Wavelength selection of vortex ripples in an oscillating cylinder: The effect of curvature and background rotation.

We present results of laboratory experiments on the formation, evolution, and wavelength selection of vortex ripples. These ripples formed on a sediment bed at the bottom of a water-filled oscillating cylindrical tank mounted on top of a rotating table. The table is made to oscillate sinusoidally in time, while a constant background rotation was added for some experiments. The changes in bed thickness are measured using a light attenuation technique. It was found that the wavelength normalized with the excursion length depends on both a Reynolds number and the Strouhal number. This differs from straight or annular geometries where the wavelength is proportional to the excursion length. The flow in an oscillating cylinder has the peculiarity that it develops a secondary flow in the radial direction that depends on the excursion length. The effect of this secondary circulation is evident in the radial transport for small values of the Strouhal number or in the orientation of the ripples for strong enough background rotation. Additionally, ripples in an oscillating cylinder present a rich dynamic behavior where the number of ripples can oscillate even with constant forcing parameters.

Extreme Small-Scale Clustering of Droplets in Turbulence Driven by Hydrodynamic Interactions.

We perform three-dimensional particle tracking measurements on droplets in a turbulent airflow. The droplets display the well-known preferential concentration of inertial particles, with an additional extreme clustering at the smallest scales. We explain this additional clustering phenomenon theoretically based on a Stokes-flow description of two spheres including their mutual hydrodynamic interaction and a perturbative small-inertia expansion.

Lanthanide-based laser-induced phosphorescence for spray diagnostics.

Laser-induced phosphorescence (LIP) is a relatively recent and versatile development for studying flow dynamics. This work investigates certain lanthanide-based molecular complexes for their use in LIP for high-speed sprays. Lanthanide complexes in solutions have been shown to possess long phosphorescence lifetimes (∼1-2 ms) and to emit light in the visible wavelength range. In particular, europium and terbium complexes are investigated using fluorescence/phosphorescence spectrometry, showing that europium-thenoyltrifluoracetone-trioctylphosphineoxide (Eu-TTA-TOPO) can be easily and efficiently excited using a standard frequency-tripled Nd:YAG laser. The emitted spectrum, with maximum intensity at a wavelength of 614 nm, is shown not to vary strongly with temperature (293-383 K). The decay constant of the phosphorescence, while independent of ambient pressure, decreases by approximately 12 µs/K between 323 and 373 K, with the base level of the decay constant dependent on the used solvent. The complex does not luminesce in the gas or solid state, meaning only the liquid phase is visualized, even in an evaporating spray. By using an internally excited spray containing the phosphorescent complex, the effect of vaporization is shown through the decrease in measured intensity over the length of the spray, together with droplet size measurements using interferometric particle imaging. This study shows that LIP, using the Eu-TTA-TOPO complex, can be used with different solvents, including diesel surrogates. Furthermore, it can be easily handled and used in sprays to investigate spray breakup and evaporation.

On the suitability of steady RANS CFD for forced mixing ventilation at transitional slot Reynolds numbers.

UNLABELLED: Accurate prediction of ventilation flow is of primary importance for designing a healthy, comfortable, and energy-efficient indoor environment. Since the 1970s, the use of computational fluid dynamics (CFD) has increased tremendously, and nowadays, it is one of the primary methods to assess ventilation flow in buildings. The most commonly used numerical approach consists of solving the steady Reynolds-averaged Navier-Stokes (RANS) equations with a turbulence model to provide closure. This article presents a detailed validation study of steady RANS for isothermal forced mixing ventilation of a cubical enclosure driven by a transitional wall jet. The validation is performed using particle image velocimetry (PIV) measurements for slot Reynolds numbers of 1000 and 2500. Results obtained with the renormalization group (RNG) k-ε model, a low-Reynolds k-ε model, the shear stress transport (SST) k-ω model, and a Reynolds stress model (RSM) are compared with detailed experimental data. In general, the RNG k-ε model shows the weakest performance, whereas the low-Re k-ε model shows the best agreement with the measurements. In addition, the influence of the turbulence model on the predicted air exchange efficiency in the cubical enclosure is analyzed, indicating differences up to 44% for this particular case. PRACTICAL IMPLICATIONS: This article presents a detailed numerical study of isothermal forced mixing ventilation driven by a low-velocity (transitional) wall jet using steady computational fluid dynamics (CFD) simulations. It is shown that the numerically obtained room airflow patterns are highly dependent on the chosen turbulence model and large differences with experimentally obtained velocity fields can be present. The renormalization group (RNG) k-ε model, which is commonly used for room airflow modeling, shows the largest deviations from the measured velocities, indicating the care that must be taken when selecting a turbulence model for room airflow prediction. As a result of the different predictions of the flow pattern in the room, large differences are present between the predicted air exchange efficiency obtained with the four tested turbulence models, which can be as high as 44%.

Large-Eddy Simulation of pollutant dispersion around a cubical building: analysis of the turbulent mass transport mechanism by unsteady concentration and velocity statistics.

Pollutant transport due to the turbulent wind flow around buildings is a complex phenomenon which is challenging to reproduce with Computational Fluid Dynamics (CFD). In the present study we use Large-Eddy Simulation (LES) to investigate the turbulent mass transport mechanism in the case of gas dispersion around an isolated cubical building. Close agreement is found between wind-tunnel measurements and the computed average and standard deviation of concentration in the wake of the building. Since the turbulent mass flux is equal to the covariance of velocity and concentration, we perform a detailed statistical analysis of these variables to gain insight into the dispersion process. In particular, the fact that turbulent mass flux in the streamwise direction is directed from the low to high levels of mean concentration (counter-gradient mechanism) is explained. The large vortical structures developing around the building are shown to play an essential role in turbulent mass transport.

CFD simulation of pollutant dispersion around isolated buildings: on the role of convective and turbulent mass fluxes in the prediction accuracy.

Computational Fluid Dynamics (CFD) is increasingly used to predict wind flow and pollutant dispersion around buildings. The two most frequently used approaches are solving the Reynolds-averaged Navier-Stokes (RANS) equations and Large-Eddy Simulation (LES). In the present study, we compare the convective and turbulent mass fluxes predicted by these two approaches for two configurations of isolated buildings with distinctive features. We use this analysis to clarify the role of these two components of mass transport on the prediction accuracy of RANS and LES in terms of mean concentration. It is shown that the proper simulation of the convective fluxes is essential to predict an accurate concentration field. In addition, appropriate parameterization of the turbulent fluxes is needed with RANS models, while only the subgrid-scale effects are modeled with LES. Therefore, when the source is located outside of recirculation regions (case 1), both RANS and LES can provide accurate results. When the influence of the building is higher (case 2), RANS models predict erroneous convective fluxes and are largely outperformed by LES in terms of prediction accuracy of mean concentration. These conclusions suggest that the choice of the appropriate turbulence model depends on the configuration of the dispersion problem under study. It is also shown that for both cases LES predicts a counter-gradient mechanism of the streamwise turbulent mass transport, which is not reproduced by the gradient-diffusion hypothesis that is generally used with RANS models.

Structure-function scaling of bounded two-dimensional turbulence.

Statistical properties of forced two-dimensional turbulence generated in two different flow domains are investigated by numerical simulations. The considered geometries are the square domain and the periodic channel domain, both bounded by lateral no-slip sidewalls. The focus is on the direct enstrophy cascade range and how the statistical properties change in the presence of no-slip boundaries. The scaling exponents of the velocity and the vorticity structure functions are compared to the classical Kraichnan-Batchelor-Leith (KBL) theory, which assumes isotropy, homogeneity, and self-similarity for turbulence scales between the forcing and dissipation scale. Our investigation reveals that in the interior of the flow domain, turbulence can be considered statistically isotropic and locally homogeneous for the enstrophy cascade range, but it is weakly intermittent. However, the scaling of the vorticity structure function indicates a steeper slope for the energy spectrum than the KBL theory predicts. Near the walls the turbulence is strongly anisotropic at all flow scales.

Scaling and asymmetry in an electromagnetically forced dipolar flow structure.

A dipolar flow structure is experimentally studied in a layer of salt solution driven by time-independent electromagnetic forcing. In particular, the response of the flow to the forcing is quantified by measuring the Reynolds number Re as a function of the Chandrasekhar number Ch (the ratio of Lorentz forces to viscous forces) and δ (the ratio of vertical to horizontal length scales of the flow domain). In agreement with theoretical predictions, two scaling regimes are found: Re~Ch/π(2) (viscous regime) and Re~Ch(1/2)δ(-1) (advective regime). The transition between the two regimes at Ch(1/2)δ~π(2) is reflected in the flow geometry in the form of an asymmetry of the dipolar flow structure.

Virial theorem for an inhomogeneous medium, boundary conditions for the wave functions, and stress tensor in quantum statistics.

On the basis of the stationary Schrödinger equation, the virial theorem in an inhomogeneous external field for the canonical ensemble is proved. It is shown that the difference in the form of virial theorem is conditioned by the value of the wave-function derivative on the surface of the volume, surrounding the system under consideration. The stress tensor in such a system is determined by the average values of the wave-function space derivatives.

Three-dimensional flow in electromagnetically driven shallow two-layer fluids.

Recent experiments on a freely evolving dipolar vortex in a homogeneous shallow fluid layer have clearly shown the existence and evolution of complex three-dimensional (3D) flow structures. The present contribution focuses on the 3D structures of a dipolar vortex evolving in a stable shallow two-layer fluid. Experimentally, Stereoscopic Particle Image Velocimetry is used to measure instantaneously all three components of the velocity field in a horizontal plane and 3D numerical simulations provide the full 3D velocity and vorticity fields over the entire flow domain. Remarkably, the experimental results, supported by the numerical simulations, show to a large extent the same 3D structures and evolution as in the single-layer case. The numerical simulations indicate that the so-called frontal circulation in the two-layer fluid is due to deformations of the internal interface. The 3D flow structures will also affect the distribution of massless passive particles released at the free surface. With numerical studies it is shown that these passive particles tend to accumulate or deplete locally where the horizontal velocity field is not divergence-free. This is in contrast with pure two-dimensional incompressible flows where the divergence of the velocity field is zero by definition.

Influence of dilated cardiomyopathy and a left ventricular assist device on vortex dynamics in the left ventricle.

Together with new developments in mechanical cardiac support, the analysis of vortex dynamics in the left ventricle has become an increasingly important topic in literature. The aim of this study was to develop a method to investigate the influence of a left ventricular assist device (LVAD) on vortex dynamics in a failing ventricle. An axisymmetric fluid dynamics model of the left ventricle was developed and coupled to a lumped parameter model of the complete circulation. Simulations were performed for healthy conditions and dilated cardiomyopathy (DCM). Vortex structures in these simulations were analysed by means of automated detection. Results show that the strength of the leading vortex ring is lower in a DCM ventricle than in a healthy ventricle. The LVAD further influences the maximum strength of the vortex and also causes the vortex to disappear earlier in time with increasing LVAD flows. Understanding these phenomena by means of the method proposed in this study will contribute to enhanced diagnostics and monitoring during cardiac support.

Spontaneous angular momentum generation of two-dimensional fluid flow in an elliptic geometry.

Spontaneous spin-up, i.e., the significant increase of the total angular momentum of a flow that initially has no net angular momentum, is very characteristic for decaying two-dimensional turbulence in square domains bounded by rigid no-slip walls. In contrast, spontaneous spin-up is virtually absent for such flows in a circular domain with a no-slip boundary. In order to acquire an understanding of this strikingly different behavior observed on the square and the circle, we consider a set of elliptic geometries with a gradual increase of the eccentricity. It is shown that a variation of the eccentricity can be used as a control parameter to tune the relative contribution of the pressure and viscous stresses in the angular momentum balance. Direct numerical simulations demonstrate that the magnitude of the torque can be related to the relative contribution of the pressure. As a consequence, the number of spin-up events in an ensemble of slightly different initial conditions depends strongly on the eccentricity. For small eccentricities, strong and rapid spin-up events are observed occasionally, whereas the majority of the runs do not show significant spin-up. Small differences in the initial condition can result in a completely different evolution of the flow and an appearance of the end state of the decay process. For sufficiently large eccentricities, all the runs in the ensemble demonstrate strong and rapid spin-up, which is consistent with the flow development on the square. It is verified that the number of spin-up events for a given eccentricity does not depend on the Reynolds number of the flow. This observation is consistent with the conjecture that it is the pressure on the domain boundaries that drives the spin-up processes.

Diffusion in a time-dependent external field.

The problem of diffusion in a time-dependent (and generally inhomogeneous) external field is considered on the basis of a generalized master equation with two times, introduced by Trigger and co-authors [S. A. Trigger, G. J. F. van Heijst, and P. P. J. M. Schram, Physica A 347, 77 (2005); J. Phys.: Conf. Ser. 11, 37 (2005)]. We consider the case of the quasi-Fokker-Planck approximation, when the probability transition function for diffusion (PTD function) does not possess a long tail in coordinate space and can be expanded as a function of instantaneous displacements. The more complicated case of long tails in the PTD will be discussed separately. We also discuss diffusion on the basis of hydrodynamic and kinetic equations and show the validity of the phenomenological approach. A type of "collision" integral is introduced for the description of diffusion in a system of particles, which can transfer from a moving state to the rest state (with some waiting time distribution). The solution of the appropriate kinetic equation in the external field also confirms the phenomenological approach of the generalized master equation.

Attractor crisis and bursting in a fluid flow with two no-slip directions.

Characteristic bursting behavior is observed in a driven, two-dimensional viscous flow, confined to a square domain and subject to no-slip boundaries. Passing a critical parameter value, an existing chaotic attractor undergoes a crisis, after which the flow initially enters a transient bursting regime. Bursting is caused by ejections from and return to a limited subdomain of the phase space, whereas the precrisis chaotic set forms the asymptotic attractor of the flow. For increasing values of the control parameter the length of the bursting regime increases progressively. Passing another critical parameter value, a second crisis leads to the appearance of a secondary type of bursting, of very large dynamical range. Within the bursting regime the flow then switches in irregular intervals from the primary to the secondary type of bursting. Peak enstrophy levels for both types of bursting are associated to the collapse of a primary vortex into a quadrupolar state.

Merger of coherent structures in time-periodic viscous flows.

Inertia-induced changes in transport properties of an incompressible viscous time-periodic flow are studied in terms of the topological properties of volume-preserving maps. In the noninertial limit, the flow admits one constant of motion and thus relates to a so-called one-action map. However, the invariant surfaces corresponding to the constant of motion are topologically equivalent to spheres rather than the common case of tori. This has fundamental ramifications for the effect of inertia and leads to a new kind of response scenario: resonance-induced merger of coherent structures.

Transition to chaos in a confined two-dimensional fluid flow.

For a two-dimensional fluid in a square domain with no-slip walls, new direct numerical simulations reveal that the transition from steady to chaotic flow occurs through a sequence of various periodic and quasiperiodic flows, similar to the well-known Ruelle-Takens-Newhouse scenario. For all solutions beyond the ground state, the phenomenology is dominated by a domain-filling circulation cell, whereas the associated symmetry is reduced from the full symmetry group of the square to rotational symmetry over an angle pi. The results complement both laboratory experiments in containers with rigid walls and numerical simulations on double-periodic domains.

Kinetic theory of Jeans instability.

Kinetic treatment of the Jeans gravitational instability, with collisions taken into account, is presented. The initial-value problem for the distribution function which obeys the kinetic equation, with the collision integral conserving the number of particles, is solved. Dispersion relation is obtained and analyzed. New modes are found. Collisions are shown not to affect the Jeans instability criterion. Although the instability growth rate diminishes, the collisions they cannot quench the instability. However, the oscillation spectrum is modified significantly: even in the neighborhood of the threshold frequency omega=0 (separating stable and unstable modes) the spectrum of oscillations can strongly depend on the collision frequency. Propagating (rather than aperiodic) modes are also found. These modes, however, are strongly damped.

Quasi-two-dimensional turbulence in shallow fluid layers: the role of bottom friction and fluid layer depth.

The role of bottom friction and the fluid layer depth in numerical simulations and experiments of freely decaying quasi-two-dimensional turbulence in shallow fluid layers has been investigated. In particular, the power-law behavior of the compensated kinetic energy E0(t)=E(t)e(2lambda t), with E(t) the total kinetic energy of the flow and lambda the bottom-drag coefficient, and the compensated enstrophy Omega(0)(t)=Omega(t)e(2lambda t), with Omega(t) the total enstrophy of the flow, have been studied. We also report on the scaling exponents of the ratio Omega(t)/E(t), which is considered as a measure of the characteristic length scale in the flow, for different values of lambda. The numerical simulations on square bounded domains with no-slip boundaries revealed bottom-friction independent power-law exponents for E0(t), Omega(0)(t), and Omega(t)/E(t). By applying a discrete wavelet packet transform technique to the numerical data, we have been able to compute the power-law exponents of the average number density of vortices rho(t), the average vortex radius a(t), the mean vortex separation r(t), and the averaged normalized vorticity extremum omega(ext)(t)/square root E(t). These decay exponents proved to be independent of the bottom friction as well. In the experiments we have varied the fluid layer depth, and it was found that the decay exponents of E0(t), Omega(0)(t), Omega(t)/E(t), and omega(ext)(t)/square root E(t) are virtually independent of the fluid layer depth. The experimental data for rho(t) and a(t) are less conclusive; power-law exponents obtained for small fluid layer depths agree with those from previously reported experiments, but significantly larger power-law exponents are found for experiments with larger fluid layer depths.

Dissipation of kinetic energy in two-dimensional bounded flows.

The role of no-slip boundaries as an enstrophy source in two-dimensional (2D) flows has been investigated for high Reynolds numbers. Numerical simulations of normal and oblique dipole-wall collisions are performed to investigate the dissipation of the kinetic energy E(t), and the evolution of the enstrophy Omega(t) and the palinstrophy P(t). It is shown for large Reynolds numbers that dE(t)/dt=-2Omega(t)/Re proportional, variant 1/sqrt[Re] instead of the familiar relation dE(t)/dt proportional, variant 1/Re as found for 2D unbounded flows.