Soliton and breather solutions of the nonlinear Schrödinger equation (NLSE) are known to model localized structures in nonlinear dispersive media such as on the water surface. One of the conditions for an accurate propagation of such exact solutions is the proper generation of the exact initial phase-shift profile in the carrier wave, as defined by the NLSE envelope at a specific time or location. Here, we show experimentally the significance of such initial exact phase excitation during the hydrodynamic propagation of localized envelope solitons and breathers, which modulate a plane wave of constant amplitude (finite background). Using the example of stationary black solitons in intermediate water depth and pulsating Peregrine breathers in deep water, we show how these localized envelopes disintegrate while they evolve over a significant long distance when the initial phase shift is zero. By setting the envelope phases to zero, the dark solitons will disintegrate into two gray-type solitons and dispersive elements. In the case of the doubly localized Peregrine breather the maximal amplification is considerably retarded; however, locally, the shape of the maximal focused wave measured together with the respective signature phase-shift are almost identical to the exact analytical Peregrine characterization at its maximal compression location. The experiments, conducted in large-scaled shallow-water as well as deep-water wave facilities, are in very good agreement with NLSE simulations for all cases.

Methylcellulose (MC), a methoxy-substituted cellulose ether, is widely used as a rheology modifier, binder, and water-retention agent in a variety of food, pharmaceutical, construction, and consumer applications. While soluble in water at low temperatures, MC reversibly transitions to a turbid hydrogel upon heating or upon the addition of NaCl, due to the formation of a fibrillar network. These complex MC solutions and gels experience a range of flow conditions in industrial processes, including shear and extensional flows. While the shear rheological behavior has been well characterized for many MC solutions, the extensional rheological behavior is often more challenging to characterize, particularly for solutions with lower molecular weights, relaxation times, and viscosities. Filament stretching using a flow-focusing microfluidic device is a promising method to resolve extensional properties of lower molecular weight and lower viscosity polymeric solutions, and it is used here to characterize MC solutions at varying NaCl concentrations. The flow-driven apparent extensional viscosity can be calculated from transient filament diameter thinning behavior of 1 wt% MC with a molecular weight of 150 kg/mol. The apparent extensional viscosity increased as the concentration of NaCl increased, from 0.947 ± 0.005 Pa s to 15.1 ± 0.6 Pa s between 0 and 8 wt% NaCl, respectively. The increase in apparent extensional viscosity is attributed to the presence of fibrils in the MC solutions containing NaCl annealed at room temperature, as demonstrated with cryogenic transmission electron microscopy. The study of the extensional behavior of this commercially relevant polymer should enable new ways to process MC, such as fiber spinning and extrusion.

Convection occurs in many settings from metal production to planetary interiors and atmospheres. To understand the dynamics of these systems it is vital to be able to predict the heat transport which is controlled by the thermal boundary layers (TBL). An important issue in the study of convective fluid dynamics is then to determine the temperature distribution within these thin layers in the vicinity of the bounding walls. Deviations from the classical Rayleigh-Bénard convection paradigm such as the addition of rotation or fixed heat-flux (rather than fixed temperature) boundaries compromise the standard ways of defining the width of the TBL. We propose an alternative method for defining the TBL using the location at which the advective and conductive contributions to the heat transport become equal. We show that this method can be robustly applied to two-dimensional (2D) nonrotating convection between no-slip boundaries with fixed temperature or fixed heat-flux thermal boundary conditions and three-dimensional (3D) rotating convection simulations with free-slip boundaries.

The addition of soluble long chain polymers to a Newtonian fluid, and the incorporation of aerophilic textures on submerged solid boundaries, have both been successfully employed as independent, stand-alone methods for drag reduction in turbulent aqueous flows. In this paper, we explore the possibility of combining the two strategies additively to obtain enhanced levels of frictional drag reduction in wall-bounded turbulence. By means of skin friction measurements in fully turbulent Taylor-Couette flow, we show that dissolved polymer chains act in concert with superhydrophobic walls to yield a net reduction in turbulent drag that is up to $50\%$ greater than that obtainable from either method employed independently. Cooperative drag reduction measurements are presented for various combinations involving one of two common water-soluble polymers (either polyacrylamide or polyethylene oxide) paired with one of two prototype drag-reducing superhydrophobic surfaces—either a regular pattern of streamwise microgrooves or a scalable random superhydrophobic texture possessing hierarchical multiscale roughness. The surface activity of polyethylene oxide is observed to adversely influence the wall slip on the randomly textured surface, leading to significant diminution in the overall drag reduction efficacy of this polymer-surface combination. In cases where such interfacial effects are absent, an additive friction law in Prandtl-von Kármán coordinates is proposed that yields fairly accurate predictions of the combined drag reduction performance anticipated from a given polymer-surface pair, each possessing known individual drag-reducing characteristics.

Turbulence has long been suspected to increase the evaporation rate of droplets via the convective effects it generates. The experimental data reported in this paper provide evidence of this increase and statistically quantify these effects. Ether droplets have been released in a quasi-isotropic homogeneous turbulence generated by synthetic jets and tracked using inline digital holography. Their Schmidt number is typically of the order of 2 and their Reynolds number is moderate $(\le 3)$. Their instantaneous positions and diameters have been measured by processing the holograms with an inverse problem approach that has been implemented in Python language for a high-performance computer. This has allowed us to drastically reduce the processing time and to reconstruct a high number of trajectories for various turbulence conditions. The Lagrangian statistics computed from these trajectories, totaling 1.3 million samples, show that the relative mean motion and turbulence seen by the droplets on average increases their evaporation rate. Within the parameter range investigated, we find that this increase is not well predicted when estimating the convective effect in the Sherwood number with the norm of the instantaneous relative velocity seen by the droplets. In contrast, this increase is very well predicted when the Sherwood number is calculated using a Reynolds number based on the norm of the mean relative velocity plus its root-mean-square fluctuation.

Dynamic similarity, while commonly applied in fluid systems, has recently been extended to locomotion problems in granular media. The previous work was limited to locomotors in cohesionless, flat beds of grains under the assumption of a simple frictional fluid rheology. However, many natural circumstances involve beds that are sloped or composed of cohesive (e.g. damp or powdery) grains. Here we derive expanded scaling relations inclusive of these phenomena. To validate the proposed scalings, we perform discrete element method simulations with inclined beds and cohesive grains using rotating “wheels” of various shape families, sizes, and loading conditions in accord with the proposed scaling laws. The data show a good agreement between scaled tests, suggesting the usage of these scalings as a potential design tool for off-road vehicles and extraplanetary rovers and as an analysis tool for biolocomotion in soils.

The dynamics of a single elastoviscoplastic drop immersed in plane shear flow of a Newtonian fluid is studied by three-dimensional direct numerical simulations using a finite-difference and level-set method combined with the Saramito model for the elastoviscoplastic fluid. This model gives rise to a yield stress behavior, where the unyielded state of the material is described as a Kelvin-Voigt viscoelastic solid and the yielded state as a viscoelastic Oldroyd-B fluid. Yielding of an initially solid drop of Carbopol is simulated under successively increasing shear rates. We proceed to examine the roles of nondimensional parameters on the yielding process; in particular, the Bingham number, the capillary number, the Weissenberg number, and the ratio of solvent and total drop viscosity are varied. We find that all of these parameters, and not only the Bingham number, have a significant influence on the drop dynamics. Numerical simulations predict that the volume of the unyielded region inside the droplet increases with the Bingham number and the Weissenberg number, while it decreases with the capillary number at low Weissenberg and Bingham numbers. A new regime map is obtained for the prediction of the yielded, unyielded, and partly yielded modes as a function of the Bingham and Weissenberg numbers. The drop deformation is studied and explained by examining the stresses in the vicinity of the drop interface. The deformation has a complex dependence on the Bingham and Weissenberg numbers. At low Bingham numbers, the droplet deformation shows a nonmonotonic behavior with an increasing drop viscoelasticity. In contrast, at moderate and high Bingham numbers, droplet deformation always increases with drop viscoelasticity. Moreover, it is found that the deformation increases with the capillary number and with the solvent to total drop viscosity ratio. A simple ordinary differential equation model is developed to explain the various behaviours observed numerically. The presented results are in contrast with the heuristic idea that viscoelasticity in the dispersed phase always inhibits deformation.

We study compressibility effects on pressure fluctuations in wall-bounded turbulent flows using DNS data of compressible turbulent channel flows at various Mach numbers. We derive a pressure Poisson equation that allows splitting pressure fluctuations into the following terms: the rapid and slow terms as in incompressible flows, an additional mass-flux term related to the temporal and spatial variation of mass-flux fluctuations, and a viscous term related to fluctuating viscous stresses. As the bulk Mach number increases, the intensity of pressure fluctuations increases in the viscous sublayer and in the outer region, resulting from the intensification of the mass-flux term, whereas it decreases in the buffer layer and logarithmic layers, after weakening of the slow term. The rapid and slow terms are further split into their solenoidal and dilatational components using Helmholtz decomposition. The variances of the solenoidal components are found to be independent of the Mach number, whereas the dilatational components increase quadratically with the Mach number. The correlations between split pressure fluctuations and dilatational fluctuations show that the solenoidal-related pressure field turns turbulent kinetic energy into internal energy, whereas dilatational and viscous terms are responsible for reverse energy transfer.

We report heat transfer and temperature profile measurements in laboratory experiments of rapidly rotating convection in water under intense thermal forcing (Rayleigh number Ra as high as $\sim {10}^{13}$) and unprecedentedly strong rotational influence (Ekman numbers $E$ as low as ${10}^{-8}$). Measurements of the midheight vertical temperature gradient connect quantitatively to predictions from numerical models of asymptotically rapidly rotating convection, separating various flow phenomenologies. Past the limit of validity of the asymptotically reduced models, we explore a regime we refer to as rotationally influenced turbulence, where rotation is important but not as dominant as in the known geostrophic turbulence regime. The temperature gradients collapse to a Rayleigh-number scaling as ${\text{Ra}}^{-0.2}$ in this regime. It is bounded from above by a critical convective Rossby number ${\text{Ro}}^{*}=0.06$ independent of domain aspect ratio $\mathrm{\Gamma }$, clearly distinguishing it from well-studied rotation-affected convection.

The effects of spinning motion on the bouncing and coalescence between a spinning droplet and a nonspinning droplet undergoing head-on collision were numerically studied by using a volume-of-fluid method. A prominent discovery is that the spinning droplet can induce significant nonaxisymmetric flow features for the head-on collision of equal-size droplets composed of the same liquid. Specifically, a nonaxisymmetric bouncing was observed, and it is caused by the conversion of the spinning angular momentum into the orbital angular momentum. This process is accompanied by the rotational kinetic energy loss due to the interaction between the rotational and radial flows of the droplets. A nonaxisymmetric internal flow and a delayed separation after temporary coalescence were also observed, and they are caused by the enhanced interface oscillation and internal-flow-induced viscous dissipation. The spinning motion can also promote the mass interminglement of droplets, because the locally nonuniform mass exchange occurs at the early collision stage by nonaxisymmetric flow and is further stretched along the filament at later collision stages. In addition, it is found that the nonaxisymmetric flow features increase with increasing the orthogonality of the initial translational motion and the spinning motion of droplets.

This paper experimentally investigates the effect of viscosity on the outcomes of collisions between a regular stream of droplets and a continuous liquid jet. A broad variation of liquid viscosity of both the drop and the jet liquid is considered, keeping other material properties unchanged. To do so, only two liquid types were used: aqueous glycerol solutions for the drop and different types of silicone oil for the jet liquid. Combining these liquids, the viscosity ratio $\lambda ={\mu }_{\mathrm{drop}}/{\mu }_{\mathrm{jet}}$ was varied between 0.25 and 3.50. The collision outcomes were classified in the form of regime maps leading to four main regimes: drops in jet, fragmented drops in jet, encapsulated drops, and mixed fragmentation. We demonstrate that, depending on the drop and jet viscosity, not all four regimes can be observed in the domain probed by our experiments. The experiments reveal that the jet viscosity mainly affects the transition between drops in jet and encapsulated drops, which is shifted towards higher drop spacing for more viscous jets. The drop viscosity leaves the previous transition unchanged but modifies the threshold of the drop fragmentation within the continuous jet. We develop a model that quantifies how the drop viscosity affects its extension, which is at first order fixing its shape during recoil and is, therefore, determining its stability against pinch-off.

The development of a separated bottom boundary layer in the footprint of a large-amplitude internal solitary wave of depression, propagating against an oncoming barotropic current, is examined in detail using high-resolution implicit large eddy simulation. The wave is supported by a continuous two-layer stratification. The Reynolds number based on the water column height is $1.6\times {10}^5$. This numerical simulation is the first to reproduce the self-sustained three-dimensional vortex shedding, resultant transition, and turbulence under an ISW, which have long been hypothesized to occur in field experiments. No artificial noise is inserted into the flow domain. Part I of this study focuses on a structural description of the sequence of flow regimes developing from a wave-induced, long, high-aspect-ratio, laminar separation bubble. Three illuminating topological features are identified. (a) The spatial development of the self-sustained turbulence is composed of three transitional stages: (i) spontaneous excitation of a global instability in the separation bubble that emanates trailing vortices, (ii) vortex breakup and degeneration into turbulent clouds, and (iii) relaxation to a spatially developing turbulent boundary layer. (b) In the separation bubble, there exists a three-dimensional linear global oscillator, which is primarily excited by the two-dimensional absolute instability of the separated shear layer. This global mode possesses a transverse coherent structure. The transverse perturbation subsequently excites an elliptic instability mode inside the shed vortex, resulting in an axial distortion of the vortex core. (c) A shortwave secondary instability is excited in the form of a series of coherent streamwise vortex streaks that wrap around each shed vortex, leading to rapid break up and burst of the vortex.

The statistical properties of the self-sustained turbulent wake downstream of a long, high-aspect-ratio, laminar separation bubble are studied. The primary focus is on the relaxation of turbulent wake to a zero pressure gradient (ZPG) turbulent boundary layer, in terms of mean flow, Reynolds stresses, and turbulent kinetic energy (TKE) budget. The bubble is initiated by the strong adverse pressure gradient (APG) induced by a large-amplitude, laboratory-scale internal solitary wave of depression propagating against an oncoming barotropic current. The high-resolution large eddy simulation data generated in Part I of this two-part article is used for analysis. It is shown that the wake development in the early stage, following the breakdown of coherent vortices toward the trailing region of the separation bubble, possesses a statistical character similar to that of a self-similar plane mixing layer. The mean streamwise velocity profile relaxes to that of a ZPG turbulent boundary layer at 15 water column depths form the wave trough. This relaxation distance normalized by the bubble length is equal to 5 which is shorter than reported by Alam and Sandham's short bubble [J. Fluid Mech. 403, 223 (2000)] that is induced by a stronger APG. In regions further downstream of the bubble, distributions of the Reynolds stresses resemble those of channel flow. The relaxation of the TKE budget to that of a ZPG turbulent boundary layer is slower far away from the wall and faster near the wall, as compared to the relaxation of the mean flow to that of a ZPG turbulent boundary layer. Large bed stresses beneath the shed vortices and persistent near-bed turbulence offer an insight into frequently observed sediment resuspension events in coastal seas.

In this study, particle-laden shear turbulence is investigated by performing direct numerical simulation under a point-particle approximation for spherical heavy particles with a diameter smaller than the Kolmogorov length scale of the flow. The ranges of the Stokes number and gravity factor considered in our study are $\text{St}=0.1,0.5,1,5$, and 10 and $W(=v_t/v_{\eta })=0,10,20,30$, and 40, respectively, where $v_t$ and $v_{\eta }$ are the terminal velocity and the Kolmogorov velocity scale, respectively. The behavior of settling particles is investigated by introducing a two-dimensional distribution function to quantify the anisotropic clustering. A principal component analysis of the two-dimensional distribution evidently indicates that the preferential orientation of clustering at different scales is identified well. Small-scale clustering displays a multifractal nature with an explicit angular distribution.

We consider the evaporation of a thin liquid layer which consists of a binary mixture of volatile liquids. The mixture is on top of a heated substrate and in contact with the gas phase that consists of the same vapor as the binary mixture. The effects of thermocapillarity, solutocapillarity, and the van der Waals interactions are considered. We derive the long-wave evolution equations for the free interface and the volume fraction that govern the two-dimensional stability of the layer subject to the above coupled mechanisms and perform a linear stability analysis. Our results demonstrate two modes of instabilities, a monotonic instability mode and an oscillatory instability mode. We supplement our results from stability analysis with transient simulations to examine the dynamics in the nonlinear regime and analyze how these instabilities evolve with time. More precisely we discuss how the effect of relative volatility along with the competition between thermal and solutal Marangoni effect define the mode of instability that develops during the evaporation of the liquid layer due to preferential evaporation of one of the components.

We report results of a series of high-resolution direct numerical simulations (DNSs) of forced incompressible isotropic turbulence with the number of grid points and the Taylor scale Reynolds number $R_{\lambda }$ up to $12{288}^3$ and $\sim 2250$, respectively. The DNSs show that there exists a scaling range (approximately $100<r/\eta <400$), at which the second-order two-point velocity structure functions $S_2\left(r\right)$ fit well with a simple power-law, $S_2\left(r\right)/{\left(〈\epsilon 〉r\right)}^{2/3}=C_2{(r/L_0)}^{\zeta }$, where $r$ is the distance between the two points, $\eta$ is the Kolmogorov length scale, $〈\epsilon 〉$ is the mean rate of energy dissipation per unit mass, and $L_0$ is the integral length scale. The exponent $\zeta$ is constant independent from $R_{\lambda }$. However, the coefficient $C_2$ is dependent of $R_{\lambda }$ or the viscosity. This implies that the power-law scaling range of $100<r/\eta <400$ for $R_{\lambda }$ up to $\sim 2250$ is not the so-called “inertial subrange” in the sense that the statistics in the range are independent from the viscosity, as assumed in various turbulence theories. This suggests that the constancy of the scaling exponent of a structure function within a certain range does not necessarily mean that the exponent is the scaling exponent in “the inertial subrange.”

A parametric numerical study of three-dimensional instability of steady flows in a helical pipe of arbitrary curvature and torsion is carried out. The computations are performed by a numerical approach verified against independent experimental and numerical results in a previous study. A possible power dependence of the friction factor on the Reynolds and Dean numbers is examined. The stability results are reported as dependences of the critical Reynolds number, critical wave number and the critical frequency on the dimensionless pipe curvature and torsion. A multiplicity of different disturbance modes becoming most unstable at different values of the governing parameters, is observed. Patterns of the most unstable modes are reported and classified. Different routes to instability including viscous and inviscid mechanisms, locally developing boundary and mixing layers, interaction between the Dean vortices, and the through flow are described.

We investigate the linear and weakly nonlinear behaviors of a gel-like elastic interface separating two viscous fluids moving in two dimensions (2D). Induced by fluid suction or injection, a 2D Stokes flow takes place and the interface deforms due to the interplay between viscous and elastic forces. By modeling the elastic boundary as having a curvature-dependent bending rigidity and by employing a perturbative mode-coupling approach, we study the linear stability of the interface and the formation of nonlinear patterned structures. In addition to capturing a number of interesting linear properties, we have identified the emergence of suction-driven, nonlinear polygonal-like patterns presenting either convex or concave edges that can develop peculiar near-cusp fingers.

The spreading of drops on surfaces is ubiquitous and has relevance to many technological applications. In this work, we present two-dimensional numerical simulations of the surface tension driven spreading of drops dispensed on a fluid-fluid interface. A comprehensive picture describing the equilibrium shapes of the drops is provided in the form of a state diagram. We show that the analysis of kinetics of drops that spread symmetrically on the fluid-fluid interface reveal several interesting features: (i) the existence of a single length scale that describes the spreading process, (ii) the power law dependence of the temporal variation of the geometrical parameters of the spreading drop, (iii) the linear dependence of the power law exponents on the equilibrium enclosing angle of the liquid drop, (iv) a strong dependence of the power law exponents on the spreading coefficient, and (v) a collapse of the spreading kinetics data into a master curve. Though restricted to two dimensions, our analysis provides a rationale for explaining experimentally determined power law exponents which have been reported to vary over a wide range and hence to understand the universal nature of the spreading process.

Visualization experiments and pore network models on evaporation of capillary porous media are presented in this work. We show that in a simple model porous medium the pores occupied by gas can be refilled with liquid, snapping off a gas bubble, which then moves to a stable configuration. This phenomenon, referred to as capillary instability, is induced due to heterogeneity in wettability of the pore surfaces and has a much smaller time scale compared to the evaporation process. The capillary instability is explored based on the optical images obtained from visualization experiments. The residual liquid in pores can suppress the capillary valve effect, which is induced by the sudden geometrical expansion and can hinder the movement of the gas-liquid interface. For better understanding of the capillary instability induced gas-liquid displacement, a pore network model that accounts for capillary and viscous forces as well as the inertial effect is developed. The pore network simulation results agree well with experimental data. The ratio of the square of the average meniscus moving speed predicted by the pore network model with the inertial effect to the average meniscus moving speed obtained from the model without the inertial effect is a linear function of the Weber number. When the Weber number exceeds a critical value, more pores are invaded by the gas-liquid interface in the pore network model with the inertial effect than in the model neglecting the inertial effect. The pore network model developed here opens up a route to better understand the role of inertial effects in two-phase transport in porous media.