Ratio Of Time Scales Research Articles

Fluid-mediated impact of soft solids

A viscous, lubrication-like response can be triggered in a thin film of fluid squeezed between a rigid flat surface and the tip of an incoming projectile. We develop a scaling for this viscous approach stage of fluid-mediated normal impact, applicable to soft impactors. Under the assumption of mediating fluid being incompressible, the impacting solid displays two limit regimes: one dominated by elasticity, and the other by inertia. The transition between the two is predicted by a dimensionless parameter, which can be interpreted as the ratio between two time scales that are the time that it takes for the surface waves to warn the leading edge of the impactor of the forthcoming impact, and the characteristic duration of the final viscous phase of the approach. Additionally, we elucidate why nearly incompressible solids feature (a) substantial ‘gliding’ prior to contact at the transition between regimes, (b) the largest size of entrapped bubble between the deformed tip of the impactor and the flat surface, and (c) a sudden drop in entrapped bubble radius past the transition between regimes. Finally, we argue that the above time scale ratio (a dimensionless number) can govern the different dynamics reported experimentally for a fluid droplet as a function of its viscosity and surface tension.

A Dimensionless Framework for the Partitioning of Fluvial Inorganic Carbon

AbstractRivers are pivotal in the global carbon cycle, transporting terrestrial carbon to the ocean while emitting significant amount of to the atmosphere. However, the partitioning of fluvial inorganic carbon (IC) between downstream transport and atmospheric evasion remains uncertain due to intricate hydrodynamic and biogeochemical processes. Inspired by Budyko's hydrological work, this study introduces a dimensionless framework to identify critical factors in fluvial IC partitioning: the IC fraction in equilibrium with the atmosphere and the ratio of advection to evasion timescales. River catchment analyses and modeling reveal that the equilibrium ratio determines the fraction of IC stably transported downstream. The hydrodynamic‐driven timescale ratio determines the fate of out‐of‐equilibrium IC, with low‐order streams favoring atmospheric evasion and higher‐order streams promoting downstream transport. This framework provides a simple yet robust approach to predicting river carbon dynamics, with implications for land‐to‐ocean transport, fluvial emissions, and climate mitigation strategies such as enhanced weathering.

Particle Concentrations and Sizes for the Onset of Settling‐Driven Gravitational Instabilities: Experimental Validation and Application to Volcanic Ash Clouds

AbstractSettling‐driven gravitational instabilities (SDGIs) can form at the base of buoyant particle‐laden suspensions, modulating particle sedimentation in various settings such as meteorological and volcanic clouds, fluvial plumes, magma chambers, submarine hydrothermal plumes, or industrial emissions. These instabilities result in the formation of rapidly descending currents called ‘fingers’ within which fine particles settle faster collectively than individually. This study investigates SDGI triggering conditions underneath volcanic ash clouds through analogue experiments considering sedimentation from aqueous particle suspensions. We confirm that the conditions for which SDGIs develop are controlled by two dimensionless numbers: Bf (ratio of the characteristic finger velocity to the individual particle settling velocity); and Bi (ratio of timescale for individual particle settling to that for collective settling controlled by inertial drag). SDGIs are triggered for values of Bf and Bi > 1 for which particles are fully coupled with the flow within fingers. Using these parameters, we produce a regime diagram for the 2010 eruption of Eyjafjallajökull (Iceland) that describes particle settling as a function of particle concentration and size. More studies are needed to produce a general regime diagram accounting for the evolution of SDGIs properties with eruption and atmospheric parameters. Nonetheless, our study confirms that fingers affect sedimentation from volcanic clouds with high ash volume fractions above 10−6 vol.%. Our validation of criteria predicting the onset of fingers due to SDGIs constitutes a step forward toward the incorporation of these collective settling processes in volcanic ash transport and dispersion models.

Nonequilibrium relaxation of soft responsive colloids.

Stimuli-responsive macromolecules display large conformational changes during their dynamics, sometimes switching between states. Such a multi-stability is useful for the development of soft functional materials. Here, we introduce a mean-field dynamical density functional theory for a model of responsive colloids to study the nonequilibrium dynamics of a colloidal dispersion in time-dependent external fields, with a focus on the coupling of translational and conformational dynamics during their relaxation. Specifically, we consider soft Gaussian particles with a bimodal size distribution between two confining walls with time-dependent (switching-on and off) external gravitational and osmotic fields. We find a rich relaxation behavior of the systems in excellent agreement with particle-based Brownian dynamics computer simulations. In particular, we find time-asymmetric relaxations of integrated observables (wall pressures, mean size, and liquid center-of-mass) for activation/deactivation of external potentials, respectively, which are tunable by the ratio of translational and conformational diffusion time scales. Our work thus paves the way for studying the nonequilibrium relaxation dynamics of complex soft matter with multiple degrees of freedom and hierarchical relaxations.

Comparison of Libration- and Precession-Driven Flows: From Linear Responses to Broadband Dynamics

Libration and precession are different body forces that are ubiquitous in many rapidly rotating systems, particularly in geophysical and astrophysical flows. Libration is a modulation of the background rotation magnitude, whereas precession is a modulation of the background rotation direction. Assessing the consequences of these body forces in large-scale flows is challenging. The Ekman number, the ratio of the rotation time scale to the viscous time scale quantifying the rotation speed, is extremely small, leading to extremely thin and intense shear layers in the flows even when the amplitudes of the body forces are very small. We consider the consequences of libration and precession numerically in a geometrically simple container, a cube, which lends itself to very efficient, accurate, and robust numerical treatment, with the axis of rotation passing through opposite vertices, so that all walls of the cube are at oblique angles to the rotation axis. This results in the geometric focusing of inertial wavebeams reflecting off the walls, whereby the energy density of the wavebeams increases along with the magnitude of their wavevector. The nature of this focusing depends on the forcing frequency but not on the body force. In the inviscid setting, wavebeams form infinitesimally thin vortex sheets, and their energy density becomes unbounded upon focusing. We present linear inviscid ray tracing to set the scene for the focusing of wavebeams and then consider viscous problems at an Ekman number that is typical of current state-of-the-art laboratory experiments. We begin by considering the linear responses, which are comprised of focusing viscous shear layers, of which their details are mostly captured via ray tracing, and particular solutions accounting for the body forces. These have complicated spatio-temporal structures, which differ for libration and precession. Increasing the forcing amplitude from zero introduces nonlinear interactions, enhances the focusing effects via vortex tilting and stretching when the shear layers reflect at the walls, and also introduces temporal superharmonics and a mean flow. When the magnitude of the mean flow is within a few percent of the magnitude of the instantaneous flow, instabilities breaking the spatio-temporal symmetries set in. These are localized in the oscillatory boundary layers where the reflections are concentrated and introduce broadband dynamics in the boundary layers, with additional inertial wavebeams emitted into the interior. The details again depend on the specifics of the body forces.

Pattern transition of flow dynamics in a highly water-absorbent granular bed

An aqueous sodium chloride solution was injected at a controlled rate into a granular bed in a quasi-two-dimensional cell. The granular bed was made of dried, highly water-absorbent gel particles whose swelling rate was controlled by the salinity of the injected fluid. At a high salinity level (low swelling rate), high injection rate, and short timescale, the injected fluid percolated between the gel particles in an isotropic manner. Meanwhile, at a low salinity level (high swelling rate), low injection rate, and long timescale, the gel particles clogged the flow path, resulting in anisotropic branch-like structures of the injected fluid front. The transition of the injection pattern could be understood based on the ratio of the characteristic timescales of swelling and injection. Moreover, the clogged pattern showed an oscillatory pressure drop whose amplitude was increased with higher salinity. Such an oscillatory behavior observed in an injection process in swelling gel particles may be relevant in geological situation, such as fluid migration underground.

Turbulent partially cracked ammonia/air premixed spherical flames

The combustion of ammonia requires, for most energy conversion systems, a combustion promoter such as hydrogen to guarantee the start-up, stability and combustion efficiency. Partially cracked ammonia (PCA) can provide sufficient hydrogen concentrations to enhance the burning velocity in comparison with pure ammonia. However, little work exists on the use of PCA blends operating under relevant turbulent conditions. To that end the outwardly propagating spherical flame configuration was employed to determine the laminar and turbulent flame propagation characteristics of PCA (NH3/(H2+N2)) and corresponding binary (NH3/H2) mixtures across various turbulent combustion regimes. First, PCA and ammonia-hydrogen blends exhibit similar flame propagation rates under various turbulent intensities, even for the laminar case. The highest turbulent burning velocity was observed at leanest conditions, as opposed to laminar flames which exhibited highest flame speed at conditions above stoichiometry. Under rich conditions, no substantial flame enhancement due to turbulence was measured irrespective of the hydrogen content. This lack of flame enhancement under turbulent conditions is attributed to the effect of preferential diffusion with good agreement observed with trends in measured Markstein numbers. The normalized turbulent flame speed is dominated by the enhanced molecular diffusivity afforded by the presence of hydrogen up to 15 % enrichment, prior to decreasing upon further hydrogen addition under lean and stoichiometric conditions. This ‘bending’ phenomenon may be the contribution of several factors including; the transitioning between combustion regimes associated with low Damköhler numbers (Da) and flame thickening; merging of flamelets due to the presence of ammonia enhancing wrinkling; and combined changes in laminar burning velocity and preferential diffusional behavior. Furthermore, good agreement for turbulent flame speed is observed with a correlation that includes the influence of turbulent stretch (Ka) and non-equidiffusion (Le), with the agreement reducing with decreasing chemical to turbulent time scale ratios (Da << 1).

Numerical investigation of drop–film interactions with a thixotropic liquid

We investigate numerically the influence of thixotropic effects on the impact of a drop onto a thin film, a fundamental process in many technical systems. Direct numerical simulations are performed with a Volume-of-Fluid (VOF) method based multiphase flow solver whose capabilities are expanded in order to enable simulations of a thixotropic liquid. The thixotropic behavior is modeled by a rate kinetic equation for the structural integrity of the assumed microstructure of the liquid. The corresponding structural parameter is described by an additional VOF-variable. After a validation of the implementations, we vary systematically the two parameters of the thixotropic model for a selected impact scenario in order to identify thixotropic effects during the impact and on the overall impact morphology. The two parameters are the mutation number Mu=texp/tθ as the ratio of the experimental time scale to the time scale of the structural rebuilding and the parameter β, which describes the effectivity of the shear-induced structural disintegration. The parameter study leads to a regime map with three different regimes. For Mu>10, the liquid behaves purely shear-thinning. High shear rates during the early stages of the impact lead to a low apparent viscosity at the crown base and to an enhanced crown growth. For Mu<0.1, the liquid behaves irreversible thixotropic or rheodestructing, respectively. Structural rebuilding is negligible and every deformation leads to a further disintegration of the microstructure. In this regime, a thin region of disintegrated microstructure develops within the liquid, spanning from the location of high shear stresses at the bottom into the crown rim. In between these two regimes, purely thixotropic effects become significant. A complex microstructure develops during the impact, in which features of both regimes occur combined, leading to a pronounced viscosity gradient along the crown wall. A comparison of the resulting maximum crown heights reveals that various combinations of Mu and β values can lead to the same maximum crown height whereas the crown shapes prior to this point in time can be very different.

Are the dynamics of wall turbulence in minimal channels and larger domain channels equivalent? A graph-theoretic approach

This work proposes two algorithmic approaches to extract critical dynamical mechanisms in wall-bounded turbulence with minimum human bias. In both approaches, multiple types of coherent structures are spatiotemporally tracked, resulting in a complex multilayer network. Network motif analysis, i.e., extracting dominant non-random elemental patterns within these networks, is used to identify the most dominant dynamical mechanisms. Both approaches, combined with network motif analysis, are used to answer whether the main dynamical mechanisms of a minimal flow unit (MFU) and a larger unconstrained channel flow, labeled a full channel (FC), at Reτ ≈ 180, are equivalent. The first approach tracks traditional coherent structures defined as low- and high-speed streaks, ejections, and sweeps. It is found that the roll-streak pairing, consistent with the current understanding of self-sustaining processes, is the most significant and simplest dynamical mechanism in both flows. However, the MFU has a timescale for this mechanism that is approximately 2.83 times slower than that of the FC. In the second approach, we use semi-Lagrangian wavepackets and define coherent structures from their energetic streak, roll, and small-scale phase space. This method also shows similar motifs for both the MFU and FC. It indicates that, on average, the most dominant phase-space motifs are similar between the two flows, with the significant events taking place approximately 2.21 times slower in the MFU than in the FC. This value is more consistent with the implied timescale ratio of only the slow speed streaks taking part in the roll-streak pairing extracted using the first multi-type spatiotemporal approach, which is approximately 2.17 slower in the MFU than the FC.

Trade-offs in concentration sensing in dynamic environments

When cells measure concentrations of chemical signals, they may average multiple measurements over time in order to reduce noise in their measurements. However, when cells are in an environment that changes over time, past measurements may not reflect current conditions—creating a new source of error that trades off against noise in chemical sensing. What statistics in the cell’s environment control this trade-off? What properties of the environment make it variable enough that this trade-off is relevant? We model a single eukaryotic cell sensing a chemical secreted from bacteria (e.g., folic acid). In this case, the environment changes because the bacteria swim—leading to changes in the true concentration at the cell. We develop analytical calculations and stochastic simulations of sensing in this environment. We find that cells can have a huge variety of optimal sensing strategies ranging from not time averaging at all to averaging over an arbitrarily long time or having a finite optimal averaging time. The factors that primarily control the ideal averaging are the ratio of sensing noise to environmental variation and the ratio of timescales of sensing to the timescale of environmental variation. Sensing noise depends on the receptor-ligand kinetics, while environmental variation depends on the density of bacteria and the degradation and diffusion properties of the secreted chemoattractant. Our results suggest that fluctuating environmental concentrations may be a relevant source of noise even in a relatively static environment.

Space–time structure of weak magnetohydrodynamic turbulence

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$ , describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$ , and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$ . The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$ ) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.

Librating Kozai–Lidov Cycles with a Precessing Quadrupole Potential Are Analytically Approximately Solved

The very long term evolution of the hierarchical restricted three-body problem with a slightly aligned precessing quadrupole potential is investigated analytically for librating Kozai–Lidov cycles (KLCs). Klein & Katz presented an analytic solution for the approximate dynamics on a very long timescale developed in the neighborhood of the KLCs' fixed point where the eccentricity vector is close to unity and aligned (or anti-aligned) with the quadrupole axis and for a precession rate equal to the angular frequency of the secular Kozai–Lidov equations around this fixed point. In this paper, we generalize the analytic solution to encompass a wider range of precession rates. We show that the analytic solution approximately describes the quantitative dynamics for systems with librating KLCs for a wide range of initial conditions, including values that are far from the fixed point, which is somewhat unexpected. In particular, using the analytic solution, we map the strikingly rich structures that arise for precession rates similar to the Kozai–Lidov timescale (ratio of a few).

Co-encapsulation of organic polymers and inorganic superparamagnetic iron oxide colloidal crystals requires matched diffusion time scales.

Nanoparticles (NPs) that contain both organic molecules and inorganic metal or metal oxide colloids in the same NP core are "composite nanoparticles" which are of interest in many applications, particularly in biomedicine as "theranostics" for the combined delivery of colloidal diagnostic imaging agents with therapeutic drugs. The rapid precipitation technique Flash NanoPrecipitation (FNP) enables continuous and scalable production of composite nanoparticles with hydrodynamic diameters between 40-200 nanometers (nm) that contain hydrophobic superparamagnetic iron oxide primary colloids. Composite NPs co-encapsulate these primary colloids (diameters of 6 nm, 15 nm, or 29 nm), a fluorescent dye (600 Daltons), and poly(styrene) homopolymer (1800, 50 000, or 200 000 Daltons) with NPs stabilized by a poly(styrene)-block-poly(ethylene glycol) (1600 Da-b-5000 Da) block copolymer. Nanoparticle assembly in FNP occurs by diffusion limited aggregation of the hydrophobic core components followed by adsorption of the hydrophobic block of the stabilizing polymer. The hydrodynamic diameter mismatch between the collapsed organic species and the primary colloids (0.5-5 nm versus 6-29 nm) creates a diffusion-aggregation time scale mismatch between components that can lead to nonstoichiometric co-encapsulation in the final nanoparticles; some nanoparticles are composites with primary colloids co-encapsulated alongside organics while others are devoid of the primary colloids and contain only organic species. We use a magnetic capture process to separate magnetic composite nanoparticles from organic-only nanoparticles and quantify the amount of iron oxide colloids and hydrophobic fluorescent dye (as a proxy for total hydrophobic polymer content) in the magnetic and nonmagnetic fractions of each formulation. Analysis of the microstructure in over 1100 individual nanoparticles by TEM imaging and composition measurements identifies the conditions that produce nonstoichiometric composite NP populations without co-encapsulated magnetic iron oxide colloids. Stoichiometric magnetically responsive composite NPs are produced when the ratio of characteristic diffusion-aggregation time scales between the inorganic primary colloid and the organic core component is less than 30 and all NPs in a dispersion contain organic and inorganic species in approximately the same ratio. These rules for assembly of colloids and organic components into homogeneous composite nanoparticles are broadly applicable.

Synchronisation of the ensemble of nonidentical FitzHugh–Nagumo oscillators with memristive couplings

The aim of the study is to investigate the features of synchronization in ensembles of nonidentical neuron-like FitzHugh–Nagumo oscillators interacting via memristor-based coupling. Methods. The collective dynamics in a ring of FitzHugh–Nagumo oscillators connected via memristive coupling was studied numerically and experimentally. The nonidentity of oscillators was achieved by detuning them by the threshold parameter responsible for the excitation of oscillator, or by detuning them by the parameter characterizing the ratio of time scales, the value of which determines the natural frequency of oscillator. We investigated the synchronization of memristively coupled FitzHugh–Nagumo oscillators as a function of the magnitude of the coupling coefficient, the initial conditions of all variables, and the number of oscillators in the ensemble. As a measure of synchronization, we used a coefficient characterizing the closeness of oscillator trajectories. Results. It is shown that with memristive coupling of FitzHugh–Nagumo oscillators, their synchronization depends not only on the magnitude of the coupling coefficient, but also on the initial states of both the oscillators themselves and the variables responsible for the memristive coupling. We compared the synchronization features of nonidentical FitzHugh–Nagumo oscillators with memristive and diffusive couplings. It is shown that, in contrast to the case of diffusive coupling of oscillators, in the case of meristive coupling, with increasing coupling strength of the oscillators, the destruction of the regime of completely synchronous in-phase oscillations can be observed, instead of which a regime of out-of-phase oscillations appears. Conclusion. The obtained results can be used when solving the problems of synchronization control in ensembles of neuronlike oscillators, in particular, for achieving or destroying the regime of in-phase synchronization of oscillations in an ensemble of coupled oscillators.

2H and 13C nuclear spin relaxation unravels dynamic heterogeneities in deep eutectic solvents of ethylene glycol, glycerol, or urea with choline chloride

Using deuteron spin-lattice and spin-spin relaxometry, the reorientational dynamics of ethaline (choline chloride/ethylene glycol) and reline (choline chloride/urea) are studied in a component-selective, isotope-edited manner over a wide temperature range, thereby complementing previous work on glyceline (choline chloride/glycerol). Differences in the hydrogen bond propensities effectuate that in reline and glyceline, the choline ions move faster than the hydrogen bond donors, glycerol and urea; in ethaline, the ethylene glycol molecules are reorienting faster. For glyceline and reline, the increase in the corresponding time scale ratio indicates a pronounced strengthening of the glycerol and urea networks upon cooling, while in ethaline, the time scale ratio remains essentially constant. For the three deep eutectic solvents, a comparison of the present component-selective results with the dielectric time constants shows that the latter are primarily sensitive to the dynamics of the respective hydrogen bond donors. In a Walden-type plot, the reorientation rates, selectively determined for the hydrogen bond donors and acceptors, are compared with their conductivity and fluidity, revealing that the dynamics of the choline ions relate most directly to the charge transport.

Model for Chapman-Jouguet deflagrations in open ended tubes with varying vent ratios

We present a gas dynamic model for Chapman-Jouguet deflagrations driving a shock in tubes or congested configurations with rear venting. The model extends the previous work of Chue, Clarke and Lee (Proc. Roy. Soc. 1993) to include rear venting. Two models are formulated, one for a perfect gas with constant heat of combustion, and the second by assuming chemical equilibrium in the product gases and temperature dependent specific heats. In the presence of rear venting, much slower flames and shock strengths are generated; these are controlled by the vent ratio, which reduces the post shock strength and speed of the gas convecting the flame forward. Calculation results are presented for small hydrocarbon-air and hydrogen-air deflagrations. The results of the model are found in good agreement with the critical deflagration speed measured experimentally in large scale weakly confined congested experiments for auto-ignition insensitive mixtures. This suggests that flames in these experiments have reached their maximum Chapman-Jouguet deflagration speed prior to transition. We present a time scale estimate for flame acceleration and auto-ignition behind reflected shocks. For sensitive mixtures for which the flame acceleration time is longer than the auto-ignition time (hydrogen, acetylene), limited experimental evidence indicate transition to detonation at critical speeds lower than the CJ deflagration condition. The time scale ratio thus provides the conditions for which reaching the CJ deflagration condition can be taken as a necessary condition for DDT.

Interesting clues to detect hidden tidal disruption events in active galactic nuclei

ABSTRACT In the manuscript, effects of tidal disruption events (TDEs) are estimated on long-term AGN variability, to provide interesting clues to detect probable hidden TDEs in normal broad line AGN with apparent intrinsic variability which overwhelm the TDEs expected variability features, after considering the unique TDEs expected variability patterns. Based on theoretical TDEs expected variability plus AGN intrinsic variability randomly simulated by Continuous AutoRegressive process, long-term variability properties with and without TDEs contributions are well analysed in AGN. Then, interesting effects of TDEs can be determined on long-term observed variability of AGN. First, more massive BHs, especially masses larger than $10^7\, {\rm M_\odot }$, can lead to more sensitive and positive dependence of τTN on RTN, with τTN as variability time-scale ratio of light curves with TDEs contributions to intrinsic light curves without TDEs contributions, and RTN as ratio of peak intensity of TDEs expected variability to the mean intensity of intrinsic AGN variability without TDEs contributions. Secondly, stronger TDEs contributions RTN can lead to τTN quite larger than 5. Thirdly, for intrinsic AGN variability having longer variability time-scales, TDEs contributions will lead τTN to be increased more slowly. The results actually provide an interesting forward-looking method to detect probable hidden TDEs in normal broad-line AGN, due to quite different variability properties, especially different DRW/CAR process expected variability time-scales, in different epochs, especially in normal broad line AGN with shorter intrinsic variability time-scales and with BH masses larger than $10^7\, {\rm M_\odot }$.

Non-Newtonian turbulent jets at low-Reynolds number

We perform direct numerical simulations of planar jets of non-Newtonian fluids at low Reynolds number, in typical laminar conditions for a Newtonian fluid. We select three different non-Newtonian fluid models mainly characterized by shear-thinning (Carreau), viscoelasticity (Oldroyd-B) and shear-thinning and viscoelasticity together (Giesekus), and perform a thorough analysis of the resulting flow statistics. We characterize the fluids using the parameter γ, defined as the ratio of the relevant non-Newtonian time scale over a flow time scale. We observe that, as γ is increased, the jet transitions from a laminar flow at low γ, to a turbulent flow at high γ. We show that the different non-Newtonian features and their combination give rise to rather different flowing regimes, originating from the competition of viscous, elastic and inertial effects. We observe that both viscoelasticity and shear-thinning can develop the instability and the consequent transition to a turbulent flowing regime; however, the purely viscoelastic Oldroyd-B fluid exhibits the onset of disordered fluid motions at a lower value of γ than what observed for the purely shear-thinning Carreau fluid. When the two effects are both present, an intermediate condition is found, suggesting that, in this case, the shear-thinning feature is acting against the fluid elasticity. Despite the qualitative differences observed in the flowing regime, the bulk statistics, namely the centerline velocity and jet thickness, follow almost the same power-law scalings obtained for laminar and turbulent Newtonian planar jets. The simulations reported here are, to the best of our knowledge, the first direct numerical simulations showing the appearance of turbulence at low Reynolds number in jets, with the turbulent motions fully induced by the non-Newtonian properties of the fluid, since the Newtonian case at the same Reynolds number is characterized by steady, laminar flow.

Evolution of Planetary Obliquity: The Eccentric Kozai–Lidov Mechanism Coupled with Tide

Planetary obliquity plays a significant role in determining the physical properties of planetary surfaces and climate. As direct detection is constrained due to the present observation accuracy, kinetic theories are helpful for predicting the evolution of planetary obliquity. Here the coupling effect between the eccentric Kozai–Lidov effect and the equilibrium tide is extensively investigated; the planetary obliquity is observed to follow two kinds of secular evolution paths, based on the conservation of total angular momentum. The equilibrium timescale of the planetary obliquity t eq varies along with r t , which is defined as the initial timescale ratio of the tidal dissipation and secular perturbation. We numerically derive the linear relationship between t eq and r t with the maximum likelihood method. The spin-axis orientation of S-type terrestrials orbiting M-dwarfs reverses over 90° when r t > 100, then enters the quasi-equilibrium state between 40° and 60°, while the maximum obliquity can reach 130° when r t > 104. Numerical simulations show that the maximum obliquity increases with the semimajor axis ratio a 1/a 2, but is not so sensitive to the eccentricity e 2. The likelihood of an obliquity flip for S-type terrestrials in general systems with a 2 < 45 au is closely related to m 1. The observed potentially oblique S-type planets HD 42936 b, GJ 86 Ab, and τ Boo Ab are explored and found to have a great possibility of rotating head-down over the secular evolution of spin.

Multiphase condensation in cluster haloes: interplay of cooling, buoyancy, and mixing

ABSTRACT Gas in the central regions of cool-core clusters and other massive haloes has a short cooling time (≲1 Gyr). Theoretical models predict that this gas is susceptible to multiphase condensation, in which cold gas is expected to condense out of the hot phase if the ratio of the thermal instability growth time-scale (tti) to the free-fall time (tff) is tti/tff ≲ 10. The turbulent mixing time tmix is another important time-scale: if tmix is short enough, the fluctuations are mixed before they can cool. In this study, we perform high-resolution (5122 × 768–10242 × 1536 resolution elements) hydrodynamic simulations of turbulence in a stratified medium, including radiative cooling of the gas. We explore the parameter space of tti/tff and tti/tmix relevant to galaxy and cluster haloes. We also study the effect of the steepness of the entropy profile, the strength of turbulent forcing and the nature of turbulent forcing (natural mixture versus compressive modes) on multiphase gas condensation. We find that larger values of tti/tff or tti/tmix generally imply stability against multiphase gas condensation, whereas larger density fluctuations (e.g. due to compressible turbulence) promote multiphase gas condensation. We propose a new criterion min (tti/min (tmix, tff)) ≲ c2 × exp (c1σs) for when the halo becomes multiphase, where σs denotes the amplitude of logarithmic density fluctuations and c1 ≃ 6, c2 ≃ 1.8 from an empirical fit to our results.