The relation between self-preservation (SP) and the Kolmogorov similarity hypotheses (Kolmogorov, The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers, Dokl. Akad. Nauk SSSR 30, 301 (1941) [Proc. R. Soc. London A 434, 9 (1991)]) is investigated through the transport equations for the second- and third-order moments of the longitudinal velocity increments $\mathrm{[}\delta u(r,t)=u(x,t)-u(x+r,t)$, where $x,t$, and $r$ are the spatial point and the time and longitudinal separation between two points, respectively]. It is shown that the fluid viscosity $\nu$ and the mean turbulent kinetic energy dissipation rate $\overline{\epsilon }$ (the overbar represents an ensemble average) emerge naturally from the equations of motion as controlling parameters for the velocity increment moments when SP is assumed. Consequently, the Kolmogorov length scale $\eta$ $[\equiv {({\nu }^3/\overline{\epsilon })}^{1/4}]$ and velocity scale $v_K$ $[\equiv {\left(\nu \overline{\epsilon }\right)}^{1/4}]$ also emerge as natural scaling parameters in conformity with SP, indicating that Kolmogorov's first hypothesis is subsumed under the more general hypothesis of SP. Further, the requirement for a very large Reynolds number is also relaxed, at least for the first similarity hypothesis. This requirement however is still necessary to derive the two-thirds law (or the four-fifths law) from the analysis. These analytical results are supported by experimental data in wake, jet, and grid turbulence. An expression for the fourth-order moment of the longitudinal velocity increments $\overline{{\left(\delta u\right)}^4}$ is derived from the analysis carried out in the inertial range. The expression, which involves the product of ${\left(\delta u\right)}^2$ and $\partial \delta p/\partial x$, does not require the use the volume-averaged dissipation ${\overline{\epsilon }}_r$, introduced by Oboukhov [Oboukhov, Some specific features of atmospheric turbulence, J. Fluid Mech. 13, 77 (1962)] on a phenomenological basis and used by Kolmogorov to derive his refined similarity hypotheses [Kolmogorov, A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, J. Fluid Mech. 13, 82 (1962)], suggesting that ${\overline{\epsilon }}_r$ is not, like $\overline{\epsilon }$, a quantity issuing from the Navier-Stokes equations.

We examine kinematic dynamo action driven by an axisymmetric large-scale flow that is superimposed with an azimuthally propagating nonaxisymmetric perturbation with a frequency $\omega$. Although we apply a rather simple large-scale velocity field, our simulations exhibit a complex behavior with oscillating and azimuthally drifting eigenmodes as well as stationary regimes. Within these nonoscillating regimes we find parametric resonances characterized by a considerable enhancement of dynamo action and by a locking of the phase of the magnetic field to the pattern of the perturbation. We find an approximate fulfillment of the relationship between the resonant frequency ${\omega }_{\mathrm{res}}$ of the excitation and the eigenfrequency ${\omega }_0$ of the undisturbed system given by ${\omega }_{\mathrm{res}}=2{\omega }_0$, which is known from paradigmatic rotating mechanical systems and our prior study [Giesecke et al., Phys. Rev. E 86, 066303 (2012)]. We find further, broader, regimes with weaker enhancement of the growth rates but without phase locking. However, this amplification regime arises only in case of a basic (i.e., unperturbed) state consisting of several different eigenmodes with rather close growth rates. Qualitatively, these observations can be explained in terms of a simple low-dimensional model for the magnetic field amplitude that is derived using Floquet theory. The observed phenomena may be of fundamental importance in planetary dynamo models with the base flow being disturbed by periodic external forces like precession or tides and for the realization of dynamo action under laboratory conditions where imposed perturbations with the appropriate frequency might facilitate the occurrence of dynamo action.

We investigate theoretically and experimentally the evaporation of liquid disks in the presence of natural convection due to a density difference between the vapor and the surrounding gas. From the analogy between thermal convection above a heated disk and our system, we derive scaling laws to describe the evaporation rate. The local evaporation rate depends on the presence of a boundary layer in the gas phase such that the total evaporation rate is given by a combination of different scaling contributions, which reflect the structure of the boundary layer. We compare our theoretical predictions to experiments performed with water in an environment controlled in humidity, which validate our approach.

The impact of wave-form shape on the wake and propulsive performance of a pitching and heaving two-dimensional foil is explored experimentally. Jacobi elliptic functions are used to define wave-form shapes that are approximately triangular, sinusoidal, or square. The triangular-like and sinusoidal waves produce qualitatively similar wakes, with a typical reverse von Kármán vortex street structure leading to a jetlike wake in the mean. Square-like motions produce very different results, with a vortex pair shed every half cycle, leading to a mean wake with two distinct off-center jets, and a significant change in the thrust production, yielding up to four times more thrust for a given Strouhal number. Performance curves indicate that to swim most efficiently sinusoidal motions are best, whereas the square-like motions lead to higher speeds. A scaling analysis indicates that the peak lateral velocity appears to be the dominant parameter in characterizing the performance of the nonsinusoidal motions.

Bifurcations of dynamos in rotating and buoyancy-driven spherical Rayleigh-Bénard convection in an electrically conducting fluid are investigated numerically. Both nonmagnetic and magnetic solution branches comprised of rotating waves are traced by path-following techniques, and their bifurcations and interconnections for different Ekman numbers are determined. In particular, the question of whether the dynamo branches bifurcate super- or subcritically and whether a direct link to the primary pure convective states exists is answered.

We investigate the flow of unsteadfy three-dimensional viscoelastic fluid through an array of symmetric and asymmetric sets of cylinders constituting a model porous medium. The simulations are performed using a finite-volume methodology with a staggered grid. The solid-fluid interfaces of the porous structure are modeled using a second-order immersed boundary method [S. De et al., J. Non-Newtonian Fluid Mech. 232, 67 (2016)]. A finitely extensible nonlinear elastic constitutive model with Peterlin closure is used to model the viscoelastic part. By means of periodic boundary conditions, we model the flow behavior for a Newtonian as well as a viscoelastic fluid through successive contractions and expansions. We observe the presence of counterrotating vortices in the dead ends of our geometry. The simulations provide detailed insight into how flow structure, viscoelastic stresses, and viscoelastic work change with increasing Deborah number De. We observe completely different flow structures and different distributions of the viscoelastic work at high De in the symmetric and asymmetric configurations, even though they have the exact same porosity. Moreover, we find that even for the symmetric contraction-expansion flow, most energy dissipation is occurring in shear-dominated regions of the flow domain, not in extensional-flow-dominated regions.

We present experimental results and a theoretical analysis for the singing of a cavitating tip vortex (SCTV), which has been occasionally observed under special conditions in a few experimental facilities around the world since the 1990s. Due to lack of repeatability, little is known about the generation mechanism of SCTV [R. E. A. Arndt, Annu. Rev. Fluid Mech. 34, 143 (2002)]. In the present work we propose an experimental procedure to produce the SCTV phenomenon at selected flow conditions in the China Ship Scientific Research Center cavitation mechanism tunnel. By analyzing the frequency characteristics of the acoustical signal and the bubble dynamics, it is found that the tone of SCTV matches the natural frequency of radial oscillation of the cylinder bubble and a formulation to predict SCTV is developed. Good agreement is obtained between the proposed formulation and the experimental data from different facilities.

Using direct numerical simulations, we demonstrate that magnetic helicity exhibits a bidirectional turbulent cascade at high but finite magnetic Reynolds numbers. Despite the injection of positive magnetic helicity in the flow, we observe that magnetic helicity of opposite signs is generated between large and small scales. We explain these observations by carrying out an analysis of the magnetohydrodynamic equations reduced to triad interactions using the Fourier helical decomposition. Within this framework, the direct cascade of positive magnetic helicity arises through triad interactions that are associated with small-scale dynamo action, while the occurrence of negative magnetic helicity at large scales is explained through triad interactions that are related to stretch-twist-fold dynamics and small-scale dynamo action, which compete with the inverse cascade of positive magnetic helicity. Our analytical and numerical results suggest that the direct cascade of magnetic helicity is a finite magnetic Reynolds number $\text{Rm}$ effect that will vanish in the limit $\text{Rm}\to \infty$.

We investigate the electrostatic stabilization of a viscous thin film wetting the underside of a horizontal surface in the presence of an electric field applied parallel to the surface. The model includes the effect of bounding solid dielectric regions above and below the liquid-air system that are typically found in experiments. The competition between gravitational forces, surface tension, and the nonlocal effect of the applied electric field is captured analytically in the form of a nonlinear evolution equation. A semispectral solution strategy is employed to resolve the dynamics of the resulting partial differential equation. Furthermore, we conduct direct numerical simulations (DNS) of the Navier-Stokes equations using the volume-of-fluid methodology and assess the accuracy of the obtained solutions in the long-wave (thin-film) regime when varying the electric field strength from zero up to the point when complete stabilization occurs. We employ DNS to examine the limitations of the asymptotically derived behavior as the liquid layer thickness increases and find excellent agreement even beyond the regime of strict applicability of the asymptotic solution. Finally, the asymptotic and computational approaches are utilized to identify robust and efficient active control mechanisms allowing the manipulation of the fluid interface in light of engineering applications at small scales, such as mixing.

New experiments with multigrain mixtures in a laterally shaken, horizontal channel show complete axial segregation of species. The channel consists of multiple concatenated trapeziums, and superficially resembles microratchets wherein asymmetric geometries and potentials transport, and sort, randomly agitated microscopic particles. However, the physics of our macroscale granular ratchet is fundamentally different, as macroscopic segregation is gravity driven. Our observations are not explained by classical granular segregation theories either. Motivated by the experiments, extensive parallelized discrete element simulations reveal that the macroratchet differentiates grains through hierarchical bidirectional segregation over two different time scales: Grains rapidly sort vertically into horizontal bands spanning the channel's length that, subsequently, slowly separate axially, driven by strikingly gentle, average interfacial pressure gradients acting over long distances. At its maximum, the pressure gradient responsible for axial separation was due to a change in height of about two big grain diameters ($d=7$ mm) over a meter-long channel. The strong directional segregation achieved by the granular macroratchet has practical importance, while identifying the underlying new physics will further our understanding of granular segregation in industrial and geophysical processes.

A decade ago, Couder and Fort [Phys. Rev. Lett. 97, 154101 (2006)] discovered that a millimetric droplet sustained on the surface of a vibrating fluid bath may self-propel through a resonant interaction with its own wave field. We here present the results of a combined experimental and theoretical investigation of the interactions of such walking droplets. Specifically, we delimit experimentally the different regimes for an orbiting pair of identical walkers and extend the theoretical model of Oza et al. [J. Fluid Mech. 737, 552 (2013)] in order to rationalize our observations. A quantitative comparison between experiment and theory highlights the importance of spatial damping of the wave field. Our results also indicate that walkers adapt their impact phase according to the local wave height, an effect that stabilizes orbiting bound states.

It is shown that a channel flow of a dilute polymer solution between two widely spaced cylinders hindering the flow is an important paradigm of an unbounded flow in the case in which the channel wall is located sufficiently far from the cylinders. The quantitative characterization of instabilities in a creeping viscoelastic channel flow between two widely spaced cylinders reveals two elastically driven transitions, which are associated with the breaking of time-reversal and mirror symmetries: Hopf and forward bifurcations described by two order parameters ${\mathbf{v}}_{\mathrm{rms}}$ and $\overline{\omega }$, respectively. We suggest that a decrease of the normalized distance between the obstacles leads to a collapse of the two bifurcations into a codimension-2 point, a situation general for many nonequilibrium systems. However, the striking and unexpected result is the discovery of a mechanism of the vorticity growth via an increase of a vortex length at the preserved streamline curvature in a viscoelastic flow, which is in sharp contrast to the well-known suppression of the vorticity in a Newtonian flow by polymer additives.

We use a variational principle to derive a mathematical model for a nematic electrolyte in which the liquid crystalline component is described in terms of a second-rank order parameter tensor. The model extends the previously developed director-based theory and accounts for the presence of disclinations and possible biaxiality. We verify the model by considering a simple but illustrative example of liquid crystal-enabled electro-osmotic flow around a stationary dielectric spherical particle placed at the center of a large cylindrical container filled with a nematic electrolyte. Assuming homeotropic anchoring of the nematic on the surface of the particle and uniform distribution of the director on the surface of the container, we consider two configurations with a disclination equatorial ring and with a hyperbolic hedgehog, respectively. The computed electro-osmotic flows show a strong dependence on the director configurations and on the anisotropies of dielectric permittivity and electric conductivity of the nematic, characteristic of liquid crystal-enabled electrokinetics. Further, the simulations demonstrate space charge separation around the dielectric sphere, even in the case of isotropic permittivity and conductivity. This is in agreement with the induced-charge electroosmotic effect that occurs in an isotropic electrolyte when an applied field acts on the ionic charge it induces near a polarizable surface.

The numerical investigation of a circular Couette flow with a radial temperature gradient is performed to elucidate the influence of the radial buoyancy on flow and heat transfer for different values of the Prandtl number when the gravitational acceleration is neglected. We consider an infinite-length cylindrical annulus of radius ratio 0.8 with the inner rotating cylinder and the outer stationary cylinder. The flow is stabilized with the outward heating while it is destabilized with the inward heating. A weakly nonlinear analysis shows that the transition to stationary axisymmetric modes is supercritical while the oscillatory axisymmetric modes occur via a subcritical bifurcation. The effect of the centrifugal buoyancy on the transfer of angular momentum (i.e., torque) is quite weak while the effect on the heat transfer is significant.

In this work, we investigate the behavior of dilute and semidilute polymer solutions flowing in a microfluidic flow focusing device, in which an inlet stream is stretched by two balanced lateral streams. By varying the flow rates in the inlet and lateral channels and their ratio, several types of flow transitions are observed and the resulting velocity fields are analyzed both upstream and downstream of the intersection. At high flow rates, the flow becomes chaotic and the path to this state depends on both the Weissenberg number and the imposed Hencky strain. The thresholds of successive elastic instabilities leading to the chaotic state are also investigated using time-resolved microparticle imaging velocimetry.

An artificial neural network (ANN) is tested as a tool for finding a new subgrid model of the subgrid-scale (SGS) stress in large-eddy simulation. An ANN is used to establish a functional relation between the grid-scale flow field and the SGS stress without any assumption of the form of function. Data required for training and test of the ANN are provided by direct numerical simulation of a turbulent channel flow. It is shown that an ANN can establish a model similar to the gradient model. The correlation coefficients between the real SGS stress and the output of the ANN are comparable to or larger than similarity models, but smaller than a two-parameter dynamic mixed model. Large-eddy simulations using the trained ANN are also performed. Although ANN models show no advantage over the Smagorinsky model, the results confirm that the ANN is a promising tool for establishing a new subgrid model with further improvement.

It is demonstrated that micron-sized particles suspended in fluid near oscillating interfaces experience strong inertial displacements above and beyond the fluid streaming. Experiments with oscillating bubbles show rectified particle lift over extraordinarily short (millisecond) times. A quantitative model on both the oscillatory and the steady time scales describes the particle displacement relative to the fluid motion. The formalism yields analytical predictions confirming the observed scaling behavior with particle size and experimental control parameters. It applies to a large class of oscillatory flows with applications from particle trapping to size sorting.

Recently Schumacher et al. [Phys. Rev. Fluids 1, 084402 (2016)] used direct numerical simulation to calculate the shear stress exerted on the top and bottom viscous boundary layers (BLs) of Rayleigh-Bénard convection with a Prandtl number $\mathrm{Pr}=0.021$ and aspect ration $\mathrm{\Gamma }=1$ for Rayleigh numbers $\mathrm{Ra}$ up to $4\times {10}^8$. By extrapolating their results to larger $\mathrm{Ra}$, they concluded that the sample would undergo a transition to turbulent BLs and enter the “ultimate state” at ${\mathrm{Ra}}^{*}\simeq {10}^{11}$ for $\mathrm{Pr}=0.021$. Here we show that their result is consistent with the experimentally determined ${\mathrm{Ra}}^{*}=2\times {10}^{13}$ for $\mathrm{Pr}=0.82$ by He et al. [Phys. Rev. Lett. 108, 024502 (2012); He et al., New J. Phys. 17, 063028 (2015)] and the $\mathrm{Pr}$ dependence of ${\mathrm{Ra}}^{*}$ predicted by Grossmann and Lohse [Phys. Rev. E 66, 016305 (2002)]. Thus the numerical results of Schumacher et al. support the interpretation of the experimentally observed transition at ${\mathrm{Ra}}^{*}=2\times {10}^{13}$ for $\mathrm{Pr}=0.82$ as the ultimate-state transition.

Lagrangian acceleration statistics in a fully developed turbulent channel flow at ${\text{Re}}_{\tau }=1440$ are investigated, based on tracer particle tracking in experiments and direct numerical simulations. The evolution with wall distance of the Lagrangian velocity and acceleration time scales is analyzed. Dependency between acceleration components in the near-wall region is described using cross-correlations and joint probability density functions. The strong streamwise coherent vortices typical of wall-bounded turbulent flows are shown to have a significant impact on the dynamics. This results in a strong anisotropy at small scales in the near-wall region that remains present in most of the channel. Such statistical properties may be used as constraints in building advanced Lagrangian stochastic models to predict the dispersion and mixing of chemical components for combustion or environmental studies.

The efficiency of fluid flow for mixing passive tracers is often limited by fundamental laws and/or design constraints, such that a perfectly homogeneous mixture cannot be obtained in finite time. Here we address the natural corollary question: Given a fluid flow, what is the optimal initial tracer pattern that leads to the most homogeneous mixture after a prescribed finite time? For ideal passive tracers, we show that this optimal initial condition coincides with the right singular vector (corresponding to the smallest singular value) of a suitably truncated Perron-Frobenius (PF) operator. The truncation of the PF operator is made under the assumption that there is a small length-scale threshold ${\ell }_{\nu }$ under which the tracer blobs are considered, for all practical purposes, completely mixed. We demonstrate our results on two examples: a prototypical model known as the sine flow and a direct numerical simulation of two-dimensional turbulence. Evaluating the optimal initial condition through this framework requires only the position of a dense grid of fluid particles at the final instance and their preimages at the initial instance of the prescribed time interval. As such, our framework can be readily applied to flows where such data are available through numerical simulations or experimental measurements.