subsequent natural evolution of the solution; (b) an artificial monochromatic ion distribution with a fixed wave number to simulate regular wave patterns. The results were studied from the viewpoint of hydrodynamic stability and bifurcation theory. The threshold of electroconvective movement was found by the linear spectral stability theory, the results of which were confirmed by numerical simulation of the entire system. The following regimes, which replace each other as the potential drop between the selective surfaces increases, were obtained: one-dimensional steady solution; two-dimensional steady electroconvective vortices (stationary point in a proper phase space); unsteady vortices aperiodically changing their parameters (homoclinic contour); periodic motion (limit cycle); and chaotic motion. The transition to chaotic motion did not include Hopf bifurcation. Numerical resolution of the thin concentration polarization layer showed spike-like charge profiles along the surface, which could be, depending on the regime, either steady or aperiodically coalescent. The numerical investigation confirmed the experimentally observed absence of regular (near-sinusoidal) oscillations for the overlimiting regimes. There is a qualitative agreement of the experimental and the theoretical values of the threshold of instability, the dominant size of the observed coherent structures, and the experimental and theoretical volt-current characteristics.

physics.flu-dyn↗

arXiv2014

Symmetry and plate-like convection in fluids with temperature-dependent viscosity

We explore the instabilities developed in a fluid in which viscosity depends on temperature. In particular, we consider a dependency that models a very viscous (and thus rather rigid) lithosphere over a convecting mantle. To this end, we study a 2D convection problem in which viscosity depends on temperature by abruptly changing its value by a factor of 400 within a narrow temperature gap. We conduct a study which combines bifurcation analysis and time-dependent simulations. Solutions such as limit cycles are found that are fundamentally related to the presence of symmetry. Spontaneous plate-like behaviors that rapidly evolve towards a stagnant lid regime emerge sporadically through abrupt bursts during these cycles. The plate-like evolution alternates motions towards either the right or the left, thereby introducing temporary asymmetries on the convecting styles. Further time-dependent regimes with stagnant and plate-like lids are found and described.

physics.flu-dyn↗

arXiv2014

Eckhaus-like instability of large scale coherent structures in a fully turbulent von Kármán flow

The notion of instability of a turbulent flow is introduced in the case of a von Kármán flow thanks to the monitoring of the spatio-temporal spectrum of the velocity fluctuations, combined with projection onto suitable Beltrami modes. It is shown that the large scale coherent fluctuations of the flow obeys a sequence of Eckhaus instabilities when the Reynolds number $\mathrm{Re}$ is varied from $10^2$ to $10^6$. This sequence results in modulations of increasing azimuthal wavenumber. The basic state is the laminar or time-averaged flow at an arbitrary $\mathrm{Re}$, which is axi-symmetric, i.e. with a $0$ azimuthal wavenumber. Increasing $\mathrm{Re}$ leads to non-axisymmetric modulations with increasing azimuthal wavenumber from $1$ to $3$. These modulations are found to rotate in the azimuthal direction. However no clear rotation frequency can be established until $\mathrm{Re}\approx 4\times 10^3$. Above, they become periodic with an increasing frequency. We finally show that these modulations are connected with the coherent structures of the mixing shear layer. The implication of these findings for the turbulence parametrization is discussed. Especially, they may explain why simple eddy viscosity models are able to capture complex turbulent flow dynamics.

physics.flu-dyn↗

arXiv2013

Propulsion by a Helical Flagellum in a Capillary Tube

We study the microscale propulsion of a rotating helical filament confined by a cylindrical tube, using a boundary-element method for Stokes flow that accounts for helical symmetry. We determine the effect of confinement on swimming speed and power consumption. Except for a small range of tube radii at the tightest confinements, the swimming speed at fixed rotation rate increases monotonically as the confinement becomes tighter. At fixed torque, the swimming speed and power consumption depend only on the geometry of the filament centerline, except at the smallest pitch angles for which the filament thickness plays a role. We find that the `normal' geometry of \textit{Escherichia coli} flagella is optimized for swimming efficiency, independent of the degree of confinement. The efficiency peaks when the arc length of the helix within a pitch matches the circumference of the cylindrical wall. We also show that a swimming helix in a tube induces a net flow of fluid along the tube.

physics.flu-dyn↗

arXiv2014

Hilbert Statistics of Vorticity Scaling in Two-Dimensional Turbulence

In this paper, the scaling property of the inverse energy cascade and forward enstrophy cascade of the vorticity filed $ω(x,y)$ in two-dimensional (2D) turbulence is analyzed. This is accomplished by applying a Hilbert-based technique, namely Hilbert-Huang Transform, to a vorticity field obtained from a $8192^2$ grid-points direct numerical simulation of the 2D turbulence with a forcing scale $k_f=100$ and an Ekman friction. The measured joint probability density function $p(C,k)$ of mode $C_i(x)$ of the vorticity $ω$ and instantaneous wavenumber $k(x)$ is separated by the forcing scale $k_f$ into two parts, which corresponding to the inverse energy cascade and the forward enstrophy cascade. It is found that all conditional pdf $p(C\vert k)$ at given wavenumber $k$ has an exponential tail. In the inverse energy cascade, the shape of $p(C\vert k)$ does collapse with each other, indicating a nonintermittent cascade. The measured scaling exponent $ζ_ω^I(q)$ is linear with the statistical order $q$, i.e., $ζ_ω^I(q)=-q/3$, confirming the nonintermittent cascade process. In the forward enstrophy cascade, the core part of $p(C\vert k)$ is changing with wavenumber $k$, indicating an intermittent forward cascade. The measured scaling exponent $ζ_ω^F(q)$ is nonlinear with $q$ and can be described very well by a log-Poisson fitting: $ζ_ω^F(q)=\frac{1}{3}q+0.45\left(1-0.43^{q}\right)$. However, the extracted vorticity scaling exponents $ζ_ω(q)$ for both inverse energy cascade and forward enstrophy cascade are not consistent with Kraichnan\rq{}s theory prediction. New theory for the vorticity field in 2D turbulence is required to interpret the observed scaling behavior.

physics.flu-dyn↗

arXiv2014

Lattice-Boltzmann simulations of the drag force on a sphere approaching a superhydrophobic striped plane

By means of lattice-Boltzmann simulations the drag force on a sphere of radius R approaching a superhydrophobic striped wall has been investigated as a function of arbitrary separation h. Superhydrophobic (perfect-slip vs. no-slip) stripes are characterized by a texture period L and a fraction of the gas area $ϕ$. For very large values of h/R we recover the macroscopic formulae for a sphere moving towards a hydrophilic no-slip plane. For h/R=O(1) and smaller the drag force is smaller than predicted by classical theories for hydrophilic no-slip surfaces, but larger than expected for a sphere interacting with a uniform perfectly slipping wall. At a thinner gap, $h\ll R$ the force reduction compared to a classical result becomes more pronounced, and is maximized by increasing $ϕ$. In the limit of very small separations our simulation data are in quantitative agreement with an asymptotic equation, which relates a correction to a force for superhydrophobic slip to texture parameters. In addition, we examine the flow and pressure field and observe their oscillatory character in the transverse direction in the vicinity of the wall, which reflects the influence of the heterogeneity and anisotropy of the striped texture. Finally, we investigate the lateral force on the sphere, which is detectable in case of very small separations and is maximized by stripes with $ϕ=0.5$.

physics.flu-dyn↗

arXiv2014

Pairwise hydrodynamic interactions and diffusion in a vesicle suspension

The hydrodynamic interaction of two deformable vesicles in shear flow induces a net displacement, in most cases an increase of their distance in the transverse direction. The statistical average of these interactions leads to shear-induced diffusion in the suspension, both at the level of individual particles which experience a random walk made of successive interactions, and at the level of suspension where a non-linear down-gradient diffusion takes place, an important ingredient in the structuring of suspension flows. We make an experimental and computational study of the interaction of a pair of lipid vesicles in shear flow by varying physical parameters, and investigate the decay of the net lateral displacement with the distance between the streamlines on which the vesicles are initially located. This decay and its dependency upon vesicle properties can be accounted for by a simple model based on the well established law for the lateral drift of a vesicle in the vicinity of a wall. In the semi-dilute regime, a determination of self-diffusion coefficients is presented.

physics.flu-dyn↗

arXiv2013

Beta-plane turbulence: experiments with altimetry

Results from a new series of experiments on barotropic and baroclinic turbulent flows generated in a rotating tank with topographic beta-effect are presented. The velocity fields are measured by the Altimetric Imaging Velocimetry. The turbulent flows observed in the experiments develop zonal jets which are latent in a stationary forced-dissipative regime of the flow but become prominent in the decaying flow. The two-dimensional energy spectra of the flows exhibit the development of anisotropy towards zonal motions. The experiments demonstrate dual turbulent cascade with energy and enstrophy ranges. The frequency-wavenumber spectra reveal the presence of Rossby waves at low wavenumbers which are excited by the turbulent motions. The experimental results are compared with available theory of beta-plane turbulence.

physics.ao-ph↗

arXiv2014

Strong anisotropy in quasi-static magnetohydrodynamic turbulence for high interaction parameters

We simulate forced quasi-static magnetohydrodynamic turbulence and investigate the anisotropy, energy spectrum, and energy flux of the flow, specially for large interaction parameters ($N$). We show that the angular dependence of the energy spectrum is well quantified using Legendre polynomials. For large $N$, the energy spectrum is exponential. Our direct computation of energy flux reveals an inverse cascade of energy at low wavenumbers, similar to that in two-dimensional turbulence. We observe the flow be two-dimensional (2D) for moderate $N$ ($N \sim 20$), and two-dimensional three-component (2D-3C) type for $N \ge 27$. In our forced simulation, the transition from 2D to 2D-3C occurs at higher value of $N$ than Favier et al., ["On the two-dimensionalization of quasistatic magnetohydrodynamic turbulence," Phys. Fluids 22, 075104 (2010)] who employ decaying simulations.

physics.flu-dyn↗

arXiv2014

Lift and wakes of flying snakes

Flying snakes use a unique method of aerial locomotion: they jump from tree branches, flatten their bodies and undulate through the air to produce a glide. The shape of their body cross-section during the glide plays an important role in generating lift. This paper presents a computational investigation of the aerodynamics of the cross-sectional shape. Two-dimensional simulations of incompressible flow past the anatomically correct cross-section of the species Chrysopelea paradisi show that a significant enhancement in lift appears at a 35-degrees angle of attack, above Reynolds numbers 2000. Previous experiments on physical models also obtained an increased lift, at the same angle of attack. The flow is inherently three-dimensional in physical experiments, due to fluid instabilities, and it is thus intriguing that the enhanced lift also appears in the two-dimensional simulations. The simulations point to the lift enhancement arising from the early separation of the boundary layer on the dorsal surface of the snake profile, without stall. The separated shear layer rolls up and interacts with secondary vorticity in the near-wake, inducing the primary vortex to remain closer to the body and thus cause enhanced suction, resulting in higher lift.

physics.flu-dyn↗

arXiv2014

Mechanical energy dissipation induced by sloshing and wave breaking in a fully coupled angular motion system. Part I: Theoretical formulation and Numerical Investigation

A dynamical system involving a driven pendulum filled with liquid, is analyzed in the present paper series. The study of such a system is conducted in order to understand energy dissipation resulting from the shallow water sloshing and induced wave breaking. This analysis is relevant for the design of Tuned Liquid Damper devices. The complexity and violence of the flow generated by the roll motion results in the impossibility of using an analytical approach, requiring in turn the use of a suitable numerical solver. In Part I, the coupled dynamical system is thoroughly described, revealing its nonlinear features associated with the large amplitude of the forcing, both in terms of mechanical and fluid dynamical aspects. A smoothed particle hydrodynamics (SPH) model, largely validated in literature, is used to calculate the frequency behavior of the whole system. For small rotation angles, a semi-analytical model of the energy dissipated by the fluid, based on a hydraulic jump solution, is developed; the energy transfer is numerically calculated in order to extend the analysis to large oscillation angles. The experimental part of the investigation is carried out in Part II of this work.

physics.flu-dyn↗

arXiv2014

Mechanical energy dissipation induced by sloshing and wave breaking in a fully coupled angular motion system. Part II: Experimental Investigation

In Part I of this paper series, a theoretical and numerical model for a a driven pendulum filled with liquid was developed. The system was analyzed in the framework of tuned liquid dampers (TLD) and hybrid mass liquid dampers (HMLD) theory. In this Part II, in order to measure the energy dissipation resulting from shallow water sloshing, an experimental investigation is conducted. Accurate evaluations of energy transfers are obtained through the recorded kinematics of the system. A set of experiments is conducted with three different liquids: water, sunflower oil and glycerine. Coherently with the results of Part I, the energy dissipation obtained when the tank is filled with water can mainly be explained by the breaking waves. For all three liquids, the effects of varying the external excitation amplitude are discussed.

physics.flu-dyn↗

arXiv2014

Undulations from amplified low frequency surface waves

We study the scattering of gravity waves in longitudinal inhomogeneous stationary flows. When the flow becomes supercritical, counterflow propagating shallow waves are blocked and converted into deep waves. We show that the reflected waves are amplified in such a way that, in the zero-frequency limit, the free surface develops an undulation, i.e., a zero-frequency wave of large amplitude with nodes located at specific places. This amplification involves negative energy waves, and implies that the unperturbed flat surface is unstable against incoming perturbations of arbitrary small amplitude. The relation between this instability and black hole radiation (the Hawking effect) is discussed.

physics.flu-dyn↗

arXiv2014

Note on specific chiral ensembles of statistical hydrodynamics: "order function" for transition of turbulence transfer scenarios

Hydrodynamic helicity signatures the parity symmetry breaking, chirality, of the flow. Statistical hydrodynamics thus respect chirality, as symmetry breaking and restoration are key to their fundamentals, such as the spectral transfer direction and its mechanism. Homochiral sub-system of three-dimensional (3D) Navier-Stokes isotropic turbulence has been numerically realized with helical representation technique to present inverse energy cascade [Biferale et al., Phys. Rev. Lett., {\bf 108}, 164501 (2012)]. The situation is analogous to 2D turbulence where inverse energy cascade, or more generally energy-enstrophy dual cascade scenario, was argued with the help of a negative temperature state of the absolute equilibrium by Kraichnan. Indeed, if the helicity in such a system is taken to be positive without loss of generality, a corresponding negative temperature state can be identified [Zhu et al., J. Fluid Mech., {\bf 739}, 479 (2014)]. Here, for some specific chiral ensembles of turbulence, we show with the corresponding absolute equilibria that even if the helicity distribution over wavenumbers is sign definite, different \textit{ansatzes} of the shape function, defined by the ratio between the specific helicity and energy spectra $s(k)=H(k)/E(k)$, imply distinct transfer directions, and we could have inverse-helicity and forward-energy dual transfers (with, say, $s(k)\propto k^{-2}$ resulting in absolute equilibrium modal spectral density of energy $U(k)=\frac{1}{α+βk^{-2}}$, exactly the enstrophy one of two-dimensional Euler by Kraichan), simultaneous forward transfers (with $s(k)=constant$), or even no simply-directed transfer (with, say, non-monotonic $s(k) \propto \sin^2k$), besides the inverse-energy and forward-helicity dual transfers (with, say, $s(k)=k$ as in the homochiral case).

physics.flu-dyn↗

arXiv2014

Plane shear flows of frictionless spheres: Kinetic theory and 3D soft-sphere discrete element method simulations

We use existing 3D Discrete Element simulations of simple shear flows of spheres to evaluate the radial distribution function at contact that enables kinetic theory to correctly predict the pressure and the shear stress, for different values of the collisional coefficient of restitution. Then, we perform 3D Discrete Element simulations of plane flows of frictionless, inelastic spheres, sheared between walls made bumpy by gluing particles in a regular array, at fixed average volume fraction and distance between the walls. The results of the numerical simulations are used to derive boundary conditions appropriated in the cases of large and small bumpiness. Those boundary conditions are, then, employed to numerically integrate the differential equations of Extended Kinetic Theory, where the breaking of the molecular chaos assumption at volume fraction larger than 0.49 is taken into account in the expression of the dissipation rate. We show that the Extended Kinetic Theory is in very good agreement with the numerical simulations, even for coefficients of restitution as low as 0.50. When the bumpiness is increased, we observe that some of the flowing particles are stuck in the gaps between the wall spheres. As a consequence, the walls are more dissipative than expected, and the flows resemble simple shear flows, i.e., flows of rather constant volume fraction and granular temperature.

cond-mat.soft↗