Despite the importance of pulsed jets for underwater propulsion, the effect of multiple-jet interactions remains poorly understood. We experimentally investigate how interactions between parallel jets in a pulsed-jet thruster affect the thruster's propulsive performance. Using high-speed fluorescence imaging, we investigate the mutual influence of two pulsed jets under conditions relevant to low-speed maneuvering in a vehicle ($\mathrm{Re}\approx 350, L/D\le 2$). Thrust production and propulsive efficiency are evaluated for different nozzle spacings using a new force estimation technique based on the fluorescence data. This analysis reveals that compared to noninteracting jets, the efficiency and thrust generated by the pair of interacting jets can fall by as much as 10% when the jets are brought into close proximity. Empirically, the thrust $T$ falls off with the nondimensional jet spacing $\tilde{\mathrm{\Delta }}$ as $T=T_{\infty }(1-Co{\tilde{\mathrm{\Delta }}}^{-6})$ for a thrust coupling coefficient $Co=2.04\pm 0.11.$ Finally, we predict this dependence of thrust on spacing using a model that relates the thrust and efficiency drop to streamline curvature and vortex induction at the nozzles.

The relationship between Koopman mode decomposition, resolvent mode decomposition, and exact invariant solutions of the Navier-Stokes equations is clarified. The correspondence rests upon the invariance of the system operators under symmetry operations such as spatial translation. The usual interpretation of the Koopman operator is generalized to permit combinations of such operations, in addition to translation in time. This invariance is related to the spectrum of a spatiotemporal Koopman operator, which has a traveling-wave interpretation. The relationship leads to a generalization of dynamic mode decomposition, in which symmetry operations are applied to restrict the dynamic modes to span a subspace subject to those symmetries. The resolvent is interpreted as the mapping between the Koopman modes of the Reynolds stress divergence and the velocity field. It is shown that the singular vectors of the resolvent (the resolvent modes) are the optimal basis in which to express the velocity field Koopman modes where the latter are not a priori known.

An experimental investigation of nonlinear scale interactions in a forced turbulent boundary layer is presented here. A dynamic wall perturbation mechanism was used to externally force two distinct large-scale synthetic modes with well-defined spatial and temporal wave numbers in a fully turbulent flow. The focus is on characterizing the nonlinear flow response at triadically consistent wave numbers that arises from the direct interactions of the two synthetic modes. These experimental results isolate triadic scale interactions in wall turbulence in a unique fashion, and provide the ability to explore the dynamics of scale coupling in a systematic and detailed manner. The ideas advanced here are intended to contribute towards modeling efforts of high-Reynolds-number wall turbulence.

The impact of a turbulent flow on wind-driven oceanic near-inertial waves is examined using a linearized shallow-water model of the mixed layer. Modeling the flow as a homogeneous and stationary random process with spatial scales comparable to the wavelengths, we derive a transport (or kinetic) equation governing wave-energy transfers in both physical and spectral spaces. This equation describes the scattering of the waves by the flow which results in a redistribution of energy between waves with the same frequency (or, equivalently, with the same wave number) and, for isotropic flows, in the isotropization of the wave field. The time scales for the scattering and isotropization are obtained explicitly and found to be of the order of tens of days for typical oceanic parameters. The predictions inferred from the transport equation are confirmed by a series of numerical simulations. Two situations in which near-inertial waves are strongly influenced by flow scattering are investigated through dedicated nonlinear shallow-water simulations. In the first, a wave packet propagating equatorward as a result from the $\beta$ effect is shown to be slowed down and dispersed both zonally and meridionally by scattering. In the second, waves generated by moving cyclones are shown to be strongly disturbed by scattering, leading again to an increased dispersion.

In a typical Richtmyer-Meshkov experiment a fast moving flat shock strikes a stationary perturbed interface between fluids $A$ and $B$ creating a transmitted and a reflected shock, both of which are perturbed. We propose shock tube experiments in which the reflected shock is stationary in the laboratory. Such a standing perturbed shock undergoes well-known damped oscillations. We present the conditions required for producing such a standing shock wave, which greatly facilitates the measurement of the oscillations and their rate of damping. We define a critical density ratio $R^{\mathrm{critical}}$, in terms of the adiabatic indices of the two fluids, and a critical Mach number $M_s^{\mathrm{critical}}$ of the incident shock wave, which produces a standing reflected wave. If the initial density ratio $R$ of the two fluids is less than $R^{\mathrm{critical}}$ then a standing shock wave is possible at $M_s=M_s^{\mathrm{critical}}$. Otherwise a standing shock is not possible and the reflected wave always moves in the direction opposite the incident shock. Examples are given for present-day operating shock tubes with sinusoidal or inclined interfaces. We consider the effect of viscosity, which affects the damping rate of the oscillations. We point out that nonlinear bubble and spike amplitudes depend relatively weakly on the viscosity of the fluids and that the interface area is a better diagnostic.

In this study we analyze the interaction of a single rising bubble with an inclined wall. We conduct experiments considering different liquids and bubble sizes, to cover a wide range of Reynolds and Weber numbers, with wall angles from nearly horizontal to nearly vertical. For all cases, the bubble initially collides with the wall; after the initial interaction, in accord with previous studies, the bubble either steadily slides on the wall or ascends, colliding repeatedly with it. Considering a force balance for the bubble motion on the wall, we propose a set of conditions for the transition from sliding to bouncing that is validated with the present and previous data.

An object immersed in a fast flow typically experiences fluid forces that increase with the square of speed. Here we explore how this high-Reynolds-number force-speed relationship is affected by unsteady motions of a body. Experiments on disks that are driven to oscillate while progressing through air reveal two distinct regimes: a conventional quadratic relationship for slow oscillations and an anomalous scaling for fast flapping in which the time-averaged drag increases linearly with flow speed. In the linear regime, flow visualization shows that a pair of counterrotating vortices is shed with each oscillation and a model that views a train of such dipoles as a momentum jet reproduces the linearity. We also show that appropriate scaling variables collapse the experimental data from both regimes and for different oscillatory motions into a single drag-speed relationship. These results could provide insight into the aerodynamic resistance incurred by oscillating wings in flight and they suggest that vibrations can be an effective means to actively control the drag on an object.

We perform experiments to investigate the relaxation of a highly deformed elastic filament at a liquid-air interface. The dynamics for filaments of differing length, diameter, and elastic modulus collapse to a single curve when the time dependence is scaled by a time scale $\tau =8\pi \mu L_o^4/B$. Even though the time $\tau$ is obtained by comparing the linear bending and viscous forces, we find that it also controls the relaxation in the highly nonlinear regime of our experiments. The relaxation, however, is completed in a very small fraction of the time $\tau$ due to a prefactor that changes with the tension in the nonlinear regime. Nonlinear numerical simulations show that the force due to tension along the filament is comparable to the bending force, producing a net elastic restoring force that is much smaller than either term. We perform particle image velocimetry at the liquid-air interface to support the results of the numerics. Finally, we find that when the filament is initialized in asymmetric shapes, it rapidly goes to a shape with symmetric stresses. This symmetrization process is entirely nonlinear; we show that the symmetric curvature state minimizes energy at arbitrarily large deformation.

Elastic capsules flowing in small enough tubes, such as red blood cells in capillaries, are well known to line up into regular single-file trains. The stability of such trains in somewhat wider channels, where this organization is not observed, is studied in a two-dimensional model system that includes full coupling between the viscous flow and suspended capsules. A diverse set of linearly amplifying disturbances, both long-time asymptotic (modal) and transient (nonmodal) perturbations, is identified and analyzed. These have a range of amplification rates and their corresponding forms are wavelike, typically dominated by one of five principal perturbation classes: longitudinal and transverse translations, tilts, and symmetric and asymmetric shape distortions. Finite-amplitude transiently amplifying perturbations are shown to provide a mechanism that can bypass slower asymptotic modal linear growth and precipitate the onset of nonlinear effects. Direct numerical simulations are used to verify the linear analysis and track the subsequent transition of the regular capsule trains into an apparently chaotic flow.

Diffusiophoresis, a ubiquitous phenomenon that induces particle transport whenever solute concentration gradients are present, was recently observed in the context of microsystems and shown to strongly impact colloidal transport (patterning and mixing) at such scales. In the present work we show experimentally that this nanoscale mechanism can induce changes in the macroscale mixing of colloids by chaotic advection. Rather than the decay of the standard deviation of concentration, which is a global parameter commonly employed in studies of mixing, we instead use multiscale tools adapted from studies of chaotic flows or intermittent turbulent mixing: concentration spectra and second and fourth moments of the probability density functions of scalar gradients. Not only can these tools be used in open flows, but they also allow for scale-by-scale analysis. Strikingly, diffusiophoresis is shown to affect all scales, although more particularly the small ones, resulting in a change of scalar intermittency and in an unusual scale bridging spanning more than seven orders of magnitude. By quantifying the averaged impact of diffusiophoresis on the macroscale mixing, we explain why the effects observed are consistent with the introduction of an effective Péclet number.

We quantify the dynamics of a prolate leaky dielectric drop upon removal of a uniform dc electric field. Experiments consisting of a castor oil drop suspended in silicone oil are compared against axisymmetric boundary integral computations that account for transient charging, or charge relaxation, of the interface. A temporal asymmetry between the drop deformation and relaxation processes is observed in the experiments and computations: The drop relaxes back to its spherical equilibrium shape faster than the time taken to achieve its steady-state deformation. During the deformation process, the electrical (Maxwell) stress deforms the drop along the direction of the applied field; it is counteracted by the capillary stress. During the relaxation process, i.e., after the field is removed, the electrical stress acts together with the capillary stress to quickly restore the drop back to equilibrium. This change in action of the electrical stress is responsible for the asymmetry between the drop deformation and relaxation. Notably, the electrical stress acts over the charge relaxation time scales of the fluids: Thus, counterintuitively, longer charging time scales yield faster drop relaxation. That is, the longer it takes for the interface to discharge, the faster the drop shape relaxes. We also present computational results for a drop that does not relax back to its initial spherical shape upon removal of the electric field; rather, the drop breaks up via an end-pinching mechanism.

An object moving through a plane interface into a fluid deforms the interface in such a way that fluid from one side of the interface is entrained into the other side, a phenomenon known as Darwin's drift. We investigate this phenomenon experimentally using a disk which is started exactly at the interface of two immiscible fluids, namely, oil and water. First, we observe that due to the density difference between the two fluids the deformation of the interface is influenced by gravity and show that there exists a time window of universal behavior. Second, we show by comparing with boundary integral simulations that, even though the deformation is universal, our results cannot be fully explained by potential flow solutions. We attribute this difference to the starting vortex, which is created in the wake of the disk. Besides contributing significantly to entrainment directly, the vortex also influences the interface deformation due to Darwin's drift. Universal behavior is preserved, however, because the size and strength of the vortex shows the same universality as the potential flow solution.

We demonstrate that porous nematic microfluidics is a potential route for the generation of nematic umbilic defects and regular umbilic defect lattices. By using numerical modeling we show that the mutual (backflow) coupling between the flow velocity and the orientation director field of the nematic liquid crystal leads to the formation of positive umbilic defects at local peaks and to the formation of negative umbilic defects at the local saddles in the flow profile. The number of flow peaks and the index of the flow saddles (i.e., the number of the valleys) are shown to be directly related to the strength of the umbilic defect, effectively relating the two fields at the geometrical level. The regular arrangement of the barriers in the porous channels is demonstrated to lead to the formation of regular lattices of umbilic defects, including square, triangular, and even kagome lattices. Experimental realization of such systems is discussed, with particular focus on microfluidic-tunable birefringent photonic band structures and lattices.

The lattice-Boltzmann method is used to compute the flow of a particle suspension of dilute volume fraction $\varphi \le 0.08$ around obstacles. The work focuses on the interaction of particles with the obstacle and the flow behavior in and around the recirculating wake behind the obstacle. Motivated by microfluidic experiments of dilute suspension flow over obstacles of circular, square, and other shapes showing depletion of particles in the wake behind the obstacle, we focus on the entry and exit from the wake for isolated particles, small groups of particles, and a suspension of many particles. All work is at conditions well below the Reynolds number for the transition to unsteady flow and vortex shedding. The dynamics of an isolated particle inside the recirculating wake flow exhibits motion toward a limit cycle near the outer boundary of the wake. By increasing particle density above the fluid and increasing the size of the particle, we determine the upper limits of these variables yielding a limit cycle trajectory. Hydrodynamic interaction between particles in a many-particle suspension is shown to lead to exchange of particles between the wake zone and free stream.

In the study of convective heat and mass transfer from a particle, key quantities of interest are usually the average rate of transfer and the mean distribution of the scalar (i.e., temperature or concentration) at the particle surface. Calculating these quantities using conventional equations requires detailed knowledge of the scalar field, which is available predominantly for problems involving uniform scalar and flux boundary conditions. Here we derive a reciprocal relation between two diffusing scalars that are advected by oppositely driven Stokes or potential flows whose streamline configurations are identical. This relation leads to alternative expressions for the aforementioned average quantities based on the solution of the scalar field for uniform surface conditions. We exemplify our results via two applications: (i) heat transfer from a sphere with nonuniform boundary conditions in Stokes flow at small Péclet numbers and (ii) extension of Brenner's theorem for the invariance of heat transfer rate to flow reversal.

We report the space-time characteristics of the wall-pressure fluctuations and wall shear-stress fluctuations from wall-modeled large eddy simulation (WMLES) of a turbulent channel flow at ${\text{Re}}_{\tau }=2000$. Two standard zonal wall models (equilibrium stress model and nonequilibrium model based on unsteady RANS) are employed, and it is shown that they yield similar results in predicting these quantities. The wall-pressure and wall shear-stress fields from WMLES are analyzed in terms of their r.m.s. fluctuations, spectra, two-point correlations, and convection velocities. It is demonstrated that the resolution requirement for predicting the wall-pressure fluctuations is more stringent than that for predicting the velocity. At least $\delta /\mathrm{\Delta }x>20$ and $\delta /\mathrm{\Delta }z>30$ are required to marginally resolve the integral length scales of the pressure-producing eddies near the wall. Otherwise, the pressure field is potentially aliased. Spurious high wave number modes dominate in the streamwise direction, and they contaminate the pressure spectra leading to significant overprediction of the second-order pressure statistics. When these conditions are met, the pressure statistics and spectra at low wave number or low frequency agree well with the DNS and experimental data. On the contrary, the wall shear-stress fluctuations, modeled entirely through the RANS-based wall models, are largely underpredicted and relatively insensitive to the grid resolution. The short-time, small-scale near-wall eddies, which are neither resolved nor modeled adequately in the wall models, seem to be important for accurate prediction of the wall shear-stress fluctuations.

Recent studies have shown Townsend's attached eddy hypothesis to be a promising basis for modeling the velocity statistics in the logarithmic region of turbulent wall flows. Accordingly, the attached eddy model is able to reliably estimate the functional forms of the mean velocity, second-order moments of the velocity fluctuations, and recently structure functions and higher-order moments of the velocity fluctuations. However, detailed quantitative comparisons with experimental results reveal differences, particularly for the higher-order moments. Specifically, the predicted flatness (kurtosis) is found to be invariably greater than 3 (i.e., super-Gaussian behavior) for all velocity components, while experimental results show sub-Gaussian behavior for the streamwise component of velocity. In this study, we show that this and other discrepancies can be resolved by considering the finite space occupied by each eddy. Earlier models had allowed each eddy to be perfectly randomly located, with no consideration for the locations of neighboring eddies (in other words, their locations can be described as a Poisson point process). Here we investigate the effect of mandating a minimum distance between any two eddies of the same height. We demonstrate that this spatial exclusion, when combined with an experimentally observed shape for the representative eddy, produces predictions that are now in better agreement with experimental observations. In particular, sub-Gaussian behavior is now attained for the streamwise component, while super-Gaussian behavior is maintained for the other velocity components, qualitatively matching experimental findings. Therefore, our findings infer that spatial exclusion between eddies is likely to play an important role in the laws that govern their spatial arrangement, which is likely to be more disperse than a Poisson point process.

The flow in a rapidly rotating cylinder forced to precess through a nutation angle $\alpha$ is investigated numerically, keeping all parameters constant except $\alpha$, and tuned to a triadic resonance at $\alpha =1^{\circ }$. When increasing $\alpha$, the flow undergoes a sequence of well-characterized bifurcations associated with triadic resonance, involving heteroclinic and homoclinic cycles, for $\alpha$ up to about $4^{\circ }$. For larger $\alpha$, we identify two chaotic regimes. In the first regime, with $\alpha$ between about $4^{\circ }$ and ${27}^{\circ }$, the bulk flow retains remnants of the helical structures associated with the triadic resonance, but there are strong nonlinear interactions between the various azimuthal Fourier components of the flow. For the larger $\alpha$ regime, large detuning effects lead to the triadic resonance dynamics being completely swamped by boundary layer eruptions. The azimuthal mean flow at large angles results in a large mean deviation from solid-body rotation and the flow is characterized by strong shear at the boundary layers with temporally chaotic eruptions.

In a recent Letter [Phys. Rev. Lett. 116, 138302 (2016)] Würger calculated the thermophoretic velocity of a colloidal sphere towards a solid boundary due to an imposed temperature gradient perpendicular to that wall in the limit where the particle-wall separation distance $h$ is small compared to the particle radius $a$. Würger obtained the approximation $u/u_0=3(h/a)[ln(a/h)-2.25]$ for the particle velocity $u$ towards the wall, $u_0$ being the corresponding velocity in the bulk. In deriving that approximation an ad hoc procedure was employed to circumvent the calculation of a diverging integral that emerges in the course of a lubrication analysis. We show here how to systematically address this problem, obtaining the approximation $u/u_0=3(h/a)[ln(a/h)+0.1087]$.

Transition to turbulence in pipe flow is investigated experimentally using a temporally resolved dual-plane particle image velocimetry approach, at a Reynolds number of 3440. The flow is analyzed using proper orthogonal decomposition and it is shown that the flow can be divided into two regions: a pseudolaminar region governed by the presence of azimuthally steady traveling waves, and turbulent slugs. The evolution of the structures within the slugs is identified by using the temporally resolved data along with the dual-plane velocity field. These structures are shown to be remarkably similar to the large-scale motions found in fully turbulent flows, with a streamwise and spatiotemporal extent about four pipe radii. The transition between structures is characterized by the detachment and decay of an old structure and the initiation of a new structure at the wall.