Papers
Passive boundary layer control of oblique disturbances by finite-amplitude streaks
- Shahab Shahinfar, Sohrab S. Sattarzadeh, Jens H. M. Fransson
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- 14 May 2014, pp. 1-36
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Recent experimental results on the attenuation of two-dimensional Tollmien–Schlichting wave (TSW) disturbances by means of passive miniature vortex generators (MVGs) have shed new light on the possibility of delaying transition to turbulence and hence accomplishing skin-friction drag reduction. A recurrent concern has been whether this passive flow control strategy would work for other types of disturbances than plane TSWs in an experimental configuration where the incoming disturbance is allowed to fully interact with the MVG array. In the present experimental investigation we show that not only TSW disturbances are attenuated, but also three-dimensional single oblique wave (SOW) and pair of oblique waves (POW) disturbances are quenched in the presence of MVGs, and that transition delay can be obtained successfully. For the SOW disturbance an unusual interaction between the wave and the MVGs occurs, leading to a split of the wave with one part travelling with a ‘mirrored’ phase angle with respect to the spanwise direction on one side of the MVG centreline. This gives rise to $\Lambda $-vortices on the centreline, which force a low-speed streak on the centreline, strong enough to overcome the high-speed streak generated by the MVGs themselves. Both these streaky boundary layers seem to act stabilizing on unsteady perturbations. The challenge in a passive control method making use of a non-modal type of disturbances to attenuate modal disturbances lies in generating stable streamwise streaks which do not themselves break down to turbulence.
Dynamics of line plumes on horizontal surfaces in turbulent convection
- G. S. Gunasegarane, Baburaj A. Puthenveettil
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- 14 May 2014, pp. 37-78
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We study the dynamics of line plumes on the bottom horizontal plate in turbulent convection over six decades of Rayleigh number $(10^5<\mathit{Ra}_w<10^{11})$ and two decades of Prandtl number or Schmidt number ($0.7<\mathit{Pr}<5.3$, $\mathit{Sc}=602$). From the visualisations of these plumes in a horizontal plane close to the plate, we identify the main dynamics as (i) motion along the plumes, (ii) lateral merging of the plumes and (iii) initiation of the plumes; various other minor types of motion also occur along with these main dynamics. In quantifying the three main motions, we first find that the spatiotemporal mean velocity along the length of the plumes ($\overline{V_{sh}}$) scales as the large-scale flow velocity ($V_{LS}$), with the fraction of the length of the plumes affected by shear increasing with $\mathit{Ra}_w$ as $L_{ps}/L_p\sim \mathit{Ra}_w^{0.054} \mathit{Pr}^{-0.12}$. The mean time of initiation of the plumes $\overline{t^{*}}$, scales as the diffusive time scale near the plate, $Z_w^2/\alpha $, where $Z_w$ is the appropriate length scale near the plate, in agreement with Howard (Proc. 11th Int. Congress Applied Mechanics, Munich, 1964, pp. 1109–1115). Merging occurs in a large fraction of the area of the plate, with ${\sim }70\, \%$ of the length of the plumes undergoing merging at $\mathit{Ra}_w\approx 10^{11}$ and $\mathit{Sc}= 602$. The fraction of the length of the plumes that undergoes merging decreases with increase in $\mathit{Ra}_w$ as, $L_{pm}/L_p \sim \mathit{Ra}_w^{-0.054} \mathit{Pr}^{0.12}$; the exponents of $\mathit{Ra}_w$ and $\mathit{Pr}$ being of the same magnitude but of opposite sign as that in the relation for $L_{ps}/L_p$. Measurements of the locational means of the velocities of merging of the plumes $(V_m)$ show that $V_m$ is a constant during each merging cycle at any location. However, the values of these constant velocities depend on the location and the time of measurement, since the merging velocities are affected by the local shear, which is a function of space and time at any $\mathit{Ra}_w-\mathit{Pr}$ combination. The merging velocities at all $\mathit{Ra}_w$ and $\mathit{Pr}$ have a common lognormal distribution, but their mean and variance increased with increasing $\mathit{Ra}_w$ and decreasing $\mathit{Pr}$. Using mass and momentum balance of the region between two merging plumes, we show that the spatiotemporal mean merging velocities ($\overline{V_m}$), which are an order lower than $\overline{V_{sh}}$, scale as the entrainment velocity at the sides of the plumes, averaged over the height of the diffusive layer near the plate. This implies that $\overline{V_m}$ scales as the diffusive velocity scale near the plate $\nu /Z_w$. The Reynolds number in terms of $\overline{V_m}$ and the layer height $H(\mathit{Re}_H)$ scales as $\mathit{Ra}_w^{1/3}$, in the same way as the Nusselt number ($\mathit{Nu}$) scales approximately; therefore $\mathit{Re}_{H}\sim \mathit{Nu}$. These relations imply that $\mathit{Re}_w= \overline{V_m}Z_w/\nu $ a Reynolds number near the plate, is an invariant for a given fluid in turbulent convection.
Estimating the value of von Kármán’s constant in turbulent pipe flow
- S. C. C. Bailey, M. Vallikivi, M. Hultmark, A. J. Smits
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- 14 May 2014, pp. 79-98
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Five separate data sets on the mean velocity distributions in the Princeton University/ONR Superpipe are used to establish the best estimate for the value of von Kármán’s constant for the flow in a fully developed, hydraulically smooth pipe. The profiles were taken using Pitot tubes, conventional hot wires and nanoscale thermal anemometry probes. The value of the constant was found to vary significantly due to measurement uncertainties in the mean velocity, friction velocity and the wall distance, and the number of data points included in the analysis. The best estimate for the von Kármán constant in turbulent pipe flow is found to be $0.40 \pm 0.02$. A more precise estimate will require improved instrumentation.
A mixture theory for size and density segregation in shallow granular free-surface flows
- D. R. Tunuguntla, O. Bokhove, A. R. Thornton
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- 14 May 2014, pp. 99-112
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In the past ten years much work has been undertaken on developing mixture theory continuum models to describe kinetic sieving-driven size segregation. We propose an extension to these models that allows their application to bidisperse flows over inclined channels, with particles varying in density and size. Our model incorporates both a recently proposed explicit formula for how the total pressure is distributed among different species of particles, which is one of the key elements of mixture theory-based kinetic sieving models, and a shear rate-dependent drag. The resulting model is used to predict the range of particle sizes and densities for which the mixture segregates. The prediction of no segregation in the model is benchmarked by using discrete particle simulations, and good agreement is found when a single fitting parameter is used which determines whether the pressure scales with the diameter, surface area or volume of the particle.
Asymptotic theory for a bathtub vortex in a rotating tank
- M. R. Foster
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- 14 May 2014, pp. 113-144
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Fluid entering the periphery of a cylindrical tank mounted on a rotating table is pumped inwards toward a central, floor drain by a potential vortex that is established in the fluid interior. We present here an asymptotic theory for small Rossby and Ekman numbers, including detailed solutions in the vortex core. Results for azimuthal velocity variation with radius agree quite well with the experiments of Andersen et al. (J. Fluid Mech., vol. 556, 2006, pp. 121–146), in spite of their free upper boundary. Modifications of the flow are presented in the instance that a short cylinder is place on the tank axis as in the work of Chen et al. (J. Fluid Mech., vol. 733, 2013, pp. 134–157). The overall flow structure found here is exactly that noted by both Andersen et al. and Chen et al.
Motion of spheroid particles in shear flow with inertia
- Wenbin Mao, Alexander Alexeev
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- 14 May 2014, pp. 145-166
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In this article, we investigate the motion of a solid spheroid particle in a simple shear flow. Using a lattice Boltzmann method, we examine individual effects of fluid inertia and particle rotary inertia as well as their combination on the dynamics and trajectory of spheroid particles at low and moderate Reynolds numbers. The motion of a single spheroid is shown to be dependent on the particle Reynolds number, particle aspect ratio, particle initial orientation and the Stokes number. Spheroids with random initial orientations are found to drift to stable orbits influenced by fluid inertia and/or particle inertia. Specifically, prolate spheroids drift towards the tumbling mode of motion, whereas oblate spheroids drift to the rolling mode. The rotation period and the variation of angular velocity of tumbling spheroids decrease as Stokes number increases. With increasing Reynolds number, both the maximum and minimum values of angular velocity decrease, whereas the particle rotation period increases. We show that particle inertia does not affect the hydrodynamic torque on the particle. We also demonstrate that superposition can be used to estimate the combined effect of fluid inertia and particle inertia on the dynamics of spheroid particles at sufficiently low Reynolds numbers.
Electro-osmotic flow through a nanopore
- M. Mao, J. D. Sherwood, S. Ghosal
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- 14 May 2014, pp. 167-183
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Electro-osmotic pumping of fluid through a nanopore that traverses an insulating membrane is considered. The density of surface charge on the membrane is assumed to be uniform and sufficiently low for the Poisson–Boltzmann equation to be linearized. The reciprocal theorem gives the flow rate generated by an applied weak electric field, expressed as an integral over the fluid volume. For a circular hole in a membrane of zero thickness, an analytical result is possible up to quadrature. For a membrane of arbitrary thickness, the full Poisson–Nernst–Planck–Stokes system of equations is solved numerically using a finite volume method. The numerical solution agrees with the standard analytical result for electro-osmotic flux through a long cylindrical pore when the membrane thickness is large compared to the hole diameter. When the membrane thickness is small, the flow rate agrees with that calculated using the reciprocal theorem.
The history force on a small particle in a linearly stratified fluid
- Fabien Candelier, Rabah Mehaddi, Olivier Vauquelin
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- 15 May 2014, pp. 184-200
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The hydrodynamic force experienced by a small spherical particle undergoing an arbitrary time-dependent motion in a weakly density-stratified fluid is investigated theoretically. The study is carried out under the Oberbeck–Boussinesq approximation and in the limit of small Reynolds and small Péclet numbers. The force acting on the particle is obtained by using matched-asymptotic expansions. In this approach, the small parameter is given by $a/\ell $, where $a$ is the particle radius and $\ell $ is the stratification length, as defined by Ardekani & Stocker (Phys. Rev. Lett., vol. 105, 2010, article 084502), which depends on the Brunt–Väisälä frequency, on the fluid kinematic viscosity and on the thermal or the concentration diffusivity (depending on the case considered). The matching procedure used here, which is based on series expansions of generalized functions, slightly differs from that generally used in similar problems. In addition to the classical Stokes drag, it is found that the particle experiences a memory force given by two convolution products, one of which involves, as usual, the particle acceleration and the other one, the particle velocity. Owing to the stratification, the transient behaviour of this memory force, in response to an abrupt motion, consists of an initial fast decrease followed by a damped oscillation with an angular frequency corresponding to the Brunt–Väisälä frequency. The perturbation force eventually tends to a constant which provides us with correction terms that should be added to the Stokes drag to accurately predict the settling time of a particle in a diffusive stratified fluid.
Dynamical interactions between the coherent motion and small scales in a cylinder wake
- F. Thiesset, L. Danaila, R. A. Antonia
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- 15 May 2014, pp. 201-226
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Most turbulent flows are characterized by coherent motion (CM), whose dynamics reflect the initial and boundary conditions of the flow and are more predictable than that of the random motion (RM). The major question we address here is the dynamical interaction between the CM and the RM, at a given scale, in a flow where the CM exhibits a strong periodicity and can therefore be readily distinguished from the RM. The question is relevant at any Reynolds number, but is of capital importance at finite Reynolds numbers, for which a clear separation between the largest and the smallest scales may not exist. Both analytical and experimental tools are used to address this issue. First, phase-averaged structure functions are defined and further used to condition the RM kinetic energy at a scale $r$ on the phase $\phi $ of the CM. This tool allows the dependence of the RM to be followed as a function of the CM dynamics. Scale-by-scale energy budget equations are established on the basis of phase-averaged structure functions. They reveal that energy transfer at a scale $r$ is sensitive to an additional forcing mechanism due to the CM. Second, these concepts are tested using hot-wire measurements in a cylinder wake, in which the CM is characterized by a well-defined periodicity. Because the interaction between large and small scales is most likely enhanced at moderate/low Reynolds numbers, and is also likely to depend on the amplitude of the CM, we choose to test our findings against experimental data at $R_{\lambda } \sim 10^2$ and for downstream distances in the range $10 \leq x/D \leq 40$. The effects of an increasing Reynolds number are also discussed. It is shown that: (i) a simple analytical expression describes the second-order structure functions of the purely CM. The energy of the CM is not associated with any single scale; instead, its energy is distributed over a range of scales. (ii) Close to the obstacle, the influence of the CM is perceptible even at the smallest scales, the energy of which is enhanced when the coherent strain is maximum. Further downstream from the cylinder, the CM clearly affects the largest scales, but the smallest scales are not likely to depend explicitly on the CM. (iii) The isotropic formulation of the RM energy budget compares favourably with experimental results.
Evolution of the scalar dissipation rate downstream of a concentrated line source in turbulent channel flow
- E. Germaine, L. Mydlarski, L. Cortelezzi
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- 15 May 2014, pp. 227-274
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The dissipation rate, $\varepsilon _{\theta }$, of a passive scalar (temperature in air) emitted from a concentrated source into a fully developed high-aspect-ratio turbulent channel flow is studied. The goal of the present work is to investigate the return to isotropy of the scalar field when the scalar is injected in a highly anisotropic manner into an inhomogeneous turbulent flow at small scales. Both experiments and direct numerical simulations (DNS) were used to study the downstream evolution of $\varepsilon _{\theta }$ for scalar fields generated by line sources located at the channel centreline $(y_s/h = 1.0)$ and near the wall $(y_s/h = 0.17)$. The temperature fluctuations and temperature derivatives were measured by means of a pair of parallel cold-wire thermometers in a flow at $Re_{\tau } = 520$. The DNS were performed at $Re_{\tau } = 190$ using a spectral method to solve the continuity and Navier–Stokes equations, and a flux integral method (Germaine, Mydlarski & Cortelezzi, J. Comput. Phys., vol. 174, 2001, pp. 614–648) for the advection–diffusion equation. The statistics of the scalar field computed from both experimental and numerical data were found to be in good agreement, with certain discrepancies that were attributable to the difference in the Reynolds numbers of the two flows. A return to isotropy of the small scales was never perfectly observed in any region of the channel for the downstream distances studied herein. However, a continuous decay of the small-scale anisotropy was observed for the scalar field generated by the centreline line source in both the experiments and DNS. The scalar mixing was found to be more rapid in the near-wall region, where the experimental results exhibited low levels of small-scale anisotropy. However, the DNS, which were performed at lower $Re_{\tau }$, showed that persistent anisotropy can also exist near the wall, independently of the downstream location. The role of the mean velocity gradient in the production of $\varepsilon _{\theta }$ (and therefore anisotropy) in the near-wall region was highlighted.
Control of jet breakup by a superposition of two Rayleigh–Plateau-unstable modes
- Theo Driessen, Pascal Sleutel, Frits Dijksman, Roger Jeurissen, Detlef Lohse
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- 16 May 2014, pp. 275-296
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We experimentally, numerically and theoretically demonstrate a novel method of producing a stream of widely spaced high-velocity droplets by imposing a superposition of two Rayleigh–Plateau-unstable modes on a liquid jet. The wavelengths of the two modes are chosen close to the wavelength of the most unstable mode. The interference pattern of the two superimposed modes causes local asymmetries in the capillary tension. The velocity of the initial droplets depends on these local asymmetries. Due to their different velocities, the droplets coalesce to produce a stream of larger droplets spaced at a much larger distance than the initial droplets. We analytically derive the perturbations that robustly induce this process and investigate the influence of the nonlinear interactions of the two Rayleigh–Plateau-unstable modes on the coalescence process. Experiments and numerical simulations demonstrate that the jet breakup and the subsequent droplet merging are fully governed by the selected modes.
On calculating forces from the flow field with application to experimental volume data
- Adam C. DeVoria, Zakery R. Carr, Matthew J. Ringuette
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- 15 May 2014, pp. 297-319
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The use of flow field information to compute the fluid dynamic force on a body is investigated with specific application to experimental volumetric measurements. The calculation method used avoids the explicit evaluation of the pressure on the boundaries. It is shown that errors in the data introduce an artificial dependence of the calculations on the position origin, and also that these errors are amplified by the position vector. A statistical description of the calculation variation associated with origin dependence is presented. A method is developed that objectively determines an origin which reduces the effect of the amplified error. The method utilises mathematical identities which relate the measurements to the main sources of error in a physically meaningful way, and is also found to be effective for changes of the external and internal boundaries of the fluid.
Inertial migration of neutrally buoyant spheres in a pressure-driven flow through square channels
- Kazuma Miura, Tomoaki Itano, Masako Sugihara-Seki
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- 15 May 2014, pp. 320-330
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The inertial migration of neutrally buoyant spherical particles in square channel flows was investigated experimentally in the range of Reynolds numbers ($\mathit{Re}$) from 100 to 1200. The observation of particle positions at several cross-sections downstream from the channel entrance revealed unique patterns of particle distribution which reflects the presence of eight equilibrium positions in the cross-section, located at the centres of the channel faces and at the corners, except for low $\mathit{Re}$. At $\mathit{Re}$ smaller than approximately 250, equilibrium positions at the corners are absent. The corner equilibrium positions were found to arise initially in the band formed along the channel face, followed by a progressive shift almost parallel to the side wall up to the diagonal line with increasing $\mathit{Re}$. Further increase in $\mathit{Re}$ moves the corner equilibrium positions slightly toward the channel corner, whereas the equilibrium positions at the channel face centres are shifted toward the channel centre. As the observation sites become downstream, the particles were found to be more focused near the equilibrium positions keeping their positions almost unchanged. These lateral migration behaviours and focusing properties of particles in square channels are different to that observed in microchannels at lower $\mathit{Re}$ and to what would be expected from extrapolating from the results for circular pipes at comparable $\mathit{Re}$.
On cumulative nonlinear acoustic waveform distortions from high-speed jets
- W. J. Baars, C. E. Tinney, M. S. Wochner, M. F. Hamilton
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- 19 May 2014, pp. 331-366
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A model is proposed for predicting the presence of cumulative nonlinear distortions in the acoustic waveforms produced by high-speed jet flows. The model relies on the conventional definition of the acoustic shock formation distance and employs an effective Gol’dberg number $\Lambda $ for diverging acoustic waves. The latter properly accounts for spherical spreading, whereas the classical Gol’dberg number $\Gamma $ is restricted to plane wave applications. Scaling laws are then derived to account for the effects imposed by jet exit conditions of practical interest and includes Mach number, temperature ratio, Strouhal number and an absolute observer distance relative to a broadband Gaussian source. Surveys of the acoustic pressure produced by a laboratory-scale, shock-free and unheated Mach 3 jet are used to support findings of the model. Acoustic waveforms are acquired on a two-dimensional grid extending out to 145 nozzle diameters from the jet exit plane. Various statistical metrics are employed to examine the degree of local and cumulative nonlinearity in the measured waveforms and their temporal derivatives. This includes a wave steepening factor (WSF), skewness, kurtosis and the normalized quadrature spectral density. The analysed data are shown to collapse reasonably well along rays emanating from the post-potential-core region of the jet. An application of the generalized Burgers equation is used to demonstrate the effect of cumulative nonlinear distortion on an arbitrary acoustic waveform produced by a high-convective-Mach-number supersonic jet. It is advocated that cumulative nonlinear distortion effects during far-field sound propagation are too subtle in this range-restricted environment and over the region covered, which may be true for other laboratory-scale jet noise facilities.
Turbulent drag reduction of boundary layer flow with non-ionic surfactant injection
- Shinji Tamano, Takuya Kitao, Yohei Morinishi
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- 15 May 2014, pp. 367-403
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We experimentally investigated streamwise variations of turbulent dynamics in drag-reducing turbulent boundary layer flows following the injection of non-ionic surfactant solutions, which mainly consisted of oleyldimethylamine oxide. We focus on the comparison of turbulence statistics between injected (i.e. heterogeneous) and premixed (i.e. homogeneous) surfactant solutions, in which the maximum drag reduction ratio of 50 % is the same at the most downstream position for both cases. The wall-normal profiles of turbulence statistics, such as streamwise and wall-normal turbulence intensities, seem to be noticeably different between heterogeneous and homogeneous surfactant solutions. However, streamwise variations in these maxima and the wall-normal locations are essentially similar to one another, except for the maximum of streamwise turbulence intensity, which is not arranged by the amount of drag reduction and is also dependent on the normalization due to outer and inner variables. Such complex behaviour of streamwise turbulence intensity would be caused by the formation of near-wall layered structures that are parallel to the wall. For both heterogeneous and homogeneous surfactant solutions, the streamwise variation in the drag reduction ratio corresponds well to those of the mean velocity in wall units and the wall-normal locations of maxima of streamwise and wall-normal turbulence intensities with both outer and inner scaling. Unlike the Reynolds shear stress, the correlation coefficient of the streamwise and wall-normal turbulent fluctuations is correlated well with the drag reduction ratio. We present plausible pictures of the development of turbulence structures such as hairpin vortices and low-speed streaks for the drag-reducing turbulent boundary layer in heterogeneous and homogeneous surfactant solutions, which are comprehensively derived from the present set of experimental measurements such as flow visualization, planar laser-induced fluorescence, two-component laser-Doppler velocimetry and particle image velocimetry on the streamwise and wall-normal plane and the streamwise and spanwise plane.
Time-analyticity of Lagrangian particle trajectories in ideal fluid flow
- Vladislav Zheligovsky, Uriel Frisch
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- 16 May 2014, pp. 404-430
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It is known that the Eulerian and Lagrangian structures of fluid flow can be drastically different; for example, ideal fluid flow can have a trivial (static) Eulerian structure, while displaying chaotic streamlines. Here, we show that ideal flow with limited spatial smoothness (an initial vorticity that is just a little better than continuous) nevertheless has time-analytic Lagrangian trajectories before the initial limited smoothness is lost. To prove these results we use a little-known Lagrangian formulation of ideal fluid flow derived by Cauchy in 1815 in a manuscript submitted for a prize of the French Academy. This formulation leads to simple recurrence relations among the time-Taylor coefficients of the Lagrangian map from initial to current fluid particle positions; the coefficients can then be bounded using elementary methods. We first consider various classes of incompressible fluid flow, governed by the Euler equations, and then turn to highly compressible flow, governed by the Euler–Poisson equations, a case of cosmological relevance. The recurrence relations associated with the Lagrangian formulation of these incompressible and compressible problems are so closely related that the proofs of time-analyticity are basically identical.
Microstructure and rheology of finite inertia neutrally buoyant suspensions
- Hamed Haddadi, Jeffrey F. Morris
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- 16 May 2014, pp. 431-459
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The microstructure and rheological properties of suspensions of neutrally buoyant hard spherical particles in Newtonian fluid under finite inertia conditions are studied using the lattice-Boltzmann method (LBM), which is based on a discrete Boltzmann model for the fluid and Newtonian dynamics for the particles. The suspensions are subjected to simple-shear flow and the properties are studied as a function of Reynolds number and volume fraction, $\phi $. The inertia is characterized by the particle-scale shear flow Reynolds number $\mathit{Re}= {(\rho \dot{\gamma }a^{2})/\mu }$, where $a$ is the particle radius, $\dot{\gamma }$ is the shear rate and $\rho $ and $\mu $ are the density and viscosity of the fluid, respectively. The influences of inertia and of the volume fraction are investigated for $0.005\leqslant \mathit{Re}\leqslant 5$ and$0.1\leqslant \phi \leqslant 0.35$. The flow-induced microstructure is studied using the pair distribution function $g(\boldsymbol {r})$. Different stress mechanisms, including those due to surface tractions (stresslet), acceleration and the Reynolds stress due to velocity fluctuations are computed and their influence on the first and second normal stress differences, the particle pressure and the viscosity of the suspensions are detailed. The probability density functions (PDFs) of linear and angular accelerations are also presented.
Acoustic invisibility in turbulent fluids by optimised cloaking
- Xun Huang, Siyang Zhong, Xin Liu
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- 16 May 2014, pp. 460-477
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Acoustic invisibility of a cloaking system in turbulent fluids is poorly understood. Here we show that evident scattering would appear in turbulent wakes due to the submergence of a classical cloaking device. The inherent physical mechanism is explained using our theoretical model, which eventually inspires us to develop an optimised cloaking approach. Both the near- and far-field scattered fields are examined using computational methods. The remarkably low scattering demonstrates the effectiveness of the proposed approach, in particular for acoustic cloaking in turbulent fluids.
Experiments on the fragmentation of a buoyant liquid volume in another liquid
- M. Landeau, R. Deguen, P. Olson
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- 16 May 2014, pp. 478-518
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We present experiments on the instability and fragmentation of volumes of heavier liquids released into lighter immiscible liquids. We focus on the regime defined by small Ohnesorge numbers, density ratios of the order of one, and variable Weber numbers. The observed stages in the fragmentation process include deformation of the released fluid by either Rayleigh–Taylor instability (RTI) or vortex ring roll-up and destabilization, formation of filamentary structures, capillary instability, and drop formation. At low and intermediate Weber numbers, a wide variety of fragmentation regimes is identified. Those regimes depend on early deformations, which mainly result from a competition between the growth of RTI and the roll-up of a vortex ring. At high Weber numbers, turbulent vortex ring formation is observed. We have adapted the standard theory of turbulent entrainment to buoyant vortex rings with initial momentum. We find consistency between this theory and our experiments, indicating that the concept of turbulent entrainment is valid for non-dispersed immiscible fluids at large Weber and Reynolds numbers.
Scale analysis of miscible density-driven convection in porous media
- Patrick Jenny, Joohwa S. Lee, Daniel W. Meyer, Hamdi A. Tchelepi
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- 16 May 2014, pp. 519-541
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Scale analysis of unstable density-driven miscible convection in porous media is performed. The main conclusions for instabilities in the developed (long time scales) regime are that (i) large-scale structures are responsible for the bulk of the production of concentration variance, (ii) variance dissipation is dominated by the small (diffusive) scales and that (iii) both the production and dissipation rates are independent of the Rayleigh number. These findings provide a strong basis for a new modelling approach, namely, large-mode simulation (LMS), for which closure is achieved by replacing the actual diffusivity with an effective one. For validation, LMS results for vertical flow in a homogeneous rectangular domain are compared with direct numerical simulations (DNS). Some of the analysis is based on the derivation and closure of the concentration mean and variance equations, whereby averaging over the ensemble of all possible initial perturbations is considered. While self-similar solutions are obtained for vertical, statistically one-dimensional fingering, triple correlation of concentration and scalar dissipation rate (rate at which the concentration variance decays due to diffusion) have to be modelled in the general case. For this purpose, an ensemble-averaged Darcy modelling (EADM) approach is proposed.