Unstable Shear Research Articles

Super-high compressive plastic deformation behaviors of Zr-based metallic glass at room temperature

The plastic deformation behavior of a Zr-based metallic glass with super-high compressive ductility was investigated. It was found that large amount of excess free volume would induce large shear transformation zone (STZ), which could stimulate multiple primary shear bands and stabilize their propagation. However, the sample with small STZ showed unstable single shear banding, and an obvious stress valley was found in the true stress–strain curve. This finding is important for understanding the plastic deformation behaviors of various metallic glasses.

Trapping of gyrotactic organisms in an unstable shear layer

To explore new mechanisms for planktonic thin layer formation, particle and continuum models of gyrotactically swimming phytoplankton are embedded in simulations of a dynamically unstable stratified shear layer. Two trapping mechanisms are observed in the developing Kelvin–Helmholtz (K–H) billow train. Within the K–H billows, a particle can remain preferentially in downwelling regions, cancelling its upward swimming motion. In the braids that separate the billows, intense shear defeats the gyrotactic stabilization mechanism and causes cells to tumble. Particle and continuum models are compared statistically to reveal both consistencies and weaknesses in each. A scaling based on Reynolds number and swimming speed is used to predict the maximum concentration generated by an instability event. Although K–H billows are short lived in comparison with planktonic thin layers observed in the coastal oceans, the resulting trapping causes rapid aggregation. We conclude that trapping in a growing K–H instability could contribute to the development of the observed cell concentrations.

Hindfoot Joint Pressure in Supination Sprains

Background: Hindfoot trauma including ankle and subtalar sprains may be followed by osteochondral lesions and persisting pain originating from posttraumatic arthritis. Hypothesis: “Acute severe” supination sprains and “mild supination sprains with increasing ligamentous incompetence” of the hindfoot lead to medial ankle and subtalar stress concentrations that may contribute to osteochondral lesions (OCLs) and subsequent arthritis. Study Design: Controlled laboratory study. Methods: “Acute severe” sprains and “mild sprains with increasing ligamentous incompetence” (consecutive anterior talofibular ligament [ATFL], calcaneofibular ligament [CFL], and lateral talocalcaneal ligament [LTCL] transections) were simulated in human lower leg specimens (7 different specimens for each condition). The effect on the migration of the center of force (COF) and on the tibiotalar and subtalar pressures at 700-N (acute severe) and 150-N (mild sprain with increasing ligamentous incompetence) axial static and dynamic loads, respectively, was recorded using pressure sensors. Results: In the “acute severe” sprain, the peak pressure increase reached the level of significance in the ankle (P = .042) and in the subtalar medial facet (P = .046). The ankle COF migrated significantly toward the medial (P = .001) and posterior (P = .023) directions. In the “mild sprain with increasing ligamentous incompetence” condition, the ankle (P = .018) and subtalar (medial facet, P = .022) peak pressure increased significantly with intact ligaments and with all ligaments cut. The ankle COF migrated significantly toward the medial direction when the ATFL and CFL or when all 3 ligaments were severed. The anteroposterior ankle COF migration was anterior when all ligaments were intact or when only the ATFL was severed but posterior when the CFL or when the CFL and the LTCL were severed in addition. Conclusion: Next to chronic inhomogeneous load distribution in the unstable hindfoot and shear stress during sprains, intra-articular pressure elevation (impact) in the ankle and subtalar joint during hindfoot supination sprains with intact ligaments or incompetent ligaments likely contributes to OCLs of the medial talar dome and the medial subtalar facet. Clinical Relevance: Intra-articular hindfoot pressure elevation (impact) in “acute severe” and in “mild hindfoot supination sprains with increasing ligamentous incompetence” is substantial for the development of OCLs at the medial midtalar dome and the medial facet of the subtalar joint.

NONLINEAR EVOLUTION OF GLOBAL HYDRODYNAMIC SHALLOW-WATER INSTABILITY IN THE SOLAR TACHOCLINE

We present a fully nonlinear hydrodynamic model of the solar tachocline. The model consists of a global spherical shell of differentially rotating fluid, which has a deformable top, thus allowing motions in radial directions along with latitudinal and longitudinal directions. When the system is perturbed, in the course of its nonlinear evolution it can generate unstable low-frequency shallow-water shear modes from the differential rotation, high-frequency gravity waves, and their interactions. Radiative and overshoot tachoclines are characterized in this model by high and low effective gravity values, respectively. Building a semi-implicit spectral scheme containing very low numerical diffusion, we perform nonlinear evolution of shallow-water modes. Our first results show that (1) high-latitude jets or polar spin-up occurs due to nonlinear evolution of unstable hydrodynamic shallow-water disturbances and differential rotation, (2) Reynolds stresses in the disturbances together with changing shell thickness and meridional flow are responsible for the evolution of differential rotation, (3) disturbance energy primarily remains concentrated in the lowest longitudinal wavenumbers, (4) an oscillation in energy between perturbed and unperturbed states occurs due to evolution of these modes in a nearly dissipation-free system, and (5) disturbances are geostrophic, but occasional nonadjustment in geostrophic balance can occur, particularly in the case of high effective gravity, leading to generation of gravity waves. We also find that a linearly stable differential rotation profile remains nonlinearly stable.

Intermittent patches of turbulence in a stratified medium with stable shear

Direct numerical simulation (DNS) is used to investigate the evolution of intermittent patches of turbulence in a background flow with the gradient Richardson number, Rig , larger than the critical value of 0.25. The base flow consists of an unstable stratified shear layer (Rig <0.25) located on top of a stable shear layer (Rig >0.25), whose shear and stratification are varied. The unstable shear layer undergoes a Kelvin–Helmholtz shear instability that develops into billows. Vortices associated with the billows are pulled into the bottom shear layer and stretched by the local shear into a horseshoe configuration. The breakdown of the horseshoe vortices generates localized patches of turbulence. Three cases with different levels of shear and stratification, but with the same Rig , in the bottom shear layer are simulated to examine the popular hypothesis that mixing is determined by local Rig . In the case with largest shear and stratification, the vortices are less likely to penetrate the bottom layer and are quickly dissipated due to the strong stratification. In the case with moderate shear and stratification, vortices penetrate across the bottom layer and generate turbulence patches with intense dissipation rate. The case with the mildest level of shear and stratification shows the largest net turbulent mixing integrated over the bottom layer. Analysis of the turbulent kinetic energy budget indicates that the mean kinetic energy in the bottom layer contributes a large amount of energy to the turbulent mixing. In all cases, the mixing efficiency is elevated during the penetration of the vortices and has a value of approximately 0.35 when the turbulence in the patches decays.

음향방출기법을 이용한 KURT 화강암의 균열 발생 특성에 관한 실험적 연구

방사성폐기물처분장 주변 암반의 수많은 불확실성을 이해하기 위해서는 무결암에서 발생하는 균열의 성장과 거동 분석은 필수이다. 이에 본 연구에서는 처분장과 유사한 지질적 구조적 특성을 지닌 한국원자력연구원 내에 위치한 지하처분연구시설에서 채취한 화강암 시료를 이용하여 균열의 성장과 이에 따른 손상도를 AE parameter와 모멘트텐서해석법을 이용하여 분석하였다. 시료의 균열개시 균열결합 균열손상응력은 최대강도의 0.45배, 0.73배, 0.84배인 것으로 나타났다. 모벤트텐서해석법을 이용한 결과 응력 초기에는 인장균열의 발달이 우세하였으나 응력 수준이 증가함에 따라 전단균열이 발달하였다. 또한 시료에 균열손상응력 이상의 응력이 가해지면 파괴면을 중심으로 불안정한 전단균열이 발생하였으며 이는 파괴에 직접적인 역할을 하는 것으로 해석되었다. The first step in improving our understanding of uncertainties suclt as rock mass strength parameters and deformation modulus in rock masses around high-level radioactive waste disposal repositories, for improved safety, is to study the process of crack development in intact rock. Therefore, in this study, the fracture process and crack development were examined in samples of KURT granite taken from the KAERI Underground Research Tunnel (KURT), based on acoustic emission (AE) and moment tensor analysis. The results show that crack initiation, coalescence, and unstable crack occurred at rock uniaxial compressive strengths of 0.45, 0.73, and 0.84, respectively. In addition, moment tensor analysis indicated that during the early stage of loading, tensile cracks were predominant. With increasing applied stress, the number of shear cracks gradually increased. When the applied stress exceeded the stress level required for crack damage, unstable shear cracks which directly result in failure of the rock were generated along the failure plane.

Steven Alan Orszag

Steven Alan Orszag

Further Characterization of the Disturbance Field in a Transversely Excited Swirl-Stabilized Flame

This paper describes an analysis of the unsteady flow field in swirl flames subjected to transverse acoustic waves. This work is motivated by transverse instabilities in annular gas turbine combustors, which are a continuing challenge for both power generation and aircraft applications. The unsteady flow field that disturbs the flame consists not only of the incident transverse acoustic wave, but also longitudinal acoustic fluctuations and vortical fluctuations associated with underlying hydrodynamic instabilities of the base flow. We show that the acoustic and vortical velocity fluctuations are of comparable magnitude. The superposition of these waves leads to strong interference patterns in the velocity field, a result of the significantly different wave propagation speeds and axial phase dependencies of these two disturbance sources. Vortical fluctuations originate from the convectively unstable shear layers and absolutely unstable swirling jet. We argue that the unsteady shear layer induced fluctuations are the most dynamically significant, as they are the primary source of flame fluctuations. We also suggest that vortical structures associated with vortex breakdown play an important role in controlling the time-averaged features of the central flow and flame spreading angle, but do not play an important role in disturbing the flame at low disturbance amplitudes. This result has important implications not only for our understanding of the velocity disturbance field in the flame region, but also for capturing important physics in future modeling efforts.

Transport layer structure in intense bed-load

[1] We report laboratory experiments on intense bed-load driven by turbulent open-channel flows. Using high-speed cameras and a laser light sheet, we measured detailed profiles of granular velocity and concentration near the sidewall. The profiles provide new information on transport layer structure and its relation to the applied Shields stress. Contrary to expectations, we find that intense bed-load layers respond to changes in flow conditions by adjusting their granular concentration at the base, slightly above the bed. Two mechanisms account for the resulting behavior: stresses generated by immersed granular collisions, and equilibration of the otherwise unstable shear layer by density stratification. Without parameter adjustment, the deduced constitutive relations capture the responses of velocity, concentration, and layer thickness to a ten-fold increase in Shields stress.

Mixing in a Moderately Sheared Salt-Fingering Layer

Abstract Mixing due to sheared salt fingers is studied by means of direct numerical simulations (DNS) of a double-diffusively unstable shear layer. The focus is on the “moderate shear” case, where shear is strong enough to produce Kelvin–Helmholtz (KH) instability but not strong enough to produce the subharmonic pairing instability. This flow supports both KH and salt-sheet instabilities, and the objective is to see how the two mechanisms work together to flux heat, salt, and momentum across the layer. For observed values of the bulk Richardson number Ri and the density ratio Rρ, the linear growth rates of KH and salt-sheet instabilities are similar. These mechanisms, as well as their associated secondary instabilities, lead the flow to a fully turbulent state. Depending on the values of Ri and Rρ, the resulting turbulence may be driven mainly by shear or mainly by salt fingering. Turbulent mixing causes the profiles of temperature, salinity, and velocity to spread; however, in salt-sheet-dominated cases, the net density (or buoyancy) layer thins over time. This could be a factor in the maintenance of the staircase and is also an argument in favor of an eventual role for Holmboe instability. Fluxes are scaled using both laboratory scalings for a thin layer and an effective diffusivity. Fluxes are generally stronger in salt-sheet-dominated cases. Shear instability disrupts salt-sheet fluxes while adding little flux of its own. Shear therefore reduces mixing, despite providing an additional energy source. The dissipation ratio Γ is near 0.2 for shear-dominated cases but is much larger when salt sheets are dominant, supporting the use of Γ in the diagnosis of observed mixing phenomena. The profiler approximation Γz, however, appears to significantly overestimate the true dissipation ratio.

Spontaneous transition of core radial electric field driven by magnetic islands in the H-1NF heliac

This paper reports an experimental observation of spontaneous transition of the core radial electric field to a large positive value (Er ∼ 5 kV m−1), with a strong electric-field shear (∼700 kV m−2) in a low temperature (Te ∼ 10 eV) radio frequency generated argon plasma in the H-1NF heliac stellarator. The transition, which seems to be driven by a spontaneous excitation of m = 2 magnetic islands near the core, is associated with a localized increase in the plasma density and excitation of coherent low frequency (∼3 kHz) oscillations possibly due to unstable Er shear driven modes. Evidence suggests development of the core electron-root scenario, which previously has been observed only at high temperature electron cyclotron heated plasmas.

Evaluation of Acoustic- and Flow-Induced Vibration of the BWR Main Steam Lines and Dryer

The boiling water reactor (BWR-3) steam dryer in the Quad Cities (QC) Unit 2 Nuclear Power Plant was damaged by high-cycle fatigue due to acoustic-induced vibration. The cause of the dryer failure was considered as flow-induced acoustic resonance at the stub pipes of the safety relief valve (SRV) in the main steam lines (MSLs). The acoustic resonance was considered to be generated by the interaction between the sound field and an unstable shear layer across the closed side branches of SRVs. We have started a research program on BWR steam dryers to develop methods of evaluating the loading. Moreover, it is necessary to evaluate the dryer integrity of BWR-5 plants, which are the main type of BWR in Japan. In the present study, we conducted 1/10-scale BWR model tests and analysis to investigate the flowinduced acoustic resonance and acoustic characteristics in MSLs. The test apparatus consisted of a steam dryer, a steam dome, and 4 MSLs with 20 SRV stub pipes. Computational fluid dynamics (CFD) analysis was conducted to evaluate the acoustic source in MSLs. Finite element method (FEM) was applied to calculate the three-dimensional wave equations for acoustic analysis. We demonstrated that large fluctuating pressure occurred in the high- and low-frequency regions. The high-frequency fluctuating pressure was generated by the flow-induced acoustic resonance in the SRV stub pipes. We evaluated the acoustic source (that is, the fluctuating pressure) in MSLs by unsteady CFD calculations, and we evaluated the pressure propagation by acoustic analysis. These results were verified by comparison with the results of scale-model tests, and they showed good agreement with the experimental results. The effects of the difference between the properties of air and steam were numerically investigated, and it was found that the effects on the acoustic resonance in the SRV stub pipes were not significant.

An Investigation of Turbine Wheelspace Cooling Flow Interactions With a Transonic Hot Gas Path—Part II: CFD Simulations

A computational model has been developed to study the mechanisms responsible for hot gas ingestion into the wheel-space cavity of a stationary high pressure turbine (HPT) cascade rig. Simulations were undertaken for the stationary rig described by Bunker et al. (2009, “An Investigation of Turbine Wheelspace Cooling Flow Interactions With a Transonic Hot Gas Path—Part I: Experimental Measurements,” ASME Paper No. GT2009-59237) in a companion paper. The rig consists of five vanes, a wheel-space cavity, and five cylinders that represent the blockage due to the leading edge of the rotor airfoils. The experimental program investigated two cylinder diameters and three clocking positions for a nominal coolant flow rate. Comparisons are made between the computed and measured flow-fields for the smaller of the two cylinders. It is demonstrated that the circumferential variation of pressure established by the vane wake and leading edge bow wave results in an unstable shear layer over the rim seal axial gap (trench) that causes hot gases to ingest for a nominal coolant flow. Steady-state computational fluid dynamics (CFD) simulations did not capture this effect and it was determined that an unsteady analysis was required in order to match the experimental data. Favorable agreement is noted between the time-averaged computed and measured pressure distributions in the circumferential direction both upstream and downstream of the trench, as well as within the trench itself. Furthermore, it is noted that time-averaged buffer cavity effectiveness agrees to within 5% of the experimental data for the cases studied. The validated CFD model is then used to simulate the effect of rotation by rotating the cylinders and disk at rotational rate that scales with a typical engine. A sliding mesh interface is utilized to communicate data between the stator and rotor domains. The stationary cases tend to ingest past the first angel-wing for a nominal coolant flow condition, whereas the effect of rotation helps pressurize the cavity and is responsible for preventing hot gas from entering the buffer cavity.

Influence of Interfacial Slip on Mechanical Adhesion of Immiscible Polymers

The impact of shear flow instability of two-layer incompatible viscous fluids on mechanical adhesion is studied in this work by numerical modeling. The interface shape evolution is tracked with the level set method using the alternating distance function vanishing at the interface between the layers. It is found that the unstable simple shear flow leads to formation of viscous fingers producing mechanical anchoring after solidification of the system. The shape and length of the viscous fingers are shown to strongly depend on layer viscosity and thickness ratio as well as on interface boundary conditions. The apparent interfacial slip is modeled by the thin intermediate layer of low viscosity. This is found to result in an acceleration of extension of viscous fingers in comparison to that revealed at stick boundary conditions. These structures should lead to strengthening of anchoring between layers and thus promote mechanical adhesion between immiscible polymers.

A Resolution of the Sommerfeld Paradox

The Sommerfeld paradox roughly says that mathematically Couette linear shear is linearly stable for all Reynolds numbers, but experimentally arbitrarily small perturbations can induce the transition from the linear shear to turbulence when the Reynolds number is large enough. The main idea of our resolution of this paradox is to show that there is a sequence of linearly unstable shears which approaches the linear shear in the kinetic energy norm but not in the enstrophy (vorticity) norm. These oscillatory shears are single Fourier modes in the Fourier series of all the shears. In experiments, such linear instabilities will manifest themselves as transient nonlinear growth leading to the transition from the linear shear to turbulence. Under the Euler dynamics, these oscillatory shears are steady, and cat's eye structures bifurcate from them as traveling waves. The three-dimensional shears $(U(y,z),0,0)$ in a neighborhood of these oscillatory shears are linearly unstable too. Under the Navier–Stokes dynamics, these oscillatory shears are not steady but rather slowly drifting. When these oscillatory shears are viewed as frozen, the corresponding Orr–Sommerfeld operator has unstable eigenvalues which approach the corresponding inviscid eigenvalues when the Reynolds number tends to infinity. All the linear instabilities mentioned above offer a resolution to the Sommerfeld paradox and an initiator for the transition from the linear shear to turbulence.

Analysis of critical length measurements for dry snow slab weak-layer shear fracture

AbstractSnow slab avalanches primarily release by propagation of shear fractures within thin weak layers under much thicker slabs. In some cases, the weak layer is on the order of 1 mm thick and such fractures may be considered to be a mode II shear fracture at initiation. In the cases analysed in this paper, the weak layer has finite thickness, and slope-normal effects may be present. Field data from &gt;500 snow shear fracture tests are analysed and applied to the problem of weak-layer fracture. The paper contains a detailed analysis using a simple analytical model to estimate the critical length prior to an unstable shear fracture. The model contains the assumption of a finite fracture process zone which may be a significant fraction of the slab depth,D, or the critical length,L, for weak-layer shear fracture. The field results show that theL/Dratio varies from ∼0.1 to just over 2, and the model results are close to the same range. The analysis also shows that both the field and model results forL/Dfollow a Gumbel probability density function. Since the experimental field data contain rate-dependent (viscoelastic) and slope-normal effects, it is imperative to account for these in the model and for snow slab instability evaluation when using test data. Detailed evaluations considering both these effects are given. The applicability of the test data to avalanche release is discussed.

Evaluation of Acoustic- and Flow-Induced Vibration of the BWR Main Steam Lines and Dryer

The boiling water reactor (BWR-3) steam dryer in the Quad Cities (QC) Unit 2 Nuclear Power Plant was damaged by high-cycle fatigue due to acoustic-induced vibration. The cause of the dryer failure was considered as flow-induced acoustic resonance at the stub pipes of the safety relief valve (SRV) in the main steam lines (MSLs). The acoustic resonance was considered to be generated by the interaction between the sound field and an unstable shear layer across the closed side branches of SRVs. We have started a research program on BWR steam dryers to develop methods of evaluating the loading. Moreover, it is necessary to evaluate the dryer integrity of BWR-5 plants, which are the main type of BWR in Japan. In the present study, we conducted 1/10-scale BWR model tests and analysis to investigate the flowinduced acoustic resonance and acoustic characteristics in MSLs. The test apparatus consisted of a steam dryer, a steam dome, and 4 MSLs with 20 SRV stub pipes. Computational fluid dynamics (CFD) analysis was conducted to evaluate the acoustic source in MSLs. Finite element method (FEM) was applied to calculate the three-dimensional wave equations for acoustic analysis. We demonstrated that large fluctuating pressure occurred in the high- and low-frequency regions. The high-frequency fluctuating pressure was generated by the flow-induced acoustic resonance in the SRV stub pipes. We evaluated the acoustic source (that is, the fluctuating pressure) in MSLs by unsteady CFD calculations, and we evaluated the pressure propagation by acoustic analysis. These results were verified by comparison with the results of scale-model tests, and they showed good agreement with the experimental results. The effects of the difference between the properties of air and steam were numerically investigated, and it was found that the effects on the acoustic resonance in the SRV stub pipes were not significant.

Mesosphere‐stratosphere‐troposphere radar observations of characteristics of lower atmospheric high‐frequency gravity waves passing through the tropical easterly jet

In this study, we have examined the characteristics of high‐frequency gravity waves (5–50 min periodicity) over a tropical region using the mesosphere‐stratosphere‐troposphere (MST) radar installed at Gadanki (13.5°N, 79.2°E), India. The MST radar (53 MHz) was operated continuously for ∼15.5 h during 1700–0840 LT on 2–3 June 2005. During this period, a strong unstable wind shear region existed above the tropical easterly jet at the height of tropopause. This has provided an excellent opportunity to study the characteristics of internal atmospheric high‐frequency (∼15–40 min periodicity) gravity waves, generated in the boundary layer and passing through the shear layer. The study reveals the generation of higher‐frequency (5–15 min periodicity) gravity waves from this strong shear region and their vertical propagation both below up to a few kilometers and above the shear layer (∼0.5 km thick). These waves showed upward propagation even above 20 km in the lower stratosphere, indicating that unstable shear layers are the important source of momentum and energy fluxes that contribute significantly to the middle atmospheric dynamics in terms of gravity waves. Further, a close association was also observed between the dissipating gravity waves and the distinctly enhanced signal‐to‐noise ratio and Doppler spectral width of the MST radar echoes. The present observation of radiation of high‐frequency gravity waves that propagate vertically upward from a strong wind shear region located immediately below a highly stratified layer is in accordance with the “direct mechanism” explained by nonlinear numerical simulation studies. For the first time, the present study illustrates the existence of layers of polarized refractive index structures in the heights of 10–15 km.

On vortex cascades in shear flow instabilities

Based on direct numerical simulation, the initial stage of turbulence development via hydrodynamic instabilities, the formation of vortices and their mixing is investigated. New results obtained from the numerical modeling of the vortex cascade phenomenon in an unstable shear flow are presented. The initial stage of the onset of turbulence in 3D free shear flows of an ideal compressible gas is studied. The development of the cascade of instabilities is initiated by pre-set random or harmonic disturbances of the initial velocity.

Inviscid Dynamical Structures Near Couette Flow

Consider inviscid fluids in a channel {-1<y<1}. For the Couette flow v_0=(y,0), the vertical velocity of solutions to the linearized Euler equation at v_0 decays in time. At the nonlinear level, such inviscid damping has not been proved. First, we show that in any (vorticity) H^{s}(s<(3/2)) neighborhood of Couette flow, there exist non-parallel steady flows with arbitrary minimal horizontal period. This implies that nonlinear inviscid damping is not true in any (vorticity) H^{s}(s<(3/2)) neighborhood of Couette flow and for any horizontal period. Indeed, the long time behavior in such neighborhoods are very rich, including nontrivial steady flows, stable and unstable manifolds of nearby unstable shears. Second, in the (vorticity) H^{s}(s>(3/2)) neighborhood of Couette, we show that there exist no non-parallel steadily travelling flows v(x-ct,y), and no unstable shears. This suggests that the long time dynamics in H^{s}(s>(3/2)) neighborhoods of Couette might be much simpler. Such contrasting dynamics in H^{s} spaces with the critical power s=(3/2) is a truly nonlinear phenomena, since the linear inviscid damping near Couette is true for any initial vorticity in L^2.