Shear-induced Mixing Research Articles

Shear-induced mixing governs codeformation of crystalline-amorphous nanolaminates.

Deformation of ductile crystalline-amorphous nanolaminates is not well understood due to the complex interplay of interface mechanics, shear banding, and deformation-driven chemical mixing. Here we present indentation experiments on 10 nm nanocrystalline Cu-100 nm amorphous CuZr model multilayers to study these mechanisms down to the atomic scale. By using correlative atom probe tomography and transmission electron microscopy we find that crystallographic slip bands in the Cu layers coincide with noncrystallographic shear bands in the amorphous CuZr layers. Dislocations from the crystalline layers drag Cu atoms across the interface into the CuZr layers. Also, crystalline Cu blocks are sheared into the CuZr layers. In these sheared and thus Cu enriched zones the initially amorphous CuZr layer is rendered into an amorphous plus crystalline nanocomposite.

Wind Shear and Buoyancy Reversal at the Top of Stratocumulus

Abstract A numerical experiment is designed to study the interaction at the stratocumulus top between a mean vertical shear and the buoyancy reversal due to evaporative cooling, without radiative cooling. Direct numerical simulation is used to eliminate the uncertainty introduced by turbulence models. It is found that the enhancement by shear-induced mixing of the turbulence caused by buoyancy reversal can render buoyancy reversal comparable to other forcing mechanisms. However, it is also found that (i) the velocity jump across the capping inversion Δu needs to be relatively large and values of about 1 m s−1 that are typically associated with the convective motions inside the boundary layer are generally too small and (ii) there is no indication of cloud-top entrainment instability. To obtain these results, parameterizations of the mean entrainment velocity and the relevant time scales are derived from the study of the cloud-top vertical structure. Two overlapping layers can be identified: a background shear layer with a thickness (⅓)(Δu)2/Δb, where Δb is the buoyancy increment across the capping inversion and a turbulence layer dominated by free convection inside the cloud and by shear production inside the relatively thin overlap region. As turbulence intensifies, the turbulence layer encroaches into the background shear layer and defines thereby the entrainment velocity. Particularized to the first research flight of the Second Dynamics and Chemistry of the Marine Stratocumulus (DYCOMS II) field campaign, the analysis predicts an entrainment velocity of about 3 mm s−1 after 5–10 min—a velocity comparable to the measurements and thus indicative of the relevance of mean shear in that case.

Phase transition and separation in compressible Cahn-Hilliard fluids

The paper provides a scheme for phase separation and transition by accounting for diffusion, dynamic equations and consistency with thermodynamics. The constituents are compressible fluids thus improving the model of a previous approach. Moreover a possible saturation effect for the concentration of a constituent is made explicit. The mass densities of the constituents are independent of temperature. The evolution of concentration is described by the standard equation for mixtures but the balance of energy and entropy of the mixture are stated as for a single constituent. However, due to the non-simple character of the mixture, an extra-energy flux is allowed to occur. Also motion and diffusion effects are considered by letting the stress in the mixture have additive viscous terms and, remarkably, the chemical potential contains a quadratic term in the stretching tensor. As a result a whole set of evolution equations is set up for the concentration, the velocity, and the temperature. Shear-induced mixing and demixing are examined. A maximum theorem is proved which implies that the concentration of the mixture has values from 0 to 1 as is required from the physical standpoint.

Shear-induced mixing in geophysical flows: does the route to turbulence matter to its efficiency?

AbstractMotivated by the importance of diapycnal mixing parameterizations in large-scale ocean general circulation models, we provide a detailed analysis of high-Reynolds-number mixing in density stratified shear flows which constitute an archetypical example of the small-scale physical processes occurring in the oceanic interior that control turbulent diffusion. Our focus is upon the issue as to whether the route to fully developed turbulence in the stratified mixing layer is in any significant way determinant of diapycnal mixing efficiency as represented by an effective turbulent diffusivity. We characterize different routes to fully developed turbulence by the nature of the secondary instabilities through which a primary Kelvin–Helmholtz billow executes the transition to this state. We then demonstrate that different mechanisms of turbulence transition characterized in these different transition mechanisms lead to considerably different values for the efficiency of diapycnal mixing and also for the effective vertical flux of buoyancy. We show that the widely employed value of 0.15–0.2 for the efficiency of mixing in shear-induced stratified turbulence based upon both laboratory measurements and similarly low-Reynolds-number numerical simulations may be too low for the high-Reynolds-number regime characteristic of geophysical flows. Our results show that the mixing efficiency tends to a value of approximately $1/ 3$ for sufficiently large Reynolds number at an intermediate value of 0.12 for the Richardson number. This is in agreement with a theoretical predictions of Caulfield, Tang and Plasting (J. Fluid Mech., vol. 498, 2004, pp. 315–332) for the asymptotic value of mixing efficiency in stratified Couette flows. In the high-Reynolds-number regime, mixing efficiency is shown to vary over a considerable range during the course of a particular shear-induced mixing event. We explain this variation on the basis of a detailed examination of the underlying dynamics. Since values in the range 0.15–0.2 for mixing efficiency have been extensively employed to infer an effective diffusivity from ocean microstructure measurements and also in energy balance analyses of the requirements of the global ocean circulation, our findings have potentially important implications for large-scale ocean modelling. We also quantify the errors introduced by employing the Osborn (J. Phys. Oceanogr., vol. 10, 1980, pp. 83–89) formula along with an efficiency of 0.15 to infer values for effective diffusivity, and explain the logical underpinnings of this conclusion. One of the more important aspects of this work from the perspective of our theoretical understanding of stratified turbulence is the demonstration that the inverse cascade of energy, which is facilitated by the vortex-merging process that is typical of laboratory experiments and of the low-Reynolds-number simulations of shear flow evolution, is strongly suppressed by increase of the Reynolds number to values typical of geophysical flows. Based on this finding, the application of results based on low-Reynolds-number (numerical or laboratory) experiments to high-Reynolds-number geophysical shear flows needs to be reconsidered.

Simulation of shear banding in heterophase co-deformation: Example of plane strain compressed Cu–Ag and Cu–Nb metal matrix composites

The co-deformation and shear localization in heterophase alloys is studied using two-dimensional crystal plasticity finite element simulations on plane strain compressed Cu–Ag and Cu–Nb metal matrix composites. The aim is to study the fundamentals of micromechanics, co-deformation and shear banding in materials with heterophase interfaces. It is observed that, depending on the initial orientations of the crystals, co-deformation of the constituent heterophases often proceeds via collective mechanisms, i.e. by pronounced shear banding triggered by stress concentration at the interfaces. This phenomenon leads to highly localized strains within the bands, exceeding the average strain in part by two orders of magnitude. Shear band development is related to the inherent mechanical properties of each crystal and also to the properties of the abutting crystals. The predicted topology and nature of the cross-phase shear bands, i.e. the extreme local strains, significant bending of the interface regions, and sharp strain localization that propagates across the interfaces, agree well with experimental observations in cold-rolled composites. The simulations reveal that cross-phase shear banding leads to large and highly localized values of stress and strain at heterophase interfaces. Such information is essential for a better understanding of the micromechanical boundary conditions inside co-deformed composites and the associated shear-induced chemical mixing.

Atomic Mixing in Metals Under Shear Deformation

The fundamental processes of shear-induced chemical mixing in heterogeneous Cu-based alloy systems have been studied by molecular dynamics computer simulations. These simulations reveal that two very disparate mechanisms operate depending on whether or not the two phases are coherent. For the coherent systems, mixing occurs as dislocations transfer across phase boundaries. The mixing in these systems is “superdiffusive,” and for spherical precipitates, the rate of mixing increases quadratically with precipitate radius. In systems that have incoherent phases, the mixing occurs by a local shuffling of atoms at the interface, and for them, the mixing is diffusive, with the mixing rates of spherical precipitates scaling linearly with particle radius. The morphologies of the interfaces for the two situations are also different. Coherent precipitates form rough interfaces that are relatively sharp, whereas the interfaces of incoherent precipitates are smooth but diffuse. These simulations also show that for incoherent precipitates, shear-induced mixing can be very different at different crystallographic interfacial planes as well as for different strain directions.

Dependence of shear-induced mixing on length scale

The critical strain for mixing was determined as a function of precipitate size in two-phase Cu90Ag10 alloys using high-pressure torsion experiments. X-ray diffraction, Z-contrast transmission electron microscopy and atom probe tomography were employed to characterize the mixing behavior. For precipitates ranging from 16 to 131 nm in radius, the critical strain increased linearly with the initial precipitate size, with the proportionality constant at ≈5.2 nm−1. These results are in agreement with model predictions based on random dislocation glide.

Morphological and rheological responses to the transient and steady shear flow for a phase-separated polybutadiene/polyisoprene blend

The morphological and rheological responses to the transient and steady shear flow for a phase-separated polybutadiene (PB)/low vinyl content polyisoprene (LPI) blend have been investigated. Under steady shear flow where the applied shear rate is not too large, the steady sheared structures become increasingly anisotropic and interconnected with an “en route” to the formation of string phases as shear rate increases. After that, the further increase of shear rate leads to a blurred domain interface. These shear-induced complex structures in turn affect the rheological response greatly and both the shear thinning and shear thickening were observed in the steady shear behavior of the phase-separated PB/LPI blend. Under transient shear flow, the time (or strain) dependence of viscosity and morphology after a shear rate jump were extensively studied in order to obtain the insight into the steady state formation and found to be mainly determined by the final shear rates. Depending on whether the transient string phases which were formed by the transient shear flow can be stabilized and with clear domain interface, three kinds of transient shear viscosity changes have been observed. Some of the observations are quite different from the model immiscible blend and believed to be closely related to the significant shear-induced mixing effect happened in the PB/LPI blend.

The response of the Ligurian and Tyrrhenian Seas to a summer Mistral event: A coupled atmosphere–ocean approach

In this paper the effect of a summer Mistral event on the Ligurian and Tyrrhenian Seas in the north-western Mediterranean is discussed, using a coupled numerical model and satellite and in situ observations. The focus is on the spatial and temporal distribution of the ocean mixed layer response to the strong winds, and on how this is affected by atmosphere–ocean coupling. The model used is the Coupled Ocean–Atmosphere Mesoscale Prediction System (COAMPS®1COAMPS® is a registered trademark of Naval Research Laboratory.1), developed at the Naval Research Laboratory. This system includes an atmospheric sigma coordinate, non-hydrostatic model, coupled to a hydrostatic sigma-z level ocean model (Naval Coastal Ocean Model), using the Earth System Modeling Framework (ESMF). The model is run at high (km scale) resolution to capture the fine structure of wind jets and surface cooling.Two non-assimilating numerical experiments, coupled and uncoupled, are run for a 3-day period of a Mistral event, to examine more closely the impact of coupling on the surface flux and sea surface temperature (SST) fields. The cooling of SST up to 3°C over 72h in the coupled run significantly reduced the surface momentum and heat fluxes, relative to the uncoupled simulation, where the SST was kept fixed at the initial value. Mixed layer depths increase by as much as 30m during the event. A heat budget analysis for the ocean is carried out to further explain and investigate the SST evolution. Shear-induced mixing in inertial waves is found to be important to the surface cooling. Effects of coupling on the atmospheric boundary layer are found to be significant, but overall the effect of coupling on the synoptic low pressure system is small.

Morphology evolution of a bisphenol A polycarbonate/poly (styrene-co-acrylonitrile) blend under shear and after shear cessation

The deformation, breakup and morphology relaxation of a commercially important polycarbonate (PC)/poly(styrene-co-acrylonitrile) (SAN) blend under and after steady shear flow have been studied in situ by combined phase contrast optical microscopy (PCOM), small angle light scattering (SALS) and rheometry. Under steady shear flow, the morphology of PC/SAN blends evolves via repeated deformation, breakup and finally string-like morphology. The data can be qualitatively interpreted with the mode-coupling renormalization group (MCRG) model. At high shear rate, shear-induced mixing effect is found to be saturated and no further shear-induced homogenization can be observed, which may be due to the fact that the experimental conditions (T, C) is far from the critical region and the shear suppression of concentration fluctuations is limited. Upon cessation of shear, different relaxation mechanisms are found. For low shear rate, the anisotropic ellipsoids retract to isotropic domains after shear cessation; while for higher shear rate, the string-like pattern breaks into necklace-like structure first and then the aligned structure relaxes to an isotropic distribution via diffusion process. The slow coarsening process upon cessation of shear is attributed to high viscosity of PC matrix and viscoelastic effects.

Mechanisms of subantarctic mode water upwelling in a hybrid-coordinate global GCM

This article presents an investigation of the global circulation and upwelling of subantarctic mode water (SAMW), which is thought to be key in the supply of nutrients to support biological production over much of the world ocean excluding the North Pacific. The HYbrid isopycnic-cartesian Coordinate Ocean general circulation Model (HYCOM) is configured to simulate the global ocean circulation for time scales of up to centuries and a SAMW-tracking online tracer experiment is conducted. The tracer re-emergence fluxes across the mixed layer base effected by a range of physical mechanisms and by numerical mixing terms in HYCOM are diagnosed and discussed. For the global ocean north of 30°S, entrainment due to surface buoyancy loss and/or wind-induced mechanical stirring accounts for almost one third of the total tracer re-emergence. Ekman upwelling and shear-induced mixing are especially significant in the tropical oceans, and account for 19% and 18% of the total tracer re-emergence, respectively. There is substantial regional variation in the relative importance of the various upwelling mechanisms. Special attention is devoted to understanding the contrasting circulations of SAMW in the North Pacific and North Atlantic oceans. The modest penetration of SAMW into the North Pacific is found to arise from the comparatively light density level that the SAMW core resides at in the South Pacific Ocean, which results in its being captured by the Equatorial Undercurrent and prevents it from entering the western boundary current of the North Pacific. In the North Atlantic, a new conceptual model of SAMW circulation and re-emergence is proposed with application to nutrient supply to the regional upper ocean. The model formulates SAMW re-emergence as a sequence of distinct processes following the seasonal cycle of the thermocline as a water column circulates around the subtropical and subpolar gyres of the North Atlantic.

Shear induced chemical mixing in heterogeneous systems

Shear-induced mixing in heterogeneous Cu alloy systems was investigated by molecular dynamics simulation. Each system, which comprised a single spherical particle within a Cu matrix, was subjected to cyclical shearing events to high strains at 100K. The particles investigated were Cu, Ag, Ni, Fe, Nb, and V. fcc particles were observed to undergo “superdiffusive” mixing with dislocations crossing the particle–matrix interface. The initial rate of mixing in these systems increased quadratically with particle radius. bcc particles showed different behaviors. For Nb and V dislocations did not cross into the particles and the initial rates of mixing increased linearly with particle radius. The Nb particles remained spherical but developed amorphous Cu–Nb shells at the particle–matrix interface. The V particle showed some faceting, but it too formed amorphous layers on non-facetted interfaces. The Fe particle behaved similarly to Nb and V particles initially, but more like fcc particles at high strains. The molecular dynamics results are compared with experimental observations.

Miscibility and rheologically determined phase diagram of poly(ethylene oxide)/poly(ε-caprolactone) blends

Poly(ethylene oxide)/poly(e-caprolactone) (PEO/PCL) blends can be widely used in lithium rechargeable battery area or as medical materials, while the miscibility and phase diagram of the blends are still unclear. The present work attempted to establish the blends’ phase diagram using rheometry and investigated the miscibility. The results showed that a miscibility window of upper critical solution temperature character of the blends is revealed. Meanwhile, the abnormal rheological behavior of PEO at temperatures higher than 130 °C has little influence on the phase diagram determination. Different rheological properties of PEO/PCL blends from those of PEO revealed the existence of interactions between PEO and PCL molecular chains. Whereas shear-induced mixing or shear-induced phase separation might occur in phase diagram determination of PEO/PCL blends using rheometry.

Flow-induced phase behaviour and structure development in aqueous emulsion of associative biopolymers

A rheo-optical methodology, based on small angle light scattering and transmitted light intensity measurements, has been used to perform an in-situ and time-resolved investigation on the effect of simple shear flow on associative phase separation, morphology development, and the interfacial tension, using a water–acid gelatin–gum arabic system as a model. It is shown that above a critical shear rate, shear-induced mixing occurs at 45 °C at the length scales probed by the laser light. Shift of the phase diagram at a fixed shear rate (100 s −1) was determined. When flow is stopped after homogenization, phase separation occurs almost instantaneously. When subsequently applying a low shear rate, the structure coarsens due to coalescence of the dispersed droplets. Shear-induced mixing does not occur at 35 °C probably due to the sharp increase of the interfacial tension from 5.5·10 −5 N/m to 9.0·10 −5 N/m.

Upper-Ocean Response to Hurricane Frances (2004) Observed by Profiling EM-APEX Floats*

Abstract Three autonomous profiling Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats were air deployed one day in advance of the passage of Hurricane Frances (2004) as part of the Coupled Boundary Layer Air–Sea Transfer (CBLAST)-High field experiment. The floats were deliberately deployed at locations on the hurricane track, 55 km to the right of the track, and 110 km to the right of the track. These floats provided profile measurements between 30 and 200 m of in situ temperature, salinity, and horizontal velocity every half hour during the hurricane passage and for several weeks afterward. Some aspects of the observed response were similar at the three locations—the dominance of near-inertial horizontal currents and the phase of these currents—whereas other aspects were different. The largest-amplitude inertial currents were observed at the 55-km site, where SST cooled the most, by about 2.2°C, as the surface mixed layer deepened by about 80 m. Based on the time–depth evolution of the Richardson number and comparisons with a numerical ocean model, it is concluded that SST cooled primarily because of shear-induced vertical mixing that served to bring deeper, cooler water into the surface layer. Surface gravity waves, estimated from the observed high-frequency velocity, reached an estimated 12-m significant wave height at the 55-km site. Along the track, there was lesser amplitude inertial motion and SST cooling, only about 1.2°C, though there was greater upwelling, about 25-m amplitude, and inertial pumping, also about 25-m amplitude. Previously reported numerical simulations of the upper-ocean response are in reasonable agreement with these EM-APEX observations provided that a high wind speed–saturated drag coefficient is used to estimate the wind stress. A direct inference of the drag coefficient CD is drawn from the momentum budget. For wind speeds of 32–47 m s−1, CD ~ 1.4 × 10−3.

Enhanced thermal stratification in a liquid storage tank with a porous manifold

Experiments were conducted to investigate the effectiveness of a porous manifold in the formation and maintenance of thermal stratification in a liquid storage tank. A thermal storage tank with a capacity of 315 L and a height-to-radius ratio of 4 was used for the experiment. The porous manifold used was made from rolling up a nylon screen into the shape of a tube. Stratification was observed at a Richardson number as low as 0.615. Flow visualization was also performed to confirm the effectiveness of the porous manifold in the promotion and maintenance of stable thermal stratification. From the results of flow visualization, one can conclude that a porous manifold is able to reduce the shear-induced mixing between fluids of different temperature, and thus is able to promote and maintain a stable stratification.

Fluxes across double-diffusive interfaces: a one-dimensional-turbulence study

This work is a parametric study of the fluxes of heat and salt across unsheared and sheared double-diffusive interfaces using one-dimensional-turbulence (ODT) simulations. It is motivated by the need to understand how these fluxes scale with parameters related to the fluid molecular properties and background shear. Comparisons are made throughout with previous models and available measurements. In unsheared interfaces, ODT simulations show that the dimensionless heat flux Nu scales with the stability parameter Rρ, Rayleigh number Ra and Prandtl number Pr as Nu ~ (Ra/Rρ)0.37±0.03 when Pr varies from 3 to 100 and as Nu ~ (Ra/Rρ)0.31Pr0.22±0.04 when Pr varies from 0.01 to 1. Here Ra/Rρ can be seen as the ratio of destabilizing and stabilizing effects. The simulation results also indicate that the ratio of salt and heat fluxes Rf is independent of Pr, scales with the Lewis number Le as Rf ~ Le0.41±0.04 when Rρ is large enough and deviates from this expression for low values of Rρ, when the interface becomes heavily eroded. In sheared interfaces, the simulations show three flow regimes. When the Richardson number Ri ≪ 1, shear-induced mixing dominates, the heat flux scales with the horizontal velocity difference across the interface and Rf = Rρ. Near Ri ~ 1 the heat and salt fluxes are seen to increase abruptly as the shear increases. The flow structure and scaling of the fluxes are similar to those of unsheared interfaces when Ri ≫ 1.

Fluxes across double-diffusive interfaces: a one-dimensional-turbulence study

This work is a parametric study of the fluxes of heat and salt across unsheared and sheared double-diffusive interfaces using one-dimensional-turbulence (ODT) simulations. It is motivated by the need to understand how these fluxes scale with parameters related to the fluid molecular properties and background shear. Comparisons are made throughout with previous models and available measurements. In unsheared interfaces, ODT simulations show that the dimensionless heat fluxNuscales with the stability parameterRρ, Rayleigh numberRaand Prandtl numberPrasNu~ (Ra/Rρ)0.37±0.03whenPrvaries from 3 to 100 and asNu~ (Ra/Rρ)0.31Pr0.22±0.04whenPrvaries from 0.01 to 1. HereRa/Rρcan be seen as the ratio of destabilizing and stabilizing effects. The simulation results also indicate that the ratio of salt and heat fluxesRfis independent ofPr, scales with the Lewis numberLeasRf~Le0.41±0.04whenRρis large enough and deviates from this expression for low values ofRρ, when the interface becomes heavily eroded. In sheared interfaces, the simulations show three flow regimes. When the Richardson numberRi≪ 1, shear-induced mixing dominates, the heat flux scales with the horizontal velocity difference across the interface andRf=Rρ. NearRi~ 1 the heat and salt fluxes are seen to increase abruptly as the shear increases. The flow structure and scaling of the fluxes are similar to those of unsheared interfaces whenRi≫ 1.

Regional simulations of the Faroe Bank Channel overflow using a σ-coordinate ocean model

Gravity-driven overflow of cold, deep and intermediate water from the Norwegian Sea through the Faroe Bank Channel carries significant volume flux and contributes to the ventilation of the deep North Atlantic Ocean. Here we present results from regional simulations of the Faroe Bank Channel overflow using a terrain-following ( σ-coordinate) ocean model with fine resolution near the sea bed. The model results are compared with observations of hydrography, currents and turbulence conducted in 2008. Turbulent dissipation rate and eddy diffusivity profiles inferred from the observations are used in refining the parameters of the turbulence closure. The model reproduces the observed vertical structure of the enhanced dissipation and diffusivity in the bottommost 50–60 m exceptionally well. In this region, shear-induced mixing dominates and is found to be well-represented by the applied second order turbulence closure models. Farther away from the boundary, however, in the 100-m thick interfacial layer and above the plume-ambient interface, the model does not resolve the observed mixing. The contribution of turbulence from breaking internal waves is one of the processes not represented in the model with significant consequences for observed entrainment and mixing. Regular sub-inertial oscillations (eddies) at 4–4.5 day period develop downstream of the sill, consistent with the observations. When averaged over several eddy events, the evolution of section-averaged plume properties over the oscillation period shows that the eddies significantly affect mixing and the descent rate of the plume. At a section 60 km downstream of the sill, eddies lead to periodic and abrupt cross-isobath descent of the overflow plume and an increase in dissipation rate by one order of magnitude.

Limitation of One-Dimensional Ocean Models for Coupled Hurricane–Ocean Model Forecasts

Abstract Wind stress imposed on the upper ocean by a hurricane can limit the hurricane’s intensity primarily through shear-induced mixing of the upper ocean and subsequent cooling of the sea surface. Since shear-induced mixing is a one-dimensional process, some recent studies suggest that coupling a one-dimensional ocean model to a hurricane model may be sufficient for capturing the storm-induced sea surface temperature cooling in the region providing heat energy to the hurricane. Using both a one-dimensional and a three-dimensional version of the same ocean model, it is shown here that the neglect of upwelling, which can only be captured by a three-dimensional ocean model, underestimates the storm-core sea surface cooling for hurricanes translating at <∼5 m s−1. For hurricanes translating at <2 m s−1, more than half of the storm-core sea surface cooling is neglected by the one-dimensional ocean model. Since the majority of hurricanes in the western tropical North Atlantic Ocean translate at <5 m s−1, the idealized experiments presented here suggest that one-dimensional ocean models may be inadequate for coupled hurricane–ocean model forecasting.