Parallel Shear Flow Research Articles

Effect of in-plane shear flow on the magnetic island coalescence instability

Using a 2D Viscoresistive Reduced MagnetoHydroDynamic model, the magnetic island coalescence problem is studied in the presence of in-plane, parallel shear flows. Extending the analytical work of Waelbroeck et al. [Phys. Plasmas 14, 022302 (2007)] and Throumoulopoulos et al., [J. Phys. A 42, 335501 (2009)] in the sub-Alfvénic flow shear regime for Fadeev equilibrium, the super-Alfvénic regime is studied for the first time numerically. A wide range of values of shear flow amplitudes and shear scale lengths have been considered to understand the effect of sub-Alfvénic and super-Alfvénic flows on the coalescence instability and its nonlinear fate. We find that for flow shear length scales greater than the magnetic island size, the maximum reconnection rate decreases monotonically from sub-Alfvénic to super-Alfvénic flow speeds. For scale lengths smaller than the island size, the reconnection rate decreases up to a critical value v0c, beyond which the shear flow is found to destabilize the islands. The value of v0c decreases with a decrease in the value of shear flow length scale. Interestingly, for our range of parameters, we find suppression of the Kelvin–Helmholtz instability in super-Alfvénic flows even when the shear scale length is smaller than the island width. Observation of velocity streamlines shows that the plasma circulation inside the islands has a stabilizing influence in strong shear flow cases. Plasma circulation is also found to be responsible for the decrease in upstream velocity, causing less pileup of magnetic flux on both sides of the reconnection sheet.

Marginal Instability Within Internal Solitary Waves

AbstractHigh‐resolution observations of the currents, hydrography, and turbulence within internal solitary waves (ISWs) reveal Kelvin‐Helmholtz (KH) billows and breaking waveforms occurring in the lower periphery and in the trailing edges, respectively, of the wave cores. Marginal instability (MI) is evident in wave cores, where the probability distribution of the Richardson number Ri, fluctuates around 0.25. The critical value for the occurrence of KH instability in ISWs is evidently 0.25, the canonical criterion of a parallel stratified shear flow. When Ri > 0.25, the turbulent diffusivity Κρ remains O (10−3) m2 s−1 with a standard deviation of one order. When Ri crosses the critical value, the logarithmic turbulent diffusivity linearly increases with a logarithmic reduction in Ri to smooth the velocity and density differences so that Ri is ultimately restored to >0.25. Therefore, the processes of MI cycling preserve ISWs against breakdowns resulting from the uninterrupted growth of KH instability.

Feedback control of charged ideal fluids

The theory of controlled mechanical systems of Bloch et al (2001 IEEE Trans. Control Syst. Technol. 45 2253–70; Bloch et al 2001 Int. J. Robust Nonlinear Control 11 191–214; Bloch et al 1992 Automatica 28 745–56; Bloch et al 1997 Current and Future Directions in Applied Mathematics) and Krishnaprasad P S (1985 Nonlinear Anal. Theor. Methods Appl. 9 1011–35) is extended to the case of ideal incompressible fluids consisting of charged particles in the presence of an external magnetic field. The resulting control is of feedback type and depends on the Eulerian state of the controlled system. Moreover, the control is set up so that the corresponding closed loop equations are Lie–Poisson. This implies that the energy–momentum method of Arnold V (1966 Ann. Inst. Fourier 16 319–61) and Holm et al (1985 Phys. Rep. 123 1–116) can be used to find a stabilizing control. As an example the case of planar parallel shear flow with an inflection point is treated. A state dependent feedback control is constructed which stabilizes the system for an arbitrarily long channel.

Orr mechanism in transition of parallel shear flow

The precise role of the Orr mechanism in transition of parallel shear flow is investigated. We found two transition scenarios, oblique and streak transition, in which the Orr mechanism plays a central role in triggering transition. In the oblique transition, the spanwise velocity perturbation amplified with the Orr mechanism initiates both streak amplification and breakdown, whereas in the streak transition, the role of the Orr mechanism is limited only to the streak breakdown at the late stage of transition.

Investigating 1st and 2nd order Fermi acceleration of energetic particles by small-scale magnetic flux ropes at 1AU

A new telegrapher-type Parker transport equation was derived from the existing underlying focused transport equation to model the acceleration of energetic particles by contracting and reconnecting small-scale magnetic flux ropes (SMFRs) in the large-scale solar wind. Time-dependent and steady-state analytical solutions were found that unify all SMFR acceleration mechanisms present in the transport equation, showing that SMFR acceleration by the parallel reconnection electric field in the mixed spatial and momentum derivative transport term is constrained by and requires the presence of 2nd order Fermi SMFR acceleration. We explore the potential of these solutions in reproducing energetic proton flux enhancements and spectral evolution between ∼50 keV-5 MeV in dynamic SMFR regions near large-scale reconnecting current sheets in the solar wind at 1 AU. It is shown that both 2nd order Fermi SMFR acceleration involving the variance in SMFR compression and incompressible parallel shear flow, and 1st order SMFR Fermi acceleration due to mean SMFR compression are both workable options in reproducing observed flux amplification factors when using reasonable SMFR parameters. However, the predicted substantial quantitative differences in the spatial evolution of the accelerated spectra through the SMFR region might provide a diagnostic to distinguish between 1st and 2nd order Fermi SMFR acceleration in observations.

Neutral particle drag on parallel flow shear driven instability

The neutral drag effect on the parallel velocity gradient driven instability (PVG) in the presence of density inhomogeneity is theoretically investigated. The dispersion relation of PVG mode with the effect of the density gradient and neutral particle drag is derived, and its solution is analytically obtained. The neutral particle drag gives rise to the phase shift between parallel flow and electrostatic potential fluctuations and modifies the parallel compression. As a result, the stability of the PVG mode changes. It is found that the neutral particle drag does not only reduce but also enhances the instability. Specifically, near the marginal condition, the neutral particle effect suppresses the density gradient effect, and the parameter region where the PVG mode is linearly unstable significantly expands.

Oscillatory strain with superposed steady shearing in noncolloidal suspensions

The rheology of noncolloidal suspensions in superposed simple shearing and oscillatory shearing was explored. With a Newtonian matrix fluid, one would expect that G′ would be zero in an oscillatory flow, but this was not found; the action of Coulomb friction between the particles appears to cause an increment of G′ at lower frequencies. To understand this frictional effect, measurements of small and medium strain oscillatory flows, up to 10% strain magnitude, were made. The matrix fluid was 12 Pa s silicone oil, and the polystyrene spheres were on average 40.3 μm in diameter. Hysteresis during tests with varying strain amplitudes was more dominant in the storage modulus than in the loss modulus, and, at a 50% volume fraction, the effect was severe. Because of the observed tendency to hysteresis, the oscillatory flow was then combined with a parallel steady shear flow to try to control or eliminate hysteresis. The hysteresis appears to be a frictional effect, and it was reduced under superposed shearing. The effect of variable oscillatory shear stress and steady shear stress was studied, and a model was proposed for the superposed storage modulus, loss modulus, and shear viscosity responses. Frictional effects are considered in the proposed model, and one observes a generally satisfactory fit to the experimental data. From the model, the average friction coefficient is shown to be less at higher frequencies due to higher relative rubbing speeds and better lubrication between the particles. Clearly, suspension rheology is dominated by friction and is essentially a study in tribology.

Long wave instability on the parallel shear flows in the presence of insoluble surfactant

Long wave instability on the parallel shear flows in the presence of insoluble surfactant

Stability of force-driven shear flows in nonequilibrium molecular simulations with periodic boundaries.

We analyze the hydrodynamic stability of force-driven parallel shear flows in nonequilibrium molecular simulations with three-dimensional periodic boundary conditions. We show that flows simulated in this way can be linearly unstable, and we derive an expression for the critical Reynolds number as a function of the geometric aspect ratio of the simulation domain. Approximate periodic extensions of Couette and Poiseuille flows are unstable at Reynolds numbers two orders of magnitude smaller than their aperiodic equivalents because the periodic boundaries impose fundamentally different constraints on the flow. This instability has important implications for simulating shear rheology and for designing nonequilibrium simulation methods that are compatible with periodic boundary conditions.

Numerical Computation of Instabilities and Internal Waves from In Situ Measurements via the Viscous Taylor–Goldstein Problem

AbstractWe explore numerical methods for the stability analysis of stratified, parallel shear flows considering the effects of small-scale turbulence represented by eddy viscosity and diffusivity. The result is an extension of the classical Taylor–Goldstein problem applicable to oceanic and atmospheric flows. Solutions with imaginary frequency describe shear and convective instabilities, whereas those with real frequency represent internal gravity waves. Application to large observational datasets can involve considerable computation and therefore requires a compromise between speed and accuracy. We compare several numerical methods to identify optimal approaches to various problems.

Linear instability of tilted parallel shear flow in a strongly stratified and viscous medium

A linear stability analysis is performed on a tilted parallel wake in a strongly stratified fluid at low Reynolds numbers. A particular emphasis of the present study is given to the understanding of the low-Froude-number mode observed by the recent experiment (Meunier in J Fluid Mech 699:174–197, 2012). In the limit of low Froude number, the linearised equations of motion can be reduced to the Orr–Sommerfeld equation on the horizontal plane, except the viscous term that contains vertical dissipation. Based on this equation, it is proposed that the low-Froude-number mode would be a horizontal inflectional instability and should remain two-dimensional at small tilting angles as long as the Reynolds number is sufficiently low. To support this claim, the asymptotic regime where this analysis is strictly valid is subsequently discussed in relation to previous work on the proper vertical length scale. The absolute and convective instability analysis of parallel wake is further performed, showing qualitatively good agreement with the experimental result. The low-Froude-number mode is found to be stabilised on increasing Froude number, as in the experiment. It is shown that the emergence of small vertical velocity at finite Froude number, the size of which is proportional to the square of Froude number, plays the key role in the stabilisation by modifying the inflectional instability and paradoxically creating stabilising buoyancy effect with the increase of Froude number.

Dipolar and Kelvin-Stuart’s cat’s eyes vortices in magnetoplasmas with non-Maxwellian electron distribution

Linear and nonlinear propagation characteristics of drift ion acoustic waves are analyzed in an inhomogeneous plasma comprising of warm ions having shear flow parallel to the magnetic field and electrons that are followed by a distribution which is dictated by spectral indices, $r$ and $q$ in low and high phase density regions. In the linear regime, the dispersion relation of the drift-ion acoustic wave is derived and the condition for the onset of shear flow instability is presented. It is found that condition for the emergence of shear flow instability gets modified by generalized $(r,q)$ distribution and ion to electron temperature ratio. In the nonlinear regime, vortex formation with non-Maxwellian electron distribution is investigated and the effects of low and high energy electrons in this context are explored in detail. Interestingly, it is found that unlike the dipolar vortices, the electrons in the high phase space density regions do not significantly affect the Kelvin-Stuart’s cat’s eyes structures, however, the converse is true for the electrons belonging to the regions of low phase space density. Estimates of the size of these vortex structures in space plasmas are also given where the distribution function presented here is frequently encountered.

Influence of parallel shearing flow on the switch-off effect of magnetic reconnection

Parallel shearing flows significantly affect the structure of the magnetic reconnection layer and generate new shock structures such as intermediate shock (IS) and time-dependent IS. The strength of shock waves (such as slow shock) can be changed and result in the switch-off of magnetic reconnection under certain conditions. In this study, we perform numerical simulations of one-dimensional resistive magnetohydrodynamic equations by using the total variation diminishing algorithm to investigate the influence of parallel shear flow on the switch-off effect of magnetic reconnection on both asymmetric and symmetric magnetic reconnection layers. Numerical results show that there exists a critical shear velocity Vzc that equals VA in symmetrical antiparallel magnetic reconnection, where VA denotes the inflow Alfvén velocity. For symmetric component magnetic reconnection, Vzc drops with the increase in guide magnetic field strength, which also equals the component of inflow Alfvén velocity along the z-axis. In regard to asymmetric magnetic reconnection, the critical shear velocity, Vzc, that leads to the switch-off of magnetic reconnection, ranging between the z-axis components of inflow Alfvén velocity in the magentosheath and in the magnetosphere. A new parameter associated with the Alfvén velocity on both sides is proposed; for both antiparallel reconnection and component reconnection, this new parameter equals the critical shear velocities.

Flow Resistance and Structures in Viscoelastic Channel Flows at Low Re.

The flow of viscoelastic fluids in channels and pipes remains poorly understood, particularly at low Reynolds numbers. Here, we investigate the flow of polymeric solutions in straight channels using pressure measurements and particle tracking. The flow friction factor f_{η} versus flow rate exhibits two regimes: a transitional regime marked by rapid increase in drag, and a turbulentlike regime characterized by a sudden decrease in drag and a weak dependence on flow rate. Lagrangian trajectories show finite transverse modulations not seen in Newtonian fluids. These curvature perturbations far downstream can generate sufficient hoop stresses to sustain the flow instabilities in the parallel shear flow.

A conjecture on the least stable mode for the energy stability of plane parallel flows

In the energy stability theory, the critical Reynolds number is usually defined as the minimum of the first positive eigenvalue $R_{1}$ of an eigenvalue equation for all wavenumber pairs $(\unicode[STIX]{x1D6FC},\unicode[STIX]{x1D6FD})$, where $\unicode[STIX]{x1D6FC}$ and $\unicode[STIX]{x1D6FD}$ are the streamwise and spanwise wavenumbers of the normal mode. We prove that $(\cos \unicode[STIX]{x1D703}\pm 1)R_{1}$ are decreasing functions of $\unicode[STIX]{x1D703}=\arctan (\unicode[STIX]{x1D6FD}/\unicode[STIX]{x1D6FC})$ for the parallel flows between no-slip or slip parallel plates with or without variations in temperature. Numerical results inspire us to conjecture that $R_{1}$ is also a decreasing function of $\unicode[STIX]{x1D703}$ for the parallel shear flows under the no-slip boundary condition and without variations in temperature. If the conjecture is correct, the least stable normal modes for the energy stability will be streamwise vortices for these base flows.

Edge tracking in spatially developing boundary layer flows

Recent progress in understanding subcritical transition to turbulence is based on the concept of the edge, the manifold separating the basins of attraction of the laminar and the turbulent state. Originally developed in numerical studies of parallel shear flows with a linearly stable base flow, this concept is adapted here to the case of a spatially developing Blasius boundary layer. Longer time horizons fundamentally change the nature of the problem due to the loss of stability of the base flow due to Tollmien–Schlichting (TS) waves. We demonstrate, using a moving box technique, that efficient long-time tracking of edge trajectories is possible for the parameter range relevant to bypass transition, even if the asymptotic state itself remains out of reach. The flow along the edge trajectory features streak switching observed for the first time in the Blasius boundary layer. At long enough times, TS waves co-exist with the coherent structure characteristic of edge trajectories. In this situation we suggest a reinterpretation of the edge as a manifold dividing the state space between the two main types of boundary layer transition, i.e. bypass transition and classical transition.

Mesoscale simulation of soft particles with tunable contact angle in multicomponent fluids.

Soft particles at fluid interfaces play an important role in many aspects of our daily life, such as the food industry, paints and coatings, and medical applications. Analytical methods are not capable of describing the emergent effects of the complex dynamics of suspensions of many soft particles, whereas experiments typically either only capture bulk properties or require invasive methods. Computational methods are therefore a great tool to complement experimental work. However, an efficient and versatile numerical method is needed to model dense suspensions of many soft particles. In this article we propose a method to simulate soft particles in a multicomponent fluid, both at and near fluid-fluid interfaces, based on the lattice Boltzmann method, and characterize the error stemming from the fluid-structure coupling for the particle equilibrium shape when adsorbed onto a fluid-fluid interface. Furthermore, we characterize the influence of the preferential contact angle of the particle surface and the particle softness on the vertical displacement of the center of mass relative to the fluid interface. Finally, we demonstrate the capability of our model by simulating a soft capsule adsorbing onto a fluid-fluid interface with a shear flow parallel to the interface, and the covering of a droplet suspended in another fluid by soft particles with different wettability.

Extension of classical stability theory to viscous planar wall-bounded shear flows

A viscous extension of Arnold’s inviscid theory for planar parallel non-inflectional shear flows is developed and a viscous Arnold’s identity is obtained. Special forms of the viscous Arnold’s identity have been revealed that are closely related to the perturbation’s enstrophy identity derived by Synge (Proceedings of the Fifth International Congress for Applied Mechanics, 1938, pp. 326–332, John Wiley) (see also Fraternaleet al.,Phys. Rev. E, vol. 97, 2018, 063102). Firstly, an alternative derivation of the perturbation’s enstrophy identity for strictly parallel shear flows is acquired based on the viscous Arnold’s identity. The alternative derivation induces a weight function. Thereby, a novel weighted perturbation’s enstrophy identity is established, which extends the previously known enstrophy identity to include general streamwise translation-invariant shear flows. Finally, the validity of the enstrophy identity for parallel shear flows is rigorously examined and established under global nonlinear dynamics imposed with two classes of wall boundary conditions. As an application of the enstrophy identity, we quantitatively investigate the mechanism of linear instability/stability within the normal modal framework. The investigation reveals a subtle interaction between a critical layer and its adjacent boundary layer, which determines the stability nature of the disturbance. As an implementation of the relaxed wall boundary conditions imposed for the enstrophy identity, a control scheme is proposed that transitions the wall settings from the no-slip condition to the free-slip condition, through which a flow is stabilized quickly in an early stage of the transition.

Shear stress-driven flow: the state space of near-wall turbulence as

An inner-scaled, shear stress-driven flow is considered as a model of independent near-wall turbulence as the friction Reynolds number $Re_{\unicode[STIX]{x1D70F}}\rightarrow \infty$. In this limit, the model is applicable to the near-wall region and the lower part of the logarithmic layer of various parallel shear flows, including turbulent Couette flow, Poiseuille flow and Hagen–Poiseuille flow. The model is validated against damped Couette flow and there is excellent agreement between the velocity statistics and spectra for the wall-normal height $y^{+}<40$. A near-wall flow domain of similar size to the minimal unit is analysed from a dynamical systems perspective. The edge and fifteen invariant solutions are computed, the first discovered for this flow configuration. Through continuation in the spanwise width $L_{z}^{+}$, the bifurcation behaviour of the solutions over the domain size is investigated. The physical properties of the solutions are explored through phase portraits, including the energy input and dissipation plane, and streak, roll and wave energy space. Finally, a Reynolds number is defined in outer units and the high-$Re$ asymptotic behaviour of the equilibria is studied. Three lower branch solutions are found to scale consistently with vortex–wave interaction (VWI) theory, with wave forcing localising around the critical layer.

Nonlinear turbulent parallel momentum transport due to blobs

The nonlinear flux term induced by blobs is derived by using an eddy damped quasi-normal Markovian method in a three dimensional Hasegawa–Wakatani system with a strong non-adiabatic assumption. It is shown that the nonlinear flux is comparable to the quasilinear flux in the case of mixing level turbulence and can become dominant in strong turbulence regimes such as blobs. Moreover, when strong non-adiabatic or strong parallel flow shear conditions are considered, for radially elongated blobs or streamers, nonlinear residual flux can provide the opposite parallel momentum flux to the quasilinear flux and negative nonlinear diffusivity, which introduces inward momentum flux, so that rotation in the edge region is possibly reversed and momentum is convected into the core region.