We consider two cases of interaction between a planar shock and a cylindrical density interface. In the first case (planar normal shock), the axis of the gas cylinder is parallel to the shock front and baroclinic vorticity deposited by the shock is predominantly two dimensional (directed along the axis of the cylinder). In the second case, the cylinder is tilted, resulting in an oblique shock interaction and a fully-three-dimensional shock-induced vorticity field. The statistical properties of the flow for both cases are analyzed based on images from two orthogonal visualization planes, using structure functions of the intensity maps of fluorescent tracer premixed with heavy gas. At later times, these structure functions exhibit power-law-like behavior over a considerable range of scales. Manifestation of this behavior is remarkably consistent in terms of dimensionless time $\tau$ defined based on Richtmyer's linear theory within the range of Mach numbers from 1.1 to 2.0 and the range of gas cylinder tilt angles with respect to the plane of the shock front ($0–{30}^{\circ }$).

In this paper we study the effects of a stiffened gas equation of state for air at high pressure and air chemistry with dissociation in numerical simulations of bubble collapse in water. Two types of bubble collapse are studied, with one corresponding to spherically symmetric collapse simulating single-bubble sonoluminescence (SBSL), and the other a GPa-shock-induced axisymmetric bubble collapse. The numerical method is a finite-volume based solver with diffuse material interface model. Verification and validation of the solver are demonstrated by comparing to analytical solutions and experimental observations. We find that for sonoluminescence, air chemistry and equation of state for air at high pressures can have significant effects on the peak temperature and pressure attained during the evolution, and that the peak temperature is on the order of 1 eV, which is close to that observed in experiments. For shock-induced bubble collapse, the pressure inside the bubble will not be as high as that in sonoluminescence due to the absence of spherical symmetry. However, the air chemistry still has a significant effect on the temperature of the bubble. We also examine the effect of multiple bubble interaction in shock-induced bubble collapse and find several mechanisms that can significantly increase the pressure in the water. These mechanisms include frontal-distal-side-collision, shock focusing, upstream-traveling shocks, and compression of the water near the centerline by the vortex generated by bubble collapse. These have important implications for cavitation erosion.

Film hydrodynamics is crucial in water-driven morphological pattern formation. A prominent example is given by icicle ripples and ice ripples, which are regular patterns developing on freezing-melting inclined surfaces bounding open-channel flows. By a suitable mathematical model based on conservation principles and the use of the cusp map method, in this paper we address the convective-absolute nature of these two kinds of instabilities. The obtained results show that icicle ripples, which develop at inverted (overhang) conditions, have subcentimetric wavelengths which are unstable when the Reynolds number of the liquid flow ($\mathrm{Re}$) is small and the supercooling is intensive. With the increase in $\mathrm{Re}$, the instability switches from absolute to convective. Ice ripples instead exhibit the opposite dependance on $\mathrm{Re}$ and are highly affected by the surface slope. In addition, the evaluation of the so-called absolute wave number, which is responsible for the asymptotic impulse response, suggests a different interpretation of some recent experiments about ice ripples.

Roughness-induced transient growth has emerged as a possible cause for transition in linearly stable boundary layer flows over spherical forebodies. This paper investigates the optimal growth of perturbations in the axisymmetric, laminar boundary layer over a hemisphere placed in a Mach 7.32 free stream, with the goals of contributing further insights and revisiting highly successful, transient-growth based prediction criteria for subcritical transition over blunt body configurations. Earlier predictions based on local-similarity approximation to the basic state are extended to a basic state that is obtained from the compressible Navier-Stokes equations and, hence, accounts for the presence of the bow shock, the nonsimilar development of the boundary layer, and the convex curvature of the body surface. The predicted transient growth characteristics are profoundly different from the previous body of results for boundary layer flows over flat plates and circular cones. More importantly, the selections of energy norm and objective function used to compute optimal growth exert a crucial influence on the optimal growth characteristics of a blunt body. With the conventional energy norm based on both kinetic and thermodynamic fluctuations, the highest energy gain from the input station to the output station occurs over relatively short optimization intervals in the vicinity of the stagnation point; however, the associated kinetic energy gain, which is more closely linked to transition via streak instabilities, is rather small in magnitude. On the other hand, the mean kinetic energy gain is maximized when the disturbance inflow location nearly coincides with the location corresponding to peak wall shear associated with the basic state. Assuming that the roughness-induced disturbance velocities are proportional to the roughness height, the maximum disturbance kinetic energy would be reached in the vicinity of the sonic point, which could explain the measured onset of transition within this region during prior wind-tunnel and flight experiments.

In this study, a wavelet-based method for extraction of clusters of inertial particles in turbulent flows is presented that is based on decomposing Eulerian particle-number-density fields into the sum of coherent (organized) and incoherent (disorganized) components. The coherent component is associated with the clusters and is extracted by filtering the wavelet-transformed particle-number-density field based on an energy threshold. The method is applied to direct numerical simulations of homogeneous-isotropic turbulence laden with small Lagrangian particles. The analysis shows that in regimes where the preferential concentration is important, the coherent component representing the clusters can be described by just $1.6\%$ of the total number of wavelet coefficients, thereby illustrating the sparsity of the particle-number-density field. On the other hand, the incoherent portion is visually structureless and much less correlated than the coherent one. An application of the method, motivated by particle-laden radiative-heat-transfer simulations, is illustrated in the form of a grid-adaptation algorithm that results in nonuniform meshes with fine and coarse elements near and away from particle clusters, respectively. In regimes where preferential concentration in clusters is important, the grid adaptation leads to a significant reduction of the number of control volumes by one to two orders of magnitude.

Direct numerical simulations are used to study the drag reduction by superhydrophobic surfaces in laminar channel flow. Resolved multiphase simulations using the volume of fluid methodology are performed to study the effects of groove geometry, interface shear rate, and meniscus penetration independently. An analytical solution for the flow in a laminar channel with a grooved surface with a gas pocket within is obtained. The solution accounts for both the groove geometry and the trapped fluid properties, and shows good agreement with simulation results. The solution is used to propose a scaling law that collapses data across fully wetted to fully gas-filled regimes. The trapped gas is simulated as both flat and meniscal interfaces. The drag reduction initially increases with interface deflection into the groove and then decreases for large deflections as the interface velocity approaches zero due to the proximity to the bottom of the groove.

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.