Large Rotation Rates Research Articles

Fast rotating blue stragglers prefer loose clusters

Blue stragglers are anomalously luminous core hydrogen-burning stars formed through mass-transfer in binary/triple systems and stellar collisions. Their physical and evolutionary properties are largely unknown and unconstrained. Here we analyze 320 high-resolution spectra of blue stragglers collected in eight galactic globular clusters with different structural characteristics and show evidence that the fraction of fast rotating blue stragglers (with rotational velocities larger than 40 km/s) increases for decreasing central density of the host system. This trend suggests that fast spinning blue stragglers prefer low-density environments and promises to open an unexplored route towards understanding the evolutionary processes of these stars. Since large rotation rates are expected in the early stages of both formation channels, our results provide direct evidence for recent blue straggler formation activity in low-density environments and put strong constraints on the timescale of the collisional blue straggler slow-down processes.

The enhancement of flow induced vibration of a circular cylinder using a rotating control rod

The enhancement of flow induced vibration of a circular cylinder by a rotating control rod is investigated through two-dimensional numerical simulations. The Reynolds number, diameter ratio, and gap ratio are 150, 0.2, and 0.2, respectively. Simulations are conducted for two rod position angles of β = 90° and 135°, rotation rates ranging from 0 to 6, and reduced velocities ranging between 1 and 20. The response of the cylinder–rod system at the rotation rates 0 and 1 has a lock-in regime where the vibration amplitude is high and the vibration frequency stops increasing with the increase in reduced velocity linearly. For rotation rates exceeding 2, the response amplitude increases with the increase in reduced velocity and enters the lock-in regime at the lower boundary reduced velocity. It remains high until the largest studied reduced velocity of 20; as a result, the higher boundary reduced velocity of the lock-in regime cannot be determined. The vibration with large amplitudes and large rotation rates repeats cyclically after every two or more vibration periods. As a result, two combined wake modes are found: 2S/P + S and 2P/P + S. In a combined mode, the vibration changes from one mode to another within each cycle. The cylinder receives power from the fluid, and the rotating rod gives power to the fluid although the net power exchange between the whole system and the fluid is zero.

Solar wind rotation rate and shear at coronal hole boundaries

Context.In situ measurements by several spacecraft have revealed that the solar wind is frequently perturbed by transient structures that have been interpreted as magnetic folds, jets, waves, and flux ropes that propagate rapidly away from the Sun over a large range of heliocentric distances. Parker Solar Probe (PSP), in particular, has detected very frequent rotations of the magnetic field vector at small heliocentric radial distances, accompanied by surprisingly large solar wind rotation rates. The physical origin of such magnetic field bends and switchbacks, the conditions for their survival across the interplanetary space, and their relation to solar wind rotation are yet to be clearly understood.Aims.We aim to characterise the global properties of the solar wind flows crossed by PSP, to relate those flows to the rotational state of the low solar corona, and to identify regions of the solar surface and corona that are likely to be sources of switchbacks and bends.Methods.We traced measured solar wind flows from the spacecraft position down to the surface of the Sun to identify their potential source regions, and used a global magneto-hydrodynamic model of the corona and solar wind to analyse the dynamical properties of those regions. We identify regions of the solar corona for which solar wind speed and rotational shear are important and long-lived that can be favourable to the development of magnetic deflections and to their propagation across extended heights in the solar wind.Results.We show that coronal rotation is highly structured, and that enhanced flow shear and magnetic field gradients develop near the boundaries between coronal holes and streamers, and around and above pseudo-streamers, even when such boundaries are aligned with the direction of solar rotation. The exact properties and amplitudes of the shears are a combined effect of the forces exerted by the rotation of the corona and of its magnetic topology. A large fraction of the switchbacks identified by PSP map back to these regions, both in terms of instantaneous magnetic field connectivity and of the trajectories of wind streams that reach the spacecraft.Conclusions.We conclude that these regions of strong shears are likely to leave an imprint on the solar wind over large distances and to increase the transverse speed variability in the slow solar wind. The simulations and connectivity analysis suggest they could be a source of the switchbacks and spikes observed by PSP.

Wheel wear comparison between motor car and trailer of intercity train

To analyze wheel wear discrepancy between motor car and trailer of an intercity train, a novel wheel wear rates calculation model was proposed, which was composed of the intercity train dynamics model, wheel-rail three-dimensional rolling contact FEM model and the wear model. The simulated results were contrasted with measured results in field test. The simulated results showed the motor car wheels had larger rotation rate and longitudinal creepage than the trailer wheels. Meanwhile, the motor car wheels encountered larger vertical forces and longitudinal forces from bogie because of the heavier car body and the impact of traction torque. The traction torque acting on motor car wheel could increase the slip rates in the rear part of wheel contact patch and weaken the spinning phenomenon of relative slip. Larger contact pressure and slip rates caused the higher wear rates of motor car wheel than those of trailer wheel. The overall trends of wheel wear depth in simulated and tested results were similar. And they both showed the motor car wheel encountered the more serious wear than the trailer wheel. These models can be used to study the effect of the traction characteristics curves on the wear of wheel.

Thin-liquid-film flow on three-dimensional topographically patterned rotating cylinders

Abstract

Experimental study of uni- and bi-directional exchange flows in a large-scale rotating trapezoidal channel

A large-scale experimental study has been conducted at the Coriolis Rotating Platform to investigate the dynamics of uni- and bi-directional exchange flows along a channel with a trapezoidal cross section under the influence of background rotation. High-resolution two-dimensional particle image velocimetry and micro-conductivity probes were used to obtain detailed velocity fields and density profiles of the exchange flow generated across the channel under different parametric conditions. Experimental measurements give new insight into the stratified-flow dynamics dependence on the magnitude of Burger number, defined as the ratio of the Rossby radius to the channel width, such that values lower than 0.5 characterize unsteady exchange flows. The measurements highlight the role that both ambient rotation and net-barotropic forcing have on the geostrophic adjustment of the dense outflowing layer and on the corresponding counter-flowing water layer fluxes. The coupled effect of these two parametric conditions largely affects the transverse velocity distribution and, for the largest net-barotropic flow in the upper fresh water layer, leads to the partial blockage of the lower saline outflow. Moreover, an increase in the mixing layer thickness, associated with larger rotation rates, and due the interface dynamics, is observed, with shear-driven interfacial instabilities analyzed to highlight the influence of both ambient rotation and net-barotropic forcing.

On the hydrodynamic stability of an imploding rotating circular cylindrical liquid liner

The hydrodynamic stability of an imploding cylindrical liquid liner is analytically and numerically investigated. Such dynamic system can be used to compress gas trapped by the liner, as one may seek in a hydrogen fusion reactor. For such system it is vital for the liner to stay intact at least up to the turnaround point, which marks the point of maximum compression of the inner gas. New two-dimensional linear stability of Bell-type equation and Wentzel-Kramers-Brillouin (WKB) approximations are derived to account for the rotation of the liner. Excellent agreement is achieved between computational fluid dynamics (CFD) and 1D analysis for the trajectory of the unperturbed liner. Very good agreement is also achieved between the Bell type linear stability solution and the CFD until non-linear effects take hold near the turnaround point. The WKB approximation also agrees well but only at the early stage of the liner motion. Viscosity, surface tension and inner gas stability waves are found to have a small effect for a liner’s radial compression of up to ten. It is seen that the rotation has little effect on the perturbation amplitude during the accelerating stage of the liner, which is dominated by a slow oscillatory growth of a Bell-Plesset type at the studied conditions. However, at the decelerating stage towards the turnaround point, Rayleigh–Taylor rapid perturbation growth is suppressed at sufficiently large rotation rates. Hence, when coupled with non-linear saturation effects, the liner stays much intact until the turnaround point for radial compression ratios of up to ten. New simple linear stability limits are derived and are analysed.

Reduced-order modelling of thick inertial flows around rotating cylinders

A new model for the behaviour of a thick, two-dimensional layer of fluid on the surface of a rotating cylinder is presented, incorporating the effects of inertia, rotation, viscosity, gravity and capillarity. Comparisons against direct numerical simulations (DNS) show good accuracy for fluid layers of thickness of the same order as the cylinder radius, even for Reynolds numbers up to . A rich and complex parameter space is revealed, and is elucidated via a variety of analytical and numerical techniques. At moderate rotation rates and fluid masses, the system exhibits either periodic behaviour or converges to a steady state, with the latter generally being favoured by greater masses and lower rotation rates. These behaviours, and the bifurcation structure of the transitions between them, are examined using a combination of both the low-order model and DNS. Specific attention is dedicated to newly accessible regions of parameter space, including the multiple steady state solutions observed for the same parameter values by Lopes et al. (J. Fluid Mech., vol. 835, 2018, pp. 540–574), where the corresponding triple limit point bifurcation structure is recovered by the new low-order model. We also inspect states in which the interface becomes multivalued – and thus outside the reach of the reduced-order model – via DNS. This leads to highly nonlinear multivalued periodic structures appearing at moderate thicknesses and relatively large rotation rates. Even much thicker films may eventually reach steady states (following complex early evolution), provided these are maintained by a combination of forces sufficiently large to counteract gravity.

Linearly forced fluid flow on a rotating sphere

We investigate generalized Navier-Stokes (GNS) equations that couple nonlinear advection with a generic linear instability. This analytically tractable minimal model for fluid flows driven by internal active stresses has recently been shown to permit exact solutions on a stationary two-dimensional sphere. Here, we extend the analysis to linearly driven flows on rotating spheres. We derive exact solutions of the GNS equations corresponding to time-independent zonal jets and superposed westward-propagating Rossby waves, qualitatively similar to those seen in planetary atmospheres. Direct numerical simulations with large rotation rates obtain statistically stationary states close to these exact solutions. The measured phase speeds of waves in the GNS simulations agree with analytical predictions for Rossby waves.

Derivation of All Attitude Error Governing Equations for Attitude Filtering and Control.

This article presents the full analytical derivations of the attitude error kinematics equations. This is done for several attitude error representations, obtaining compact closed-forms expressions. Attitude error is defined as the rotation between true and estimated orientations. Two distinct approaches to attitude error kinematics are developed. In the first, the estimated angular velocity is defined in the true attitude axes frame, while in the second, it is defined in the estimated attitude axes frame. The first approach is of interest in simulations where the true attitude is known, while the second approach is for real estimation/control applications. Two nonlinear kinematic models are derived that are valid for arbitrarily large rotations and rotation rates. The results presented are expected to be broadly useful to nonlinear attitude estimation/control filtering formulations. A discussion of the benefits of the derived error kinematic models is included.

Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations

Viscous fingering experiments in Hele-Shaw cells lead to striking pattern formations which have been the subject of intense focus among the physics and applied mathematics community for many years. In recent times, much attention has been devoted to devising strategies for controlling such patterns and reducing the growth of the interfacial fingers. We continue this research by reporting on numerical simulations, based on the level set method, of a generalised Hele-Shaw model for which the geometry of the Hele-Shaw cell is altered. First, we investigate how imposing constant and time-dependent injection rates in a Hele-Shaw cell that is either standard, tapered or rotating can be used to reduce the development of viscous fingering when an inviscid fluid is injected into a viscous fluid over a finite time period. We perform a series of numerical experiments comparing the effectiveness of each strategy to determine how these non-standard Hele-Shaw configurations influence the morphological features of the inviscid–viscous fluid interface. Surprisingly, a converging or diverging taper of the plates leads to reduced metrics of viscous fingering at the final time when compared to the standard parallel configuration, especially with carefully chosen injection rates; for the rotating plate case, the effect is even more dramatic, with sufficiently large rotation rates completely stabilising the interface. Next, we illustrate how the number of non-splitting fingers can be controlled by injecting the inviscid fluid at a time-dependent rate while increasing the gap between the plates. Our simulations compare well with previous experimental results for various injection rates and geometric configurations. We demonstrate how the number of non-splitting fingers agrees with that predicted from linear stability theory up to some finger number; for larger values of our control parameter, the fully nonlinear dynamics of the problem leads to slightly fewer fingers than this linear prediction.

Generation of a magnetic field by a double vortex in a rotating cylinder.

In this paper we use simulations of the magnetohydrodynamic equations coupled with heat to show the generation of magnetic field by the dynamical interaction of a pair of vortices in a fluid electrically conducting within a cylindrical domain nonhomogeneously heated from below, setting in a rotation frame. For large enough rotation rates we show that the formation of a pair of vortices inside the primary whirl gives rise to a magnetic field. The magnetic field has a strong horizontal component, and the magnetic lines go from one vortex to the other.

Flow periodicity and convection modes in rotating Rayleigh–Bénard convection at low Rayleigh numbers

A three-dimensional numerical study on rotating Rayleigh–Bénard convection of water in a cylindrical container with a specific aspect ratio is performed in the present work. The simulations are carried out at four different Rayleigh numbers ( $$3\times 10^4, 5\times 10^4,7\times 10^4$$ and $$10^5$$ ) and a fixed Prandtl number ( $$Pr=7$$ ) for a range of rotation rates. Flow structures and their evolution with the addition of rotation to the system are studied in detail. Emphasis is given on the analysis of wall mode and bulk mode convection that appear at different rotation rates. The changes in heat transfer and stability of the system are also investigated. Heat transfer rate is measured by calculating the average Nusselt number at the hot wall. The results show that rotation primarily has an inhibiting effect on heat transfer. For $$Ra\le 7\times 10^4$$ the decrease in heat transfer is negligible at lower rotation rates, while it declines steeply for higher rotation rates. At $$Ra=10^5$$ a small increase in Nusselt number is obtained at low rotation rates before it drops at higher rotation rates. Numerous probes placed at different points within the flow domain are used to investigate the flow regimes and convection modes. The flow initially remains steady at low rotation rates and transforms to a periodic stage with bulk-mode-dominated convection at moderate rotation rates. Further increase in rotation gives a wall mode convection accompanied by a drastic drop in heat transfer rate before finally approaching a static conductive stage. The dual role of rotation on the stability of Rayleigh–Bénard convection is clearly identified in the present study. At moderate rotation rates, the rotation force destabilizes the system to reach a periodic flow whereas extremely large rotation rate stabilizes it.

Convective Models of Jupiter’s Zonal Jets with Realistic and Hyper-Energetic Excitation Source

Numerical simulations of Jupiter’s zonal jets are presented, which are generated with realistic and hyper energetic source. The models are three dimensional and nonlinear, applied to a gas that is convective, stratified and compressible. Two solutions are presented, one for a shallow 0.6% envelope, the other one 5% deep. For the shallow model (SM), Jupiter’s small energy flux was applied with low kinematic viscosity. For the deep model (DM), the energy source and viscosity had to be much larger to obtain a solution with manageable computer time. Alternating zonal winds are generated of order 100 m/s, and the models reproduce the observed width of the prograde equatorial jet and adjacent retrograde jets at 20° latitude. But the height variations of the zonal winds differ markedly. In SM the velocities vary radially with altitude, but in DM Taylor columns are formed. The dynamical properties of these divergent model results are discussed in light of the computed meridional wind velocities. With large planetary rotation rate Ω, the zonal winds are close to geostrophic, and a quantitative measure of that property is the meridional Rossby number, Rom. In the meridional momentum balance, the ratio between inertial and Coriolis forces produces Rom = V2/ΩLU, U zonal, V meridional winds, L horizontal length scale. Our analysis shows that the meridional winds vary with the viscosity like ν1/2. With much larger viscosity and meridional winds, the Rossby number for DM is much larger, Rom(DM) >> Rom(SM). Compared to the shallow model with zonal winds varying radially, the deeper and more viscous model with Taylor columns is much less geostrophic. The zonal winds of numerical models in the literature tend to be independent of the energy source, in agreement with the present results. With 104 times larger energy flux, the zonal winds for DM only increase by a factor of 3, and the answer is provided by the zonal momentum budget with meridional winds, VU/L = ΩV, yielding U = ΩL, independent of the source. The same relationship produces the zonal Rossby number, Roz = U/ΩL, of Order 1, which is commonly used as a dimensionless measure of the zonal wind velocities.

Effect of the crucible/crystal rotation on thermocapillary instability in a shallow Czochralski configuration

To understand the effects of crucible/crystal rotation on the instability of thermocapillary flow in a shallow Czochralski configuration, a series of linear stability analysis were performed by using Legendre spectral element method, and the energy analysis was applied to explore the instability mechanism. The results indicate that there are two types of instabilities with the increase of dimensionless crucible rotation rate ωc. Thermocapillary force and crucible rotation are the main causes of flow instability for low and high crucible rotation rate, respectively. In the interval 1627<ωc < 1822, with the increase of Marangoni number, three turning points were observed, indicating three transitions between two-dimensional axisymmetric steady flow and three-dimensional oscillatory flow due to the interaction between thermocapillary force and crucible rotation. For crystal rotation, two oscillatory modes for flow instability were observed. When the dimensionless crystal rotation rate is small (ωs < 3600), the oscillatory flow rotates in the opposite direction of the crystal rotation, but in the same direction in the case of large crystal rotation rate (ωs > 3600), and the thermocapillary force is the primary inducement of flow instability.

Critical gravitational collapse with angular momentum. II. Soft equations of state

We study critical phenomena in the collapse of rotating ultrarelativistic perfect fluids, in which the pressure $P$ is related to the total energy density $\rho$ by $P=\kappa\rho$, with $\kappa$ a constant. We generalize earlier results for radiation fluids with $\kappa=1/3$ to other values of $\kappa$, focussing on $\kappa < 1/9$. For $1/9<\kappa \lesssim 0.49$, the critical solution has only one unstable, growing mode, which is spherically symmetric. For supercritical data it controls the black hole mass, while for subcritical data it controls the maximum density. For $\kappa<1/9$, an additional axial $l=1$ mode becomes unstable. This controls either the black hole angular momentum, or the maximum angular velocity. In theory, the additional unstable $l=1$ mode changes the nature of the black hole threshold completely: at sufficiently large initial rotation rates $\Omega$ and sufficient fine-tuning of the initial data to the black hole threshold we expect to observe nontrivial universal scaling functions (familiar from critical phase transitions in thermodynamics) governing the black hole mass and angular momentum, and, with further fine-tuning, eventually a finite black hole mass almost everywhere on the threshold. In practice, however, the second unstable mode grows so slowly that we do not observe this breakdown of scaling at the level of fine-tuning we can achieve, nor systematic deviations from the leading-order power-law scalings of the black hole mass. We do see systematic effects in the black-hole angular momentum, but it is not clear yet if these are due to the predicted non-trivial scaling functions, or to nonlinear effects at sufficiently large initial angular momentum (which we do not account for in our theoretical model).

Hysteretic transitions between quasi-two-dimensional flow and three-dimensional flow in forced rotating turbulence

Conflict between formation of a cyclonic vortex and isotropization in forced homogeneous rotating turbulence is numerically investigated. It is well known that a large rotation rate of the system induces columnar vortices to result in quasi-two-dimensional (Q2D) flow, while a small rotation rate allows turbulence to be three-dimensional (3D). It is found that the transition from the Q2D turbulent flow to the 3D turbulent flow and the reverse transition occur at different values of the rotation rates. At the intermediate rotation rates, bistability of these two statistically steady states is observed. Such hysteretic behavior is also observed for the variation of the amplitude of an external force.

Are pulsars spun up or down by SASI spiral modes?

Pulsars may either be spun up or down by hydrodynamic instabilities during the supernova explosion of massive stars. Besides rapidly-rotating cases related to bipolar explosions, stellar rotation may affect the explosion of massive stars in the more common situations where the centrifugal force is minor. Using 2D simulations of a simplified setup in cylindrical geometry, we examine the impact of rotation on the Standing Accretion Shock Instability (SASI) and the corotation instability, also known as low-T/|W|. The influence of rotation on the saturation amplitude of these instabilities depends on the specific angular momentum in the accretion flow and the ratio of the shock to the neutron star radii. The spiral mode of SASI becomes more vigorous with faster rotation only if this ratio is large enough. A corotation instability develops at large rotation rates and impacts the dynamics more dramatically, leading to a strong one-armed spiral wave. Non-axisymmetric instabilities are able to redistribute angular momentum radially and affect the pulsar spin at birth. A systematic study of the relationship between the core rotation period of the progenitor and the initial pulsar spin is performed. Stellar rotation rates for which pulsars are spun up or down by SASI are estimated. Rapidly spinning progenitors are modestly spun down by spiral modes, less than $\sim 30\%$, when a corotation instability develops. Given the observational constraints on pulsar spin periods at birth, this suggests that rapid rotation might not play a significant hydrodynamic role in most core-collapse supernovae.

Nonlinear Zel'dovich Effect: Parametric Amplification from Medium Rotation.

The interaction of light with rotating media has attracted recent interest for both fundamental and applied studies including rotational Doppler shift measurements. It is also possible to obtain amplification through the scattering of light with orbital angular momentum from a rotating and absorbing cylinder, as proposed by Zel'dovich more than forty years ago. This amplification mechanism has never been observed experimentally yet has connections to other fields such as Penrose superradiance in rotating black holes. Here we propose a nonlinear optics system whereby incident light carrying orbital angular momentum drives parametric interaction in a rotating medium. The crystal rotation is shown to take the phase-mismatched parametric interaction with negligible energy exchange at zero rotation to amplification for sufficiently large rotation rates. The amplification is shown to result from breaking of anti-PT symmetry induced by the medium rotation.

Incidence of stellar rotation on the explosion mechanism of massive stars

AbstractHydrodynamical instabilities may either spin-up or down the pulsar formed in the collapse of a rotating massive star. Using numerical simulations of an idealized setup, we investigate the impact of progenitor rotation on the shock dynamics. The amplitude of the spiral mode of the Standing Accretion Shock Instability (SASI) increases with rotation only if the shock to the neutron star radii ratio is large enough. At large rotation rates, a corotation instability, also known as low-T/W, develops and leads to a more vigorous spiral mode. We estimate the range of stellar rotation rates for which pulsars are spun up or down by SASI. In the presence of a corotation instability, the spin-down efficiency is less than 30%. Given observational data, these results suggest that rapid progenitor rotation might not play a significant hydrodynamical role in the majority of core-collapse supernovae.