Shear Instability Research Articles

Magnetohydrodynamic mixed convection flow of liquid metals in a vertical channel: A stability analysis

The impact of applied magnetic field on liquid metal flows has good prospects for the industry. For a better understanding of flow dynamics, the stability analysis of liquid metal flows through a confined transverse magnetic field is of fundamental importance in designing advanced magnetohydrodynamic (MHD) devices for the next generation. In this paper, we report the linear stability analysis of mixed convection flow of electrically conducting liquid metals with low Prandtl number (Pr) in a vertical channel under a transverse magnetic field. The flow is described by quasi-static MHD approximation. The instability properties are examined numerically through a spectral collocation method. The influence of magnetic field on instability mechanism is examined for a good range of Pr. The results demonstrate that the growth of the infinitesimal disturbance decreases with increasing strength of the applied magnetic field due to the effective Lorentz force exerted on the flow, i.e., stability of the flow increases. In contrast, the stability of the basic flow decreases on increasing the value of Pr, except for a small range of Pr, where it increases. The kinetic energy balance shows that for very small values of Pr, the shear instability dominates the flow, whereas for relatively larger values of Pr, thermal-buoyant instability plays a significant role in the instability mechanism. The dissipation of energy in the kinetic energy balance occurs prominently due to the presence of the applied magnetic field. The secondary flow pattern shows that the applied magnetic field suppresses the disturbance in the vicinity of channel walls. In contrast, a decrease in thermal diffusivity provokes instability by inviting a strong disturbance cell in the middle portion of the channel. The energy dissipation in the kinetic energy balance occurs mainly due to the presence of the magnetic field.

37. Anatomic contributions to the stability of the L5-S1 segment under combined shear and compression: implications to isthmic/lytic spondylolisthesis

37. Anatomic contributions to the stability of the L5-S1 segment under combined shear and compression: implications to isthmic/lytic spondylolisthesis

Dynamics of dusty vortices – II. Stability of 2D dust-laden vortices

ABSTRACT Vortices have long been speculated to play a role in planet formation, via the collection of dust in the pressure maxima that arise at the cores of vortices in protoplanetary discs (PPDs). The question remains, however: as dust collects in the core of a vortex, when does that vortex remain stable and able to collect further dust, and when and why does it break up? We study this question by running high-resolution 2D simulations of dust-laden vortices. By using the terminal velocity approximation in a local shearing box, it was possible to efficiently run simulations of back-reacting dust in a gas at high resolution. Our results show how the stability of 2D dust-laden vortices in PPDs depends on their size relative to the disc scale height, as well as the dust coupling. We find small vortices with semiminor axis much smaller than the scale height to be stable for the duration of the simulations (t > 2000 orbits). Larger vortices, with semiminor axis smaller than but of the order of scale height, exhibit a drag instability after undergoing a long period of contraction where the core becomes progressively more dust rich. The lifetime of these vortices depends on the dust size, with larger dust grains causing the instability to occur sooner. For the size ranges tested in this paper, micrometre- to millimetre-sized grains, vortices survived for several hundreds of orbits. The result implies that the stability of vortices formed by vertical shear instability and zombie vortex instability, or the breakup of larger vortices through hydrodynamic instabilities, is affected by the presence of dust in the disc. The lifetimes observed in this paper, while shortened by the presence of dust for larger vortices, were still long enough to lead to considerable dust enrichment in the vortex cores.

Robust Subsurface Biological Response During the Decaying Stage of an Extreme Indian Ocean Dipole in 2019

AbstractThe Indian Ocean Dipole (IOD) is the predominant interannual climate mode and is critical in regulating the biogeochemical cycles of the equatorial Indian Ocean (EIO). However, the dynamics of nutrient supply and the magnitude of biological responses are less understood. Here, by comparing the biophysical in situ observations across the eastern EIO during the decaying period of a positive IOD in 2019 and neutral condition in 2017, we identify that the shoaling thermocline, initiated by reinforced easterly wind, lifts the nutricline into the euphotic layer under positive IOD condition. Coincidently, the strong turbulent mixing induced by the shear instability between the opposite‐flowing surface current and subsurface Equatorial Undercurrent increases the upward turbulent nutrient flux into the euphotic zone. Their combined effect triggers a vigorous subsurface biological response over the eastern EIO, with approximately twofold higher integrated chlorophyll‐a contents in the water column during a positive IOD than under neutral condition.

On the formation mechanisms of intragranular shear bands in olivine by stress-induced amorphization

Intragranular amorphization shear lamellae are found in deformed olivine aggregates. The detailed transmission electron microscopy analysis of intragranular lamella arrested in the core of a grain provides novel information on the amorphization mechanism. The deformation field is complex and heterogeneous, corresponding to a shear crack type instability involving mode I, II and III loading components. The formation and propagation of the amorphous lamella is accompanied by the formation of crystal defects ahead of the tip. These defects are geometrically necessary [001] dislocations, characteristics of high-stress deformation in olivine, and rotational nanodomains which are tentatively interpreted as disclinations. We show that these defects play an important role in dictating the path followed by the amorphous lamella. Stress-induced amorphization in olivine would thus result from a direct crystal-to-amorphous transformation associated with a shear instability and not from a mechanical destabilization due to the accumulation of high number of defects from an intense preliminary deformation. The preferential alignment of some lamellae along (010) is a proof of the lower ultimate mechanical strength of these planes.

Internal Wave and Turbulence Observations with Very High-Resolution Temperature Sensors along the Cabauw Mast

Abstract Knowledge about the characteristics of the atmospheric boundary layer is vital for the understanding of redistribution of air and suspended contents that are particularly driven by turbulent motions. Despite many modeling studies, detailed observations are still demanded of the development of turbulent exchange under stable and unstable conditions. In this paper, we present an attempt to observationally describe atmospheric internal waves and their associated turbulent eddies in detail, under varying stable conditions. Therefore, we mounted 198 high-resolution temperature (T) sensors with 1-m spacing on a 200-m-long cable. The instrumented cable was attached along the 213-m-tall meteorological mast of Cabauw, Netherlands, during late summer 2017. The mast has standard meteorological equipment at extendable booms at six levels in height. A sonic anemometer is at 60 m above ground. The T sensors have a time constant in air of τa ≈ 3 s and an apparent drift about 0.1°C month−1. Also due to radiation effects, short-term measurement instability is 0.05°C h−1 during nighttime and 0.5°C h−1 during daytime. These T-sensor characteristics hamper quantitative atmospheric turbulence research, due to a relatively narrow inertial subrange of maximum one order of magnitude. Nevertheless, height–time images from two contrasting nights show internal waves up to the buoyancy period of about 300 s, and shear and convective deformation of the stratification over the entire 197-m range of observations, supported by nocturnal marginally stable stratification. Moderate winds lead to 20-m-tall convection across weaker stratification, weak winds to episodic <10-m-tall shear instability across larger stratification.

Shear softening of earth's inner core as indicated by its high poisson ratio and elastic anisotropy

Earth's inner core exhibits an unusually high Poisson ratio and noticeable elastic anisotropy. The mechanisms responsible for these features are crucial to understanding the nature of Earth's core. Although different mechanisms have been proposed, few can explain both observations simultaneously. The results of this study indicated that the crystal with noticeable shear softening would have strong anisotropy and an exceptionally high Poisson ratio simultaneously. Body-centered-cubic (bcc) iron exhibits shear instability at inner-core pressures and can be dynamically stabilized by high temperature and the presence of light elements. The bcc-lattice iron alloy could have strong anisotropy and a Poisson ratio of Earth's inner core before shear instability. Identifying which light elements can stabilize the bcc-lattice iron alloy will provide an independent constraint on the chemical composition of the inner core.

Observation of strong turbulent mixing in the Australian North West Shelf

The North West Shelf (NWS) of Australia is a region with strong barotropic tides up to 10 m, which provide a source for intense turbulent mixing. In the study, we used turbulent mixing measurements obtained on the NWS from October to November 2017 to investigate the mixing characteristics during the austral spring season. In the surface mixed layer, the averaged dissipation rate reached 1 × 10−5 W/kg. The dissipation rate decreased to 1 × 10−8 W/kg in the thermocline and increased to 7 × 10−8 W/kg near the bottom. The averaged diffusivity in the surface mixed layer reached 7 × 10−1 m2/s, decreased to 1 × 10−4 m2/s in the thermocline, and increased to 7 × 10−3 m2/s near the seafloor. These values were significantly larger than those in the open ocean. The study proposed a parameterization method that scaled the diffusivity in a function of the Richardson number, κρ=κ0+κm(Ri)−1.5, where κ0 and κm were derived from the observation data, to take into account the strong shear instability conditions in our observation. Applications of this method for other shelf regions need further validation.

Measurements of Turbulence Generated by Wake Eddies Near a Steep Headland

AbstractTidal and low‐frequency flows interact with abrupt topographic features, giving rise to a variety of small‐scale phenomena including lee waves, vortical motions and turbulence. With the goal of identifying the processes that transfer momentum and energy between the larger‐scale and smaller‐scale flows, detailed tidally‐resolving shipboard surveys were conducted near a sharp and steep headland north of Velasco Reef, Palau, in the Western Pacific. We present velocity, microstructure and rapid‐cycling conductivity and temperature measurements, contextualized with a nearby 10‐month moored record, to examine wake and vortex structures. Observed flow near Velasco Reef was layered and multi‐directional in depth such that the “downstream” side of the headland depended on depth. Downstream of the headland, during a period where mean flow dominated over the tide in the top 100 m of the water column, turbulent kinetic energy dissipation rates were enhanced by up to three orders of magnitude relative to those upstream. During a period dominated by tides, the flow reversed periodically and wake eddies were associated with turbulent dissipation rates up to . Turbulent dissipation rates in the wake increased with inverse Richardson number for both tidal and mean flows past the headland, and were larger for stronger vorticity flows. Our analysis suggests that the eddies themselves lead to shear instabilities and subsequent turbulence, either through tilting or their limited vertical extent. We associate the enhanced downstream dissipation with a combination of breaking internal tides and either these eddy processes or a multi‐scaled turbulent wake.

Scratch damage on guiding surfaces of high-speed bearings under oil cut-off condition

The scratch damage mechanism on guiding surfaces of high-speed bearings due to impact-sliding coupling action under the oil cut-off condition was investigated. The surface topography and element composition on the scratch surfaces were tested. The impact-sliding contact behavior between the cage and outer ring was analyzed by using the finite element method. The results showed that scratch wear with obvious adhesion and oxidation occurred on the guiding surface of the outer ring. Plastic deformation was generated in near-surface layers with a depth of about 15 µm. The thermal shear instability and tribochemical reaction were the root causes of the scratch damage on guiding surfaces. Under the oil cut-off condition, the impact-sliding contact between the cage and ring generated high temperature rise, leading to material softening and surface oxidation. Consequently, adhesion occurred with obvious plastic deformation due to the shear instability of near-surface material at impact-sliding contact.

Velocity perturbations and Reynolds stresses in Holmboe instabilities

The velocity perturbations and Reynolds stresses associated with finite-amplitude Holmboe instabilities are investigated using linear stability analysis, numerical simulations, and laboratory experiments. The rightward and leftward propagating Holmboe instabilities are separated, allowing for a direct comparison of the perturbation fields between the numerical simulations and the linear stability analysis. The decomposition and superposition of the perturbation fields provide insights into the structure and origin of Reynolds stresses in Holmboe instabilities. Shear instabilities in stratified flows introduce a directional preference (anisotropy) in velocity perturbation fields, thereby generating Reynolds stresses. Here, we investigate this anisotropy by comparing pairs of horizontal and vertical velocity perturbations (u′,w′), obtained from the simulations and the laboratory experiment, with predictions from linear stability analysis. For an individual Holmboe mode, both the simulations and linear theory yield elliptical (u′,w′)-pairs that are oriented toward the second and fourth quadrants (u′w′<0), corresponding to the tilted elliptical trajectories of particle movement. Combining the leftward and rightward Holmboe modes yields (u′,w′) ellipses whose orientation and aspect ratio are phase-dependent. When averaged over a full cycle, the joint probability density functions of (u′,w′) in the linear theory and single wavelength simulations exhibit “steering wheel” structures. This steering wheel is smeared out in multiple wavelength simulations and the laboratory experiment due to varying wavelengths, resulting in an elliptical cloud. All of the approaches adopted in the present study yield Reynolds stresses that are comparable to those reported in previous laboratory and field investigations.

Gravity Wave Generation in Balanced Sheared Flow Revisited

Abstract The generation of internal gravity waves from an initially geostrophically balanced flow is diagnosed in nonhydrostatic numerical simulations of shear instabilities for varied dynamical regimes. A nonlinear decomposition method up to third order in the Rossby number (Ro) is used as the diagnostic tool for a consistent separation of the balanced and unbalanced motions in the presence of their nonlinear coupling. Wave emission is investigated in an Eady-like and a jet-like flow. For the jet-like case, geostrophic and ageostrophic unstable modes are used to initialize the flow in different simulations. Gravity wave emission is in general very weak over a range of values for Ro. At sufficiently high Ro, however, when the condition for symmetric instability is satisfied with negative values of local potential vorticity, significant wave emission is detected even at the lowest order. This is related to the occurrence of fast ageostrophic instability modes, generating a wide spectrum of waves. Thus, gravity waves are excited from the instability of the balanced mode to lowest order only if the condition of symmetric instability is satisfied and ageostrophic unstable modes obtain finite growth rates. Significance Statement We aim to understand the generation of internal gravity waves in the atmosphere and ocean from a flow field that is initially balanced, i.e., free from any internal gravity waves. To examine this process, we use simulations from idealized numerical models and nonlinear flow decomposition method to identify waves. Our results show that a prominent mechanism by which waves can be generated is related to symmetric or ageostrophic instabilities of the balanced flow possibly occurring during frontogenesis. This process can be a significant mechanism to dissipate the energy of the geostrophic flow in the ocean.

Wavy regime of a colloidal falling film

We explore the linear stability and subsequent formation of nonlinear waves in a colloidal, gravity-driven falling film flow. The problem of a gravity-driven falling film devoid of any microstructure has been well studied. However, the role of particulate suspensions in the stability and dynamics of such systems is less explored. We perform a linear stability analysis and observe that the presence of colloidal particles stabilizes both the long-wave surface and short-wave shear instability modes. We also derive nonlinear models in the framework of long-wave theory using Benney's gradient expansion and the Integral Boundary Layer (IBL) approach to study the systems' wavy dynamics.

Minimal nonlinear dynamical system for the interaction between vorticity waves and shear flows.

This study is a direct follow-up of the paper by Heifetz and Guha [Phys. Rev. E 100, 043105 (2019)2470-004510.1103/PhysRevE.100.043105] on a minimal nonlinear dynamical system, describing a prototype of linearized two-dimensional shear instability. In that paper, the authors describe the instability in terms of an action at a distance between two vorticity waves, each of which propagates counter to its local mean flow as well as counter to the other. Here we add to the model the effect of mutual interaction between the waves and the mean flow, where growth of the waves reduces the mean shear and vice versa. This addition yields oscillatory Hamiltonian dynamics, including states of phase slipping and libration with finite-size wave amplitude oscillations. We find that wave-mean-flow dynamics emerging from unstable normal modes in the linearized stage are doomed to librate around the antiphased neutral configuration in which the waves hinder each other's counterpropagation rate. We discuss as well how the given dynamics relates to familiar models of phase oscillators.

Wavelike nature of the vertical shear instability in global protoplanetary discs

ABSTRACT The vertical shear instability (VSI) is a robust phenomenon in irradiated protoplanetary discs (PPDs). The majority of previous numerical simulations have focused on the turbulent properties of its saturated state. However, the saturation of the VSI manifests as large-scale coherent radially travelling inertial waves. In this paper, we study inertial-wave-disc interactions and their impact on VSI saturation. Inertial-wave linear theory is developed and applied to a representative global 2D simulation using the athena++ code. It is found that the VSI saturates by separating the disc into several radial wave zones roughly demarcated by Lindblad resonances (turning points); this structure also manifests in a modest radial variation in the vertical turbulence strength. Future numerical work should employ large radial domains to accommodate this radial structure of the VSI, while concurrently adopting sufficiently fine resolutions to resolve the parametric instability that attacks the saturated VSI inertial waves.

Direct simulation of flow-boiling crisis and its porous-metasurface control for very large dryout limit

The Zuber pool-boiling hydrodynamic instability theory establishes that the critical heat flux qCHF,Z is based on rising surface vapor columns with liquid counterflow in a unit cell the of size of the critical wavelength λc determined by the Kelvin-Helmholtz and Rayleigh-Taylor interfacial instabilities. In the flow boiling, the forced velocity ul,o creates a leading-edge region complementing these phase-buoyant flows and breaking the periodicity of the Zuber unit cell. Here, with the direct numerical simulations (DNS), i.e., CFD-VOF-LES, of the Zuber unit cell for saturated water (one atm), the effect of ul,o on the hydrodynamic dryout qCHF,h is examined. The results show that the upstream liquid flow penetrates the boiling region, forming surface liquid tracks meandering between the vapor columns, and upon qCHF,h these tracks become unstable causing surface dryout. For ul,o as small as 5 cm/s, the axial liquid inertia deflects the vapor track and establishes the surface liquid track, raising qCHF,h noticeably over qCHF,Z and this is in good agreement with the available experiments. From the available theories, DNS-results and dimensional analysis, a relation is found between ul,o and λc establishing the wavelength modulation enhancement of the qCHF,h by increasing ul,o which decreases λc. In this new relation qCHF,h is proportional to ul,o1/6. The limit on this modulation enhancement is the capillarity limit qCHF,c= 3.3 MW/m2 compared to qCHF,Z= 1.1 MW/m2Next, the DNS results show that anisotropic arrangement of the vapor sites stabilizes the surface liquid track, thus increasing the qCHF,h. This geometric control of the vapor sites is achieved with a 3-D perforated porous coating, e.g., the flow-boiling canopy wick (FBCW). This geometric-modulated CHF enhancement is much larger than the wavelength-modulation enhancement and its vapor shear instability limit is overcome with the use of levees (geometric confinement) allowing for q> 10 MW/m2. However, the FBCW has an internal capillary-viscous limit qCHF,c−v (about 5.2 MW/m2 using sintered-powder wick) which favors small λc and currently is the bottleneck for achieving extremely large qCHF,h (which favors large λc).

Bistability of turbulent flow in open-channel expansion: Characterization and suppression

Three-dimensional turbulent bistable flow (TBF) in an open-channel expansion is predicted using large eddy simulation. The free surface of TBF is tracked using the volume of fluid method, coupled with the level-set method. This paper aims to reveal the ensemble-average flow characteristics and explore effective ways to control bistability. For a given condition of flow approaching an expansion, either of two stable flow states can possibly occur, depending on the flow history. The predicted pressure field agrees well with experimental data. The velocity field is decomposed into deformation regions and eddy-rotation regions using the Okubo–Weiss parameter. Turbulent eddies initiated by shear instability dominate those associated with sidewall-friction force; this condition is responsible for the occurrence of bistability. Fitting a simple hump at a flat-bottom expansion is an effective way to suppress bistability. The presence of the hump shrinks eddy cores and breaks the interaction between eddies triggered by instabilities and eddies induced by friction forces; the result is an increase in flow uniformity and control of turbulence, flow separation, and vortex behavior.

Shear Instability and Turbulent Mixing in the Stratified Shear Flow Behind a Topographic Ridge at High Reynolds Number

Observations on the lee of a topographic ridge show that the turbulence kinetic energy (TKE) dissipation rate due to shear instabilities is three orders of magnitude higher than the typical value in the open ocean. Laboratory-scale studies at low Reynolds number suggest that high turbulent dissipation occurs primarily within the core region of shear instabilities. However, field-scale studies indicate that high turbulence is mainly populated along the braids of shear instabilities. In this study, a high-resolution, resolving the Ozmidov-scale, non-hydrostatic model with Large Eddy Simulation (LES) turbulent closure is applied to investigate dominant mechanisms that control the spatial and temporal scales of shear instabilities and resulting mixing in stratified shear flow at high Reynolds number. The simulated density variance dissipation rate is elevated in the cusp-like bands of shear instabilities with a specific period, consistent with the acoustic backscatter taken by shipboard echo sounder. The vertical length scale of each cusp-like band is nearly half of the vertical length scale of the internal lee wave. However, it is consistent with instabilities originating from a shear layer based on linear stability theory. The model results indicate that the length scale and/or the period of shear instabilities are the key parameters to the mixing enhancement that increases with lateral Froude number FrL, i.e. stronger shear and/or steeper ridge.

Enhanced resistance to shear instability by gradient nanolayered structures in sputtered Cu/Zr composites

Nanolayered metallic composites have exhibited ultrahigh strength but compromised ductility due to their vulnerability to shear instability during deformation. Here we show that a gradient nanolayer design is effective in tuning the resistance to shear instability of the layered composites. The gradient design is realized by architecting a gradient distribution in the constituent layer thickness from the surface to the core. A combination of nano and micro-indentation tests and scanning transmission electron microscopy is employed to investigate the shear instability of the newly designed gradient nanolayered Cu/Zr composites. The nanoindentation tests show that the plastic pileup (sign of shear banding) is eliminated in the gradient nanolayered sample with more thin layers, while the microindentation tests show that less shear bands are formed by increasing the number of thin layers. Both tests demonstrated an enhanced resistance to shear instability by an appropriate gradient nanolayer design, which can be attributed to the improved strain delocalization capability and high dislocation density.

Simultaneous velocity–density measurements of downslope density clouds

We present results from laboratory experiments of the downslope propagation of a finite volume released gravity current by means of combined PIV/PLIF measurements. The experimental data were used to estimate the global characteristics of the current, such as the propagation speed, the lateral surface and the buoyancy, revealing that thermal theory is a robust model that can predict such quantities properly, especially the models of Beghin et al. (1981), Maxworthy (2010) and the theoretical model of Dai (2013a). The collected data allowed also for the determination of the entrainment rates based on the turbulent fluxes instead using the variation of the volume flux, and the regions of entrainment/detrainment have been identified. The results support previous observations of the mechanism responsible for the buoyancy loss of the cloud and its consequent deceleration down the slope, as a large scale recirculation vortex at the back of the cloud. A very complex interior structure of the cloud is observed, with a large variety of turbulent processes taking place, such as the large-scale convectively unstable recirculation vortex at the scale of the current itself, the small-scale convectively unstable motions inside the head of the cloud and close to the bottom boundary and shear (Kelvin–Helmholtz) instabilities at the boundary between the current and the ambient water. The synoptic velocity and density measurements allowed also to test existent parametrizations of turbulent fluxes, that have been quantified in 2D fields with a high spatial resolution. Results confirm that parametrization laws based on the assumption of a constant turbulent diffusivity or mixing length do not apply for buoyancy clouds due to their high spatial heterogeneity. Hence, the parametrization of the turbulent diffusivities in such flows should be based on scalar quantities that avoid the problem of spatial heterogeneity and takes into account the different sources of turbulence production, e.g. using energetic considerations that compare the terms having a definite exchange of energy and acts as a source or a sink.