Solid-body Rotation Research Articles

Hydrodynamic coupling of a cilia–mucus system in Herschel–Bulkley flows

The yield stress and shear thinning properties of mucus are identified as critical for ciliary coordination and mucus transport in human airways. We use here numerical simulations to explore the hydrodynamic coupling of cilia and mucus with these two properties using the Herschel–Bulkley model, in a lattice Boltzmann solver for the fluid flow. Three mucus flow regimes, i.e. a poorly organized regime, a swirly regime, and a fully unidirectional regime, are observed and analysed by parametric studies. We systematically investigate the effects of ciliary density, interaction length, Bingham number and flow index on the mucus flow regime formation. The underlying mechanism of the regime formation is analysed in detail by examining the variation of two physical quantities (polarization and integral length) and the evolution of the flow velocity, viscosity and shear-rate fields. Mucus viscosity is found to be the dominant parameter influencing the regime formation when enhancing the yield stress and shear thinning properties. The present model is able to reproduce the solid body rotation observed in experiments (Loiseau et al., Nat. Phys., vol. 16, 2020, pp. 1158–1164). A more precise prediction can be achieved by incorporating non-Newtonian properties into the modelling of mucus as proposed by Gsell et al. (Sci. Rep., vol. 10, 2020, 8405).

Emergent chirality in active solid rotation of pancreas spheres

Collective cell dynamics play a crucial role in many developmental and physiological contexts. While two-dimensional (2D) cell migration has been widely studied, how three-dimensional (3D) geometry and topology interplay with collective cell behavior to determine dynamics and functions remains an open question. In this work, we elucidate the biophysical mechanism underlying rotation in spherical tissues, a phenomenon widely reported both and . Using murine pancreas-derived organoids as a model system, we find that epithelial spheres exhibit persistent rotation, rotational axis drift, and rotation arrest. Using a 3D vertex model, we demonstrate how the combined action of traction force and polarity alignment can account for these distinct rotational dynamics near a solid to flow transition. Furthermore, our analysis shows that the spherical tissue rotates as an active solid occasionally switching to a flowing state and exhibits spontaneous chiral symmetry breaking. Using a continuum model, we demonstrate how the topological defects in the polarity field underlie this symmetry breaking process, which is revealed by asymmetries in the cell elongation pattern. For cell elongation to reveal the chiral asymmetry, shear flow is required in addition to the solid body rotation. Altogether, our work reveals a robust chiral symmetry breaking mechanism with potential implications for left-right symmetry breaking processes in morphogenetic events. Published by the American Physical Society 2024

Wave-driven current and vortex patterns at an open beach: Insights from phase-resolving numerical computations and Lagrangian measurements

Wave-driven currents have a substantial impact on local circulation patterns in and across the surf zone, and are responsible for cross-shore and longshore exchange of mass and momentum over a broad range of spatial and temporal scales. Nearshore currents may drive sediment transport, lead to beach erosion, and also affect the spread of bacteria and other marine microorganisms, as well as the distribution of pollutants such as chemicals and microplastics. In addition, surf zone currents can cause hazardous conditions for beach-goers in the form of rip currents.It is known from previous work (Chen et al., 2003; Feddersen et al., 2011; Hally-Rosendahl and Feddersen, 2016) that Boussinesq-type models in combination with appropriate boundary conditions and wave breaking capabilities can function as powerful tools for the analysis of circulation patterns in the surf zone. In the present work, data from a recent field campaign reported on in Bjørnestad et al. (2021) are used to further validate the capability of Boussinesq systems to simulate nearshore dynamics.The numerical model is then used to study the influence of tidal elevation, peak direction and directional spread of the incoming wavefield on the quantity, extent, and circulatory magnitude of the nearshore circulation. In addition, fundamental features such as horizontal eddies are investigated, and comparisons are made to solid-body rotation and irrotational vortices.Overall, it is observed that local variations in the bathymetry across the surf zone are the controlling factor regarding the size of these circulations, and an increasing tidal level, which can be seen as a uniform offset to the bathymetry, favors the generation of larger vortex patterns. For a given tidal stage, the directional spread of the incoming wavefield has the most pronounced influence on the size and strength of the nearshore eddies while the peak direction has the strongest effect on the total number of circulations.

Protostellar disk accretion in turbulent filaments

Context. Recent observations of protostellar cores suggest that most of the material in the protostellar phase is accreted along streamers. Streamers in this context are defined as velocity coherent funnels of denser material potentially connecting the large-scale environment to the small scales of the forming accretion disk. Aims. Using simulations that simultaneously resolve the driving of turbulence on the filament scale as well as the collapse of the core down to protostellar disk scales, we aim to understand the effect of the turbulent velocity field on the formation of overdensities in the accretion flow. Methods. We performed a three-dimensional numerical study on a core collapse within a turbulent filament using the RAMSES code and analysed the properties of overdensities in the accretion flow. Results. We find that overdensities are formed naturally by the initial turbulent velocity field inherited from the filament and subsequent gravitational collimation. This leads to streams that are not really filamentary but show a sheet-like morphology. Moreover, they have the same radial infall velocities as the low density material. As a main consequence of the turbulent initial condition, the mass accretion onto the disk does not follow the predictions for solid body rotation. Instead, most of the mass is funneled by the overdensities to intermediate disk radii.

On the use of the Astarita flow field for viscoelastic fluids to develop a generalised Newtonian fluid model incorporating flow type (GNFFTy)

The two-dimensional, steady, homogeneous flow field proposed by Astarita (J. Rheol., vol. 35, 1991, pp. 687–689) is studied for a range of viscoelastic constitutive equations of differential form including the models due to Oldroyd (the upper and lower convected Maxwell; UCM/LCM), Phan-Thien and Tanner (simplified, linear form; sPTT) and Giesekus. As the flow is steady and homogeneous, the sPTT model results also give the FENE-P model solutions via a simple transformation of parameters. The flow field has the interesting feature that a scalar parameter may be used to vary the flow ‘type’ continuously from solid-body rotation to simple shearing to planar extension whilst the rate of deformation tensor $\boldsymbol{\mathsf{D}}$ remains constant (i.e. independent of flow type). The response of the models is probed in order to determine how a scalar ‘viscosity’ function may be rigorously constructed which includes flow-type dependence. We show that for most of these models – the Giesekus being the exception – the first and second invariants of the resulting extra stress tensor are linearly related, and for models based on the upper convected derivative, this link is simply via a material property, i.e. half the modulus. By defining a frame-invariant coordinate system with respect to the eigenvectors of $\boldsymbol{\mathsf{D}}$ , we associate a ‘viscosity’ for each of the flows to a deviatoric stress component and show how this quantity varies with the flow-type parameter. For elliptical motions, rate thinning is always observed and all models give essentially the UCM response. For strong flows, i.e. flow types containing at least some extension, thickening occurs and only a small element of extension is required to remove any shear thinning inherent in the model (e.g. as occurs in steady simple shearing for the sPTT/Giesekus models). Finally, a functional form of a viscosity equation which could incorporate flow type, but be otherwise inelastic, the so-called GNFFTy (generalised Newtonian fluid model incorporating flow type, pronounced ‘nifty’), is proposed. In the frame-invariant coordinate system proposed, this model is also capable of capturing normal-stress differences.

Fluid dynamics and mixing in a novel intermittently rotating bioreactor for CAR-T cell therapy: Spin-down from incomplete spin-up

This work explores the fluid flow and mixing within a new type of intermittently rotating bioreactor used for the automated manufacturing of CAR-T cell therapy products; CAR-T is a novel cell-based gene therapy which offers a single-dose cure for several forms of advanced blood cancer. The rotating cylinder bioreactor has a free surface and a liquid height to radius ratio of 0.5. Agitation is achieved via intermittent rotation of the entire vessel around its central vertical axis. No comprehensive engineering characterisation of the fluid dynamics in a bioprocessing context exists to date for this type of bioreactor. The present study examines the fluid dynamics and mixing during spin-down to rest following incomplete spin-up (i.e. the starting state of the fluid is not solid body rotation). Novel Particle Image Velocimetry (PIV) and Planar Laser-Induced Fluorescence (PLIF) data is presented, shedding light on the different transient flow regions inside the intermittently rotating bioreactor, and on the impact spin-up time has on the mixing efficiency of the subsequent spin-down stage. The results presented can be used to inform the design of a custom intermittent agitation pattern for any resembling cylinder bioreactors, the adoption of which could lead to higher yields and reduced costs for the cell expansion step of the manufacturing process.

Asteroseismic modelling of the chemically peculiar B-type pulsator with an asymptotic period spacing – a Cen

ABSTRACT A Cen is recognized as a magnetic variable star with peculiar helium abundance. The presence of large surface spots induces flux modulation, allowing for the derivation of the surface rotational period (∼8.8 d). TESS photometry has unveiled additional signals that we interpreted as SPB-type pulsation. Furthermore, we managed to find a regular period spacing pattern and hence identified pulsational modes. We performed an asteroseismic analysis that resulted in constraints for internal structure of the star. Taking into account the surface rotation period derived from spots and the internal rotation obtained from asteroseismology, we concluded that the gradient of the rotational velocity in the radial direction is very small, indicating nearly solid body rotation. We also constrained overshooting from the convective core, as well as the mass and metallicity of the star.

LES of pilot n-heptane ignition and its interaction with the lean premixed methane–air mixture in a dual-fuel combustion engine

Large eddy simulations of pilot fuel ignited, lean premixed, natural gas engines are performed to study the pilot-ignition process and its subsequent interaction with the premixed charge. The injection pressure (Pinj) and injection duration (Δinj) are varied (i.e. 800 bar/760μs, 800 bar/500μs, and 400bar/760μs) to study the impact of the injection process on the subsequent combustion evolution. Open-cycle simulations considering the full engine geometry are used to predict the in-cylinder flows, while combustion is modeled using a finite-rate chemistry model. In-cylinder methane (CH4) is shown to delay the low-temperature ignition of the pilot fuel, regardless of the pilot injection setting, which subsequently prolongs the overall pilot fuel ignition delay. Moreover, all simulated cases show the occurrence of back-supported combustion (BSC), where the burning of CH4-air mixture is “back-supported” by pilot fuel radicals. Despite both the 800 bar/500μs and 400 bar/760μs cases having the same injected pilot fuel mass, the peak in-cylinder pressure and burning rate of the premixed CH4-air mixture in the former case are higher. Higher Pinj and shorter Δinj lead to better mixing between the pilot fuel and the premixed CH4-air charge. Subsequently, this forms a larger volume of regions with elevated equivalence ratio due to the presence of pilot fuel (ϕ>ϕCH4) which, consequently promotes the formation of BSC. The impact of in-cylinder flow fields on the dual-fuel combustion process is investigated by performing two closed-cycle 800 bar/500μs cases with one assuming solid-body rotation and another without solid-body rotation (i.e. zero velocity field). In-cylinder flow field is shown to have a visible impact on the transition stage between the pilot ignition stage and the premixed flame propagation stage, but have an insignificant effect on the pilot fuel ignition process. In the transition stage, slower flame propagation is observed in the zero-velocity case. The results show that this is not only due to the turbulence effect on premixed flame but also due to differences in the volume and distribution of pilot fuels that impacts BSC.

Titan’s Atmospheric Albedo Asymmetry and Seasonal Variability Observed through the Cassini Imaging Science Subsystem

Using images from Cassini, we analyzed the north–south albedo asymmetry that has been observed in the atmosphere of Saturn’s moon, Titan. Suitable images from the Cassini Imaging Science Subsystem taken at 889 nm spanned from 2004 to 2017—around half of a Titan year—and revealed seasonal changes in the characteristics and orientation of the north–south asymmetry boundary. Such circumglobal features provide insight into the dynamics and circulation of the atmosphere more broadly. The albedo asymmetry has been observed to reverse for part of the Titan year, inverting the brighter and darker hemispheres; we also observed this inversion, along with the formation of additional banding briefly during the transition (around 2014–2016). A tilt in the rotation axis of Titan’s atmosphere with respect to the solid body rotation has previously been noted. Using robust edge-detection techniques, we likewise identified a tilt offset of a few degrees in the albedo transition boundaries. The azimuth of this tilt axis remained roughly fixed in inertial space, with some smaller possible seasonal fluctuations around the fixed direction noted.

Wave-like motions and torques in Earth's core as inferred from geomagnetic data: A synthetic study

Here, we present a synthetic validation for the inversion of transient fluid motions at the surface of Earth's core. It is based on a numerical simulation of the geodynamo in which the main time-scales (based on rotation, magnetic field and velocity) are sufficiently separated to give rise to a variety of hydro-magnetic waves. We focus the study on wave-like motions with periods commensurate to the Alfvén time, which is based on the strength of the magnetic field in the core interior. Synthetic magnetic data are generated over 90 Alfvén times, representative of the era covered by observatory and satellite measurements. These synthetic data are inverted to estimate a magnetic field model. Thereafter, we apply the pygeodyn data assimilation tool to recover core surface flows. We investigate the quality of their reconstruction as a function of their time scale. The success of the reconstruction depends on the data accuracy and coverage and on the magnitude of the flow. We also retrieve axi-symmetric torsional Alfvén waves, despite their relatively weak magnitude.We use the synthetic data to investigate the exchanges of angular momentum between core and mantle that induce length-of-day (LOD) changes. These exchanges result from the electromagnetic torque between the fluid core and the mantle and the gravitational torque between the inner core and the mantle. The inverted flows convincingly predict LOD variations in the dynamo calculation. We find that core surface zonal motions match well with the geostrophic (axially invariant) motions at the origin of the LOD changes, on all considered time-scales. We also investigate the different contributions to the electro-magnetic torque. In the dynamo simulation, only a small part can be attributed to the leakage torque caused by electrical currents flowing from the core to the mantle. The relative contribution from the poloidal field induced in the mantle, which amounts to about 1/3 of the total torque, is significantly larger than estimated in previous studies, based on geomagnetic observations. The remaining torque, which is associated with the toroidal induced field, mostly stems from the solid body rotation interacting with the radial magnetic field up to spherical harmonic degree 30.

Effect of Hematocrit and Elevated Beat Rate on the 12cc Penn State Pediatric Ventricular Assist Device.

Congenital heart disease affects approximately 40,000 infants annually in the United States with 25% requiring invasive treatment. Due to limited number of donor hearts and treatment options available for children, pediatric ventricular assist devices (PVADs) are used as a bridge to transplant. The 12cc pneumatic Penn State PVAD is optimized to prevent platelet adhesion and thrombus formation at patient nominal conditions; however, children demonstrate variable blood hematocrit and elevated heart rates. Therefore, with pediatric patients exhibiting greater variability, particle image velocimetry is used to evaluate the PVAD with three non-Newtonian hematocrit blood analogs (20%, 40%, and 60%) and at two beat rates (75 and 120 bpm) to understand the device's performance. The flow fields demonstrate a strong inlet jet that transitions to a solid body rotation during diastole. During systole, the rotation dissipates and reorganizes into an outlet jet. This flow field is consistent across all hematocrits and beat rates but at a higher velocity magnitude during 120 bpm. There are also minor differences in flow field timing and surface washing due to hematocrit. Therefore, despite patient differences in hematocrit or required pumping output, thorough surface washing can be achieved in the PVAD by altering operating conditions, thus reducing platelet adhesion potential.

Density-mediated spin correlations drive edge-to-bulk flow transition in active chiral matter.

We demonstrate that edge currents develop in active chiral matter due to boundary shielding over a wide range of densities corresponding to a gas, fluid, and crystal. The system is composed of spinning disk-shaped grains with chirally arranged tilted legs confined in a circular vibrating chamber. The edge currents are shown to increasingly drive circulating bulk flows with area fraction as percolating clusters develop due to increasing spin-coupling between neighbors mediated by frictional contacts. Edge currents are observed even in the dilute limit. While, at low area fraction, the average flux vanishes except within a distance that is of the order of a particle diameter of the boundary, the penetration depth grows with increasing area fraction until a solid-body rotation is achieved corresponding to the highest packing, where the particles are fully caged with hexagonal order and spin in phase with the entire packing. A coarse-grained model, based on the increased collisional interlocking of the particles with area fraction and the emergence of order, captures the observed flow fields.

Alignment of dense molecular core morphology and velocity gradients with ambient magnetic fields

ABSTRACT Studies of dense core morphologies and their orientations with respect to gas flows and the local magnetic field have been limited to only a small sample of cores with spectroscopic data. Leveraging the Green Bank Ammonia Survey alongside existing sub-millimeter continuum observations and Planck dust polarization, we produce a cross-matched catalogue of 399 dense cores with estimates of core morphology, size, mass, specific angular momentum, and magnetic field orientation. Of the 399 cores, 329 exhibit 2D vLSR maps that are well fit with a linear gradient, consistent with rotation projected on the sky. We find a best-fit specific angular momentum and core size relationship of J/M ∝ R1.82 ± 0.10, suggesting that core velocity gradients originate from a combination of solid body rotation and turbulent motions. Most cores have no preferred orientation between the axis of core elongation, velocity gradient direction, and the ambient magnetic field orientation, favouring a triaxial and weakly magnetized origin. We find, however, strong evidence for a preferred anti-alignment between the core elongation axis and magnetic field for protostellar cores, revealing a change in orientation from starless and prestellar populations that may result from gravitational contraction in a magnetically-regulated (but not dominant) environment. We also find marginal evidence for anti-alignment between the core velocity gradient and magnetic field orientation in the L1228 and L1251 regions of Cepheus, suggesting a preferred orientation with respect to magnetic fields may be more prevalent in regions with locally ordered fields.

Visible Emission Line Spectroscopy of the Solar Corona During the 2019 Total Solar Eclipse

Spectroscopic measurements of the low solar corona are crucial to understanding the mechanisms that heat the corona and accelerate the solar wind, yet the lowest solar radii (R_{odot }) of the corona are difficult to observe. Our expedition collected narrow wavelengths of visible light at 530.3, 637.4, and 789.2 nm emitted by Fe xiv, x, and xi ions, respectively, from the total solar eclipse on 2019 July 2 at 20:40 UTC in Rodeo, Argentina with a bespoke 3-channel spectrometer. This paper describes the instrument and data calibration method that enables diagnostics out to {approx},1.0~R_{odot } above the solar limb within a bright helmet streamer. We find that Fe x and xi lines are dominant through 0.3~R_{odot }, with Fe xiv maintaining a stronger signal at higher elevations. Thermal line width broadening is consistent with 1.5 MK for the cooler Fe x, 2 MK for Fe xi, and 3 MK for the hotter Fe xiv line, which can be interpreted as differing density scale heights within isolated, isothermal flux tubes. The Doppler measurements correspond to bulk plasma motion ranging from −12 to +2.5 km s−1, with Fe xiv moving at nearly an assumed solid body rotation rate throughout 1.0~R_{odot }. After considering coronal rotation, these measurements are likely associated with plasma motion along the dominant longitudinal orientation of the magnetic field at the streamer base within 0.4~R_{odot }. These results show that high-resolution spectroscopy of visible light offers valuable diagnostics of the low corona, and lend insight into the interconnected loop complexity within helmet streamers.

Accounting for differential rotation in calculations of the Sun’s angular momentum-loss rate

Context. Sun-like stars shed angular momentum due to the presence of magnetised stellar winds. Magnetohydrodynamic models have been successful in exploring the dependence of this ‘wind-braking torque’ on various stellar properties; however the influence of surface differential rotation is largely unexplored. As the wind-braking torque depends on the rotation rate of the escaping wind, the inclusion of differential rotation should effectively modulate the angular momentum-loss rate based on the latitudinal variation of wind source regions. Aims. Here we aim to quantify the influence of surface differential rotation on the angular momentum-loss rate of the Sun, in comparison to the typical assumption of solid-body rotation. Methods. To do this, we exploited the dependence of the wind-braking torque on the effective rotation rate of the coronal magnetic field, which is known to be vitally important in magnetohydrodynamic models. This quantity has been evaluated by tracing field lines through a potential field source surface (PFSS) model, driven by ADAPT-GONG magnetograms. The surface rotation rates of the open magnetic field lines were then used to construct an open-flux weighted rotation rate, from which the influence on the wind-braking torque could be estimated. Results. During solar minima, the rotation rate of the corona decreases with respect to the typical solid-body rate (the Carrington rotation period is 25.4 days), as the sources of the solar wind are confined towards the slowly rotating poles. With increasing activity, more solar wind emerges from the Sun’s active latitudes which enforces a Carrington-like rotation. Coronal rotation often displays a north-south asymmetry driven by differences in active region emergence rates (and consequently latitudinal connectivity) in each hemisphere. Conclusions. The effect of differential rotation on the Sun’s current wind-braking torque is limited. The solar wind-braking torque is ∼10 − 15% lower during solar minimum, (compared with the typical solid body rate), and a few percent larger during solar maximum (as some field lines connect to more rapidly rotating equatorial latitudes). For more rapidly rotating Sun-like stars, differential rotation may play a more significant role, depending on the configuration of the large-scale magnetic field.

The Earth's rotational modes revisited

In the conventional treatment of the Earth's rotational dynamics using the Earth's angular momentum description (AMD), it is customary to assume that the velocity/displacement of a mass element in the liquid core (LC) has a displacement as well as an explicit rigid rotation component in addition to the uniform (solid-body) rotation. This makes for a very complex set of non-linear differential equations in the treatment of the dynamics of this body. In this work, I will use a simple three-layer Earth model with a rigid mantle (MT), a rigid inner core (IC), and an incompressible and homogeneous LC to show that in the alternative linearised dynamics of this body, it is redundant to assign a rigid rotation component to the motion. Next, I will use an approximation commonly used in dealing with the Earth's rotational dynamics, and further assume that the MT rotates uniformly, to show that the linearised equations yield identical analytical results to those in the literature for the periods of the inner-core wobble (ICW) and the free inner-core nutation (FICN).

A direct numerical simulation display of the rotational frame preference of turbulence

An elementary observation of a laminar cylindrical Poiseuille–Couette flow profile reveals no distinction in the parabolic streamwise profile, from one without a cross-stream flow, in whatever reference frame the observation is made. This is because the laminar flow is in solid-body rotation and there is no fluid intrinsic rotation. Hence, the main streamwise Poiseuille flow is unaffected. On the contrary, in turbulent (unsteady) cylindrical axial-Couette flow, the rotational reference frame must be considered, and any observation from an external inertial reference frame can give outright incorrect results. However, even in axial turbulent pipe flow with axial rotation, the resultant effect of azimuthal velocity on the flow profile is still usually too low. Hence, the importance of consideration in the rotational frame is often overlooked. A common misconception in the study of fluid mechanics is that the position of the observer does not matter. In this direct numerical simulation study, firstly turbulent flow in a pipe with axial rotation is established. Then turbulent flow in the concentric pipe, with inner wall rotation, is used to show how tilted wall streak direction is oriented by the rotational reference frame and not the inertial reference frame.

A semi-implicit slip algorithm for mesh deformation in complex geometries, implemented in OpenFOAM

Many engineering applications of computational fluid dynamics (CFD) comprise extensive movement of objects that necessitate complex dynamic mesh treatments. In particular, the mesh motion process frequently requires a proper slipping of mesh points on highly curved surfaces. The currently available implementation of explicit slip boundary conditions in OpenFOAM fails to allow large deformations of the mesh without severely degrading the mesh quality and inverting some of the cells. Thus, a robust semi-implicit slip algorithm, based on the Laplacian smoothing methodology, is developed in the present work to tackle this issue. The algorithm is in fact performed in two steps, one explicit and one implicit. The OpenFOAM implementation of the algorithm includes different mesh motion solvers and boundary conditions, based on the displacement or velocity of points. The method is first verified using simple, yet relevant, test cases, and it is shown that the developed algorithm significantly outperforms some of the well-known proprietary CFD codes. Then, it is applied to a complex practical CFD case study. An engineering application that requires the features of the developed mesh motion algorithm is the transient operation of Kaplan turbines. These double-regulated machines simultaneously adjust the guide vane and runner blade angles while changing the operating condition. CFD simulations of such transient operations are highly complex, as they involve mesh deformation of the guide vane passage and simultaneous mesh deformation and rigid-body rotation of the runner blade passage. The mesh deformation requires points to slip on the curved hub and shroud surfaces while preserving the cell quality in tiny blade clearances. Therefore, the feasibility of the developed algorithm is evaluated for a load rejection sequence of a Kaplan turbine model. Program summaryProgram Title: Semi-implicit slip mesh motionCPC Library link to program files:https://doi.org/10.17632/wztc26vh7b.1Developer's repository link:https://github.com/salehisaeed/semiImplicitSlipLicensing provisions: GPLv3Programming language: C++Nature of problem: CFD simulations of numerous engineering fluid flows, such as transient operation of hydraulic turbines, involve an immensely complicated mesh motion process consisting of simultaneous mesh deformation and mesh slipping on highly curved surfaces. The available standard mesh motion methodology in OpenFOAM lacks some features to simulate this elaborate mesh motion. The introduced program addresses this problem by developing a new dynamic mesh algorithm.Solution method: The program implements a robust semi-implicit algorithm for slipping the mesh points on curved surfaces. The algorithm includes two steps, namely, an explicit step based on the general slip condition and an implicit step based on the Dirichlet condition. It employs the Laplacian smoothing equations to spread the mesh deformation into the domain. Additionally, a solid-body rotation may be added on top of the deformed mesh, which could be useful for modeling the runner region in transient operation of Kaplan turbines which contains simultaneous mesh deformation and solid-body rotation of the mesh.

Simulating the Collapse of Rotating Primordial Gas Clouds to Study the Possibility of the Survival of Population III Protostars

It has been argued that the low-mass primordial stars (m Pop III ≤ 0.8 M ⊙) are likely to enter the main sequence and hence may possibly be found in present-day galaxies. However, due to limitations in existing numerical capabilities, current three-dimensional (3D) simulations of disk fragmentation are only capable of following a few thousand years of evolution after the formation of the first protostar. In this work, we use a modified version of the Gadget-2 smoothed particle hydrodynamics code to present the results of the nonlinear collapse of the gas clouds associated with various degrees of initial solid body rotation (parameterized by β) using a piecewise polytropic equation of state. The 3D simulations are followed until the epoch that occurs when 50M ⊙ of mass has been accreted in protostellar objects, which is adequate enough to investigate the dynamics of the protostars with the surrounding gaseous medium and to determine the mass function, accretion rate, and possibility of the survival of these protostellar objects to the present epoch. We found that evolving protostars that stay within slow-rotating parent clouds can become massive enough to survive, due to accretion in the absence of radiative feedback, whereas 10%–12% of those formed within fast-rotating clouds (β ≥ 0.1) could possibly be ejected from the gravitational bound cluster as low-mass stars.

A study of the rapid rotator ζ Aql: differential surface rotation?

ABSTRACT We report new, extremely precise photopolarimetry of the rapidly-rotating A0 main-sequence star ζ Aql, covering the wavelength range ∼400–900 nm, which reveals a rotationally-induced signal. We model the polarimetry, together with the flux distribution and line profiles, in the framework of Roche geometry with ω-model gravity darkening, to establish the stellar parameters. An additional constraint is provided by TESS photometry, which shows variability with a period, Pphot, of 11.1 h. Modelling based on solid-body surface rotation gives rotation periods, Prot, that are in only marginal agreement with this value. We compute new ester stellar-structure models to predict horizontal surface-velocity fields, which depart from solid-body rotation at only the ∼2 per cent level (consistent with a reasonably strong empirical upper limit on differential rotation derived from the line-profile analysis). These models bring the equatorial rotation period, Prot(e), into agreement with Pphot, without requiring any ‘fine tuning’ (for the Gaia parallax). We confirm that surface abundances are significantly subsolar ([M/H] ≃ −0.5). The star’s basic parameters are established with reasonably good precision: $M = 2.53\pm 0.16\, \mbox{M}_{\odot }$, log (L/L⊙) = 1.72± 0.02, $R_{\rm p}= 2.21\pm 0.02\, \mbox{R}_{\odot }$, Teff = 9693 ± 50 K, $i = 85{^{+5}_{-7}}^\circ$, and ωe/ωc = 0.95 ± 0.02. Comparison with single-star solar-abundance stellar-evolution models incorporating rotational effects shows excellent agreement (but somewhat poorer agreement for models at [M/H] ≃ −0.4).