Presence Of Shear Flow Research Articles

Conditions for Relativistic Magnetic Reconnection under the Presence of Shear Flow and Guide Field

The scaling of the relativistic reconnection outflow speed is studied in the presence of both shear flows parallel to the reconnecting magnetic fields and guide fields pointing out of the reconnection plane. In nonrelativistic reconnection, super-Alfvénic shear flows have been found to suppress reconnection. We extend the analytical model of this phenomenon to the relativistic regime and find similar behavior, which is confirmed by particle-in-cell simulations. Unlike the nonrelativistic limit, the addition of a guide field lowers the in-plane Alfvén velocity, contributing to slower outflow jets and the more efficient suppression of reconnection in strongly magnetized plasmas.

Effects of shear flows on columnar dendritic microstructure during rapid solidification of IN718 alloy: A cellular automaton-lattice Boltzmann modeling study

The growth of columnar dendrites during rapid directional solidification of IN718 alloy in the presence of shear flows is simulated by using a coupled cellular automaton-lattice Boltzmann (CA-LB) model. The developed CA-LB model is benchmarked by the mesh independency of the steady-state dendrite growth velocity and the primary dendrite arm spacing (PDAS) under different cooling rates. The CA-LB model is then applied to simulate the columnar dendrite growth under different shear flows and cooling rates in the conditions of rapid solidification. The values of PDAS under different conditions are determined from the simulation results, and are correlated with the shear flow rate (Ush) and cooling rate (CR). A unified fitting formula is developed to represent the effects of Ush and CR on the evolution of PDAS. The PDAS is found to decrease with CR increasing, but increase with Ush increasing. Moreover, it is revealed that the influence of Ush on PDAS becomes stronger as CR increases.

Analysis of supersonic shear effects on flame characteristics of an evaporating flame-holder

Flame stabilization and its interaction with flow characteristics are crucial to the development of air-breathing propulsion engine. In this paper, experiments and numerical simulations have been conducted in both uniform and nonuniform inflowing streams to investigate supersonic shear effects on flame characteristics of an evaporating-flame holder. Specifically, supersonic shear is imposed by introducing a mixing layer between a subsonic stream of Mach number Ma=0.15 and a supersonic stream of Ma=1.55. The flames are imaged by high-speed photography with the flame boundary being identified. Three dimensional simulations with k-ε turbulence model, discrete phase model (DPM) for liquid droplets, and eddy-dissipation-concept (EDC) combustion model, are further performed to shed lights on the complex flow characteristics and interactions with flame shapes. Results show that the vortex structure and the size of recirculation zone after the flame holder are similar with and without shear implying that the presence of shear flow will not affect flame stabilization. The supersonic shear instead can modulate the flame shape and location within a combustor by shortening 30% of the overall flame length. Specifically, the hot products can be pulled away from the top wall and entrained towards the mixing layer. The flame shape is less sensitive to the increase of fuel supply due to the blockage of flame development from the recirculation zone in further downstream and the flame being entrained toward the mixing layer. Further flow and fuel/air mixing analysis shows that the outer shear layer of the recirculation zone after the flame holder plays an important role on flame stabilization. The flame front adjusts adaptively with the spatial distribution of the outer shear layer, which would be modulated by the presence of supersonic shear.

Continuous-in-time approach to flow shear in a linearly implicit local gyrokinetic code

A new algorithm for toroidal flow shear in a linearly implicit, local $\delta f$ gyrokinetic code is described. Unlike the current approach followed by a number of codes, it treats flow shear continuously in time. In the linear gyrokinetic equation, time-dependences arising from the presence of flow shear are decomposed in such a way that they can be treated explicitly in time with no stringent constraint on the time step. Flow shear related time dependences in the nonlinear term are taken into account exactly, and time dependences in the quasineutrality equation are interpolated. Test cases validating the continuous-in-time implementation in the code GS2 are presented. Lastly, nonlinear gyrokinetic simulations of a JET discharge illustrate the differences observed in turbulent transport compared with the usual, discrete-in-time approach. The continuous-in-time approach is shown, in some cases, to produce fluxes that converge to a different value than with the discrete approach. The new approach can also lead to substantial computational savings by requiring radially narrower boxes. At fixed box size, the continuous implementation is only modestly slower than the previous, discrete approach.

Nonlinear phase dynamics of ideal kink mode in the presence of shear flow

We investigate nonlinear phase dynamics of an ideal kink mode, induced by E × B flow. Here the phase is the cross phase (θ c) between perturbed stream function of velocity () and magnetic field (), i.e. θ c = θ ϕ − θ ψ . A dimensionless parameter, analogous to the Richardson number, (γ kink: the normalized growth rate of the pure kink mode; : normalized E × B shearing rate) is defined to measure the competition between phase pinning by the current density and phase detuning by the flow shear. When R i > 1, θ c is locked to a fixed value, corresponding to the conventional eigenmode solution. When R i ≤ 1, θ c enters a phase slipping or oscillating state, corresponding to a nonmodal solution. The nonlinear phase dynamics method provides a more intuitive explanation of the complex dynamical behavior of the kink mode in the presence of E × B shear flow.

Experimental observation of resonance manifold shrinking under zonal flow shear.

In two-dimensional turbulent systems the redistribution of energy can be described by quadratic nonlinear three-wave interactions, which are limited by resonance conditions. The set of coupling modes can be understood as resonant manifold. It has been predicted by theory that, in the presence of a shear flow, the resonant manifold in wave-number space shrinks in time favoring large-scale structures. The phenomenon of manifold shrinking in the presence of shear flows is studied the first time experimentally in drift wave turbulence at the stellarator TJ-K by bicoherence analysis. By estimating effective mode numbers characterizing the width of the manifold, it is demonstrated that increasing shear leads to a shrinking of the resonance manifold.

The effects of toroidal equilibrium flow on the stabilization of ballooning modes in tokamaks

Effects of toroidal flows on ballooning mode instabilities have been studied extensively in recent years. In the published works, toroidal flow effects are taken into account only in the perturbation equation while the tokamak equilibrium is assumed to be unchanged. In this work, the influence of a toroidal flow on ballooning mode instabilities is numerically investigated by using the BOUT++ code while the modification of the tokamak equilibrium due to the flow has been taken into account in fixing the profiles of the quasi-toroidal magnetic field, quasi-density, and quasi-pressure and only changing the toroidal Mach number. A toroidal flow can significantly modify the safety factor q profile and the pressure gradient ∇P, which then affects the ballooning instability. The simulation results show that in the presence of shear flows, the growth rate of the ballooning mode will be affected if the modified equilibrium is considered. For a shear flow, the growth rates of high-n modes are significantly reduced.

Vortices evolution in the solar atmosphere

Aims. We study vortex dynamics in the solar atmosphere by employing and deriving the analytical evolution equations of two vortex identification criteria. Methods. The two criteria used are vorticity and the swirling strength. Vorticity can be biased in the presence of shear flows, but its dynamical equation is well known; the swirling strength is a more precise criterion for the identification of vortical flows, but its evolution equation is not known yet. Therefore, we explore the possibility of deriving a dynamical equation for the swirling strength. We then apply the two equations to analyze radiative magneto-hydrodynamical simulations of the solar atmosphere produced with the CO5BOLD code. Results. We present a detailed review of the swirling strength criterion and the mathematical derivation of its evolution equation. This equation did not exist in the literature before and it constitutes a novel tool that is suitable for the analysis of a wide range of problems in (magneto-)hydrodynamics. By applying this equation to numerical models, we find that hydrodynamical and magnetic baroclinicities are the driving physical processes responsible for vortex generation in the convection zone and the photosphere. Higher up in the chromosphere, the magnetic terms alone dominate. Moreover, we find that the swirling strength is produced at small scales in a chaotic fashion, especially inside magnetic flux concentrations. Conclusions. The swirling strength represents an appropriate criterion for the identification of vortices in turbulent flows, such as those in the solar atmosphere. Moreover, its evolution equation, which is derived in this paper, is pivotal for obtaining precise information about the dynamics of these vortices and the physical mechanisms responsible for their production and evolution. Since this equation is available, the swirling strength is now the ideal quantity to study the dynamics of vortices in (magneto-)hydrodynamics.

Coagulation behavior of spherical particles embedded in laminar shear flow in presence of DLVO-and non-DLVO forces

HypothesisComplex and coupled interaction between coagulation mechanisms results in a nonlinear variation of coagulation rate with shear rate. CalculationsCoagulation behavior of colloidal dispersions is investigated in a laminar shear flow by solving the Fokker-Plank equation for pair probability density function, simultaneously incorporating the effect of (i) Brownian diffusion, (ii) fluid flow, (iii) van der Waals attraction and (iv) double layer repulsion force. Furthermore, analysis foremost studies the effect of non-DLVO solvation force. FindingsTheoretical analysis with experimental validation reveals that, coagulation rate varies non-linearly with the shear rate in presence of double-layer repulsion force, due to the strong coupling of coagulation mechanisms. This is observed by an occurrence of coagulation minima at intermediate shear rate. Increase in double layer repulsion force either facilitates or hinders the occurrence of redistribution of particles, as observed by early or late fall of coagulation rate. Systems with different ionic strengths show a crossover of coagulation rates, whereas those with different solvation forces do not show similar trend. Analysis also shows that, ad hoc additivity assumption of individual Brownian and shear coagulation rates does not hold in case of laminar shear flow, against to that observed in extensional flow [Melis et al. (AIChE J., 999, 1383)].

Three-dimensional observation of Brownian particles under steady shear flow by stereo microscopy.

Three-dimensional observation of Brownian particles under shear flow is performed with a stereo microscope to examine the nature of the Brownian motion that occurs in the presence of shear flow. From the three-dimensional trajectories of the particles, we clearly demonstrate the occurrence of anomalous diffusion in the flow direction and the coupling of the displacements in the flow and velocity gradient directions. Furthermore, we experimentally obtain the probability distribution function and current density, which also exhibit characteristic features, and compare the obtained results with theoretical results derived using the Fokker-Planck equation.

The effect of background flow shear on gyrokinetic turbulence in the cold ion limit

The cold ion limit of the local gyrokinetic model is rigorously taken to produce a nonlinear system of fluid equations that includes background flow shear. No fluid closure is required. By considering a simple slab geometry with magnetic drifts, but no magnetic shear, these fluid equations reduce to the Charney–Hasegawa–Mima model in the presence of flow shear. Analytic solutions to this model are found to study the impact of E × B flow shear on the stability of a single parallel velocity gradient driven mode. Additionally, the model is used to investigate the effect of background E × B flow shear on the basic three-mode nonlinear coupling, which reveals differences between zonal and non-zonal modes. These analytic results agree with gyrokinetic simulations and can serve to benchmark the numerical implementation of flow shear and nonlinear coupling.

Charged Grains and Kelvin–Helmholtz Instability in Molecular Clouds

Abstract The presence of dust grains profoundly affects the diffusion of the magnetic field in molecular clouds. When the electrons and ions are well coupled to the magnetic field and charged grains are only indirectly coupled, emergent Hall diffusion may dominate over all the other non-ideal magnetohydrodynamic (MHD) effects in a partially ionized dusty cloud. The low-frequency, long (∼0.01–1 pc) wavelength dispersive MHD waves will propagate in such a medium with the polarization of the waves determined by the dust charge density or the dust size distribution. In the presence of shear flows, these waves may become Kelvin–Helmholtz unstable with the dust charge density or the grain size distribution operating as a switch to the instability. When Hall diffusion time is long (compared to the time over which waves are sheared), the growth rate of the instability in the presence of sub-Alfvénic flow increases with the charge number on the grain, while it is quenched in the presence of Alfvénic or super-Alfvénic flows. However, when Hall diffusion is fast, the growth rate of the instability depends on the dust charge only indirectly.

Growth rates of ITG modes in the presence of flow shear

Plasma microinstabilities in toroidal magnetic confinement devices can be driven unstable by a radial ion temperature gradient and stabilized by rotational flow shear. In this study, we argue that these nonlinear dynamics can be captured by the linear stabilization of Floquet modes. To that end, we propose a novel method (the τAC method) to calculate growth rates by averaging over linear Floquet modes. The τAC method is compared to nonlinear and other linear approaches and is shown to work well at low parallel velocity gradient drive. As such, the method provides a promising approach to explore the parameter dependencies of flow shear stabilization.

Simplified gentlest ascent dynamics for saddle points in non-gradient systems.

The gentlest ascent dynamics (GAD) [W. E and X. Zhou, Nonlinearity 24, 1831 (2011)] is a time continuous dynamics to efficiently locate saddle points with a given index by coupling the position and direction variables together. These saddle points play important roles in the activated process of randomly perturbed dynamical systems. For index-1 saddle points in non-gradient systems, the GAD requires two direction variables to approximate, respectively, the eigenvectors of the Jacobian matrix and its transposed matrix. In the particular case of gradient systems, the two direction variables are equal to the single minimum mode of the Hessian matrix. In this note, we present a simplified GAD which only needs one direction variable even for non-gradient systems. This new method not only reduces the computational cost for the direction variable by half but also avoids inconvenient transpose operation of the Jacobian matrix. We prove the same convergence property for the simplified GAD as that for the original GAD. The motivation of our simplified GAD is the formal analogy with Hamilton's equation governing the noise-induced exit dynamics. Several non-gradient examples are presented to demonstrate our method, including a two dimensional model and the Allen-Cahn equation in the presence of shear flow.

High speed observation of damage created by a collapse of a single cavitation bubble

One of the remaining open questions in cavitation erosion research is the one on the importance of the microjet and the shock wave on the formation of the pit. Up until now, no successful attempt has been made to study this in detail, mainly because the damage could only be detected and evaluated after several successive bubble collapses.A bubble with a maximum diameter of up to 3.3 mm was created during photoionization using a Nd:YAG laser. The damage was observed on a 9 µm thick aluminum foil attached to a glass substrate. Two high speed cameras were simultaneously used. One captured the dynamics of the bubble, while the other recorded the damage of the foil.We also observed the collapse of a bubble in the presence of shear flow, where most of the damage is created by the microjet mechanism. Sometimes, the collapse of the bubble rim, at the rebound of the initial bubble causes pits in a well-known circular pattern. From the recordings at the very fastest acquisition rate, we determined that the material deforms and then partially relaxes, while a significant deformation remains. The whole process is only 2–3 µs long.

An unusual promotion of γ-crystals in metallocene-made isotactic polypropylene from orientational relaxation and favorable temperature window induced by shear

Combined effects of shear flow and non-isothermal processing, which were akin to the practical industrial processing, on the crystallization of metallocene-made isotactic polypropylene (m-iPP) were investigated by in-situ synchrotron wide-angle X-ray diffraction (WAXD) and small-angle X-ray scattering (SAXS) techniques. The simultaneous appearance of α- and γ-crystals was observed in quiescent samples, while shear flow led to the occurrence of α-crystals prior to γ-crystals at the initial stage of crystallization. Although the local alignment of chain segments promoted by shear flow facilitated the α-crystals, the relaxation of oriented chains was experimentally confirmed to boost the formation of γ-crystals. Interestingly, the resultant γ-crystal content was higher in the sheared samples than the quiescent counterparts at a given cooling rate and further increased with the decrease of cooling rates. Such a discrepancy was not only related to shear-induced orientation and relaxation, but also was accredited to the advanced crystallization temperature window, which was favorable for the γ-crystal growth. It was quite different from the isothermal crystallization situation, where the formation of γ-crystals was depressed in presence of shear flow. The dynamic competition between α-crystal and γ-crystal formation under the effects of shear during the non-isothermal crystallization was discussed. Our work is of valuable reference to tailor the crystalline structure of m-iPP during practical processing and hence to acquire the desired performance of products.

Ion-scale turbulence in MAST: anomalous transport, subcritical transitions, and comparison to BES measurements

We investigate the effect of varying the ion temperature gradient (ITG) and toroidal equilibrium scale sheared flow on ion-scale turbulence in the outer core of MAST by means of local gyrokinetic simulations. We show that nonlinear simulations reproduce the experimental ion heat flux and that the experimentally measured values of the ITG and the flow shear lie close to the turbulence threshold. We demonstrate that the system is subcritical in the presence of flow shear, i.e., the system is formally stable to small perturbations, but transitions to a turbulent state given a large enough initial perturbation. We propose that the transition to subcritical turbulence occurs via an intermediate state dominated by low number of coherent long-lived structures, close to threshold, which increase in number as the system is taken away from the threshold into the more strongly turbulent regime, until they fill the domain and a more conventional turbulence emerges. We show that the properties of turbulence are effectively functions of the distance to threshold, as quantified by the ion heat flux. We make quantitative comparisons of correlation lengths, times, and amplitudes between our simulations and experimental measurements using the MAST BES diagnostic. We find reasonable agreement of the correlation properties, most notably of the correlation time, for which significant discrepancies were found in previous numerical studies of MAST turbulence.

Nonlinear electrostatic periodic waves and solitons in an inhomogeneous magnetized dusty plasma

Low frequency nonlinear electrostatic cnoidal and solitary waves are investigated in an inhomogeneous magnetized dusty plasma in the presence of shear flow. The Sagdeev potential approach is used to find the nonlinear wave solution. It is found that nonlinear electrostatic potential rarefactive (dip) structures are formed for cnoidal waves and solitons in a magnetized inhomogeneous dusty plasma instead of compressive (hump) nonlinear electrostatic wave structures formed in an inhomogeneous magnetized electron-ion plasma. The amplitude of the nonlinear electrostatic potential structure is found to be increased in the case of decreasing shear flow parameter values in comparison with the case of increasing shear flow parameter values. The D'Angelo instability in an inhomogeneous magnetized dusty plasma in the presence of shear flow is also discussed. The numerical plots are also presented for illustrations which are applicable to space dusty plasma regions containing shear flows. The Hamiltonian function of such a dynamical planar system is also discussed for its phase portrait analysis.

Synergistic effects of shear flow and nucleating agents on the crystallization mechanisms of Poly (Lactic Acid)

This paper presents a study of the effects of microscopic particles of talc on the crystallization kinetics of PLA. Our study covers the quiescent conditions and the case where a shear flow is applied “short term shearing”. The incorporation of talc increases the crystallization rate; it enhances the nucleation mechanism through additional heterogeneous nuclei. The microstructure is highly affected by the addition of talc due to the increase of the number of nuclei (i.e. reduced crystalline size). The application of a shear flow increases the ability of PLA to crystallize even in the presence of talc particles. The impact of shear rate becomes dramatically important just after a critical shear rate of 0.1 s−1. It turns out that the shear rate enhances more the crystallization of PLA with talc than the pure PLA under quiescent conditions. Consequently, a supplementary contribution “synergistic effects” is responsible of the relative enhancement of the crystallization of PLA in the presence of shear flow and talc. With combining different experimental analysis techniques and modeling of the crystallization kinetics, the synergistically effects were quantified in terms of the nucleation density induced by the mutual interaction between shear flow and particles.

Heat/mass transport in shear flow over a reactive surface with inert defects

We study the problem of mass transport to surfaces with heterogeneous reaction rates in the presence of shear flow over these surfaces. The reactions are first order and the heterogeneity is due to the existence of inert regions on the surfaces. Such problems are ubiquitous in the field of heterogeneous catalysis, electrochemistry and even biological mass transport. In these problems, the microscale reaction rate is characterized by a Damköhler number $\unicode[STIX]{x1D705}$, while the Péclet number $P$ is the dimensionless ratio of the bulk shear rate to the inverse diffusion time scale. The area fraction of the reactive region is denoted by $\unicode[STIX]{x1D719}$. The objective is to calculate the yield of reaction, which is directly related to the mass flux to the reactive region, denoted by the dimensionless Sherwood number $S$. Previously, we used boundary element simulations and examined the case of first-order reactive disks embedded in an inert surface (Shah & Shaqfeh J. Fluid Mech., vol. 782, 2015, pp. 260–299). Various correlations for the Sherwood number as a function of $(\unicode[STIX]{x1D705},P,\unicode[STIX]{x1D719})$ were obtained. In particular, we demonstrated that the ‘method of additive resistances’ provides a good approximation for the Sherwood number for a wide range of values of $(\unicode[STIX]{x1D705},P)$ for $0<\unicode[STIX]{x1D719}<0.78$. When $\unicode[STIX]{x1D719}\approx 0.78$, the reactive disks are in a close packed configuration where the inert regions are essentially disconnected from each other. In this work, we develop an understanding of the physics when $\unicode[STIX]{x1D719}>0.78$, by examining the inverse problem of inert disks on a reactive surface. We show that the method of resistances approach to obtain the Sherwood number fails in the limit as $\unicode[STIX]{x1D719}\rightarrow 1$, i.e. in the dilute limit of periodic inert disks, due to the existence of a surface concentration boundary layer around each disk that scales with ($1/\unicode[STIX]{x1D705}$). This boundary layer controls the screening length between inert disks and allows us to introduce a new theory, thus providing new correlations for the Sherwood number that are highly accurate in the limit of $\unicode[STIX]{x1D719}\rightarrow 1$.