scholarly journals On the instability of Saturn’s hypothetical retrograde co-orbitals

2019 ◽  
Vol 488 (2) ◽  
pp. 2543-2548 ◽  
Author(s):  
Yukun Huang ◽  
Miao Li ◽  
Junfeng Li ◽  
Shengping Gong
Keyword(s):  
Numerical Simulations ◽  
Time Scale ◽  
Slow Growth ◽  
Small Bodies ◽  
Secular Resonances ◽  
Interesting Fact ◽  
Resonance Overlap ◽  
Orbital Space

ABSTRACT We find an interesting fact that fictitious retrograde co-orbitals of Saturn, or small bodies inside the retrograde 1:1 resonance with Saturn, are highly unstable in our numerical simulations. It is shown that, in the presence of Jupiter, the retrograde co-orbitals will get ejected from Saturn’s co-orbital space within a time-scale of 10 Myr. This scenario reminds us of the instability of Saturn Trojans caused by both the great inequality and the secular resonances. Therefore, we carry out in-depth inspections of both mechanisms and prove that the retrograde resonance overlap, raised by great inequality, cannot serve as an explanation for the instability of the retrograde co-orbitals, due to the weakness of the retrograde 2:5 resonance with Jupiter at low eccentricity. However, we discover that both ν5 and ν6 secular resonances contribute to the slow growth of the eccentricity and are therefore possibly the primary causes of the instability inside Saturn’s retrograde co-orbital space.

Lagrangian characteristics of turbulence and scalar transport in direct numerical simulations

2001 ◽  
Vol 427 ◽  
pp. 241-274 ◽  
Author(s):  
P. K. YEUNG
Keyword(s):  
Reynolds Number ◽  
Correlation Function ◽  
Numerical Simulations ◽  
Time Scales ◽  
Time Scale ◽  
Cross Correlation ◽  
Scalar Fields ◽  
Direct Numerical Simulations ◽  
Cross Correlation Function ◽  
Differential Diffusion

A study of the Lagrangian statistical properties of velocity and passive scalar fields using direct numerical simulations is presented, for the case of stationary isotropic turbulence with uniform mean scalar gradients. Data at higher grid resolutions (up to 5123 and Taylor-scale Reynolds number 234) allow an update of previous velocity results at lower Reynolds number, including intermittency and dimensionality effects on vorticity time scales. The emphasis is on Lagrangian scalar time series which are new to the literature and important for stochastic mixing models. The variance of the ‘total’ Lagrangian scalar value (ϕ˜+, combining contributions from both mean and fluctuations) grows with time, with the velocity–scalar cross-correlation function and fluid particle displacements playing major roles. The Lagrangian increment of ϕ˜+ conditioned upon velocity and scalar fluctuations is well represented by a linear regression model whose parameters depend on both Reynolds number and Schmidt number. The Lagrangian scalar fluctuation is non-Markovian and has a longer time scale than the velocity, which is due to the strong role of advective transport, and is in contrast to results in an Eulerian frame where the scalars have shorter time scales. The scalar dissipation is highly intermittent and becomes de-correlated in time more rapidly than the energy dissipation. Differential diffusion for scalars with Schmidt numbers between 1/8 and 1 is characterized by asymmetry in the two-scalar cross-correlation function, a shorter time scale for the difference between two scalars, as well as a systematic decrease in the Lagrangian coherency spectrum up to at least the Kolmogorov frequency. These observations are consistent with recent work suggesting that differential diffusion remains important in the small scales at high Reynolds number.

scholarly journals A severe blizzard event in Romania – a case study

2009 ◽  
Vol 9 (2) ◽  
pp. 623-634 ◽  
Author(s):  
F. Georgescu ◽  
S. Tascu ◽  
M. Caian ◽  
D. Banciu
Keyword(s):  
Numerical Simulations ◽  
Time Scale ◽  
Large Scale ◽  
Forecast Accuracy ◽  
Horizontal Resolution ◽  
Maximum Temperature ◽  
Small Scale ◽  
Relative Role ◽  
Snow Layer ◽  
Strong Winds

Abstract. During winter cold strong winds associated with snowfalls are not unusual for South and Southeastern Romania. The episode of 2–4 January 2008 was less usual due to its intensity and persistence. It happened after a long period (autumn 2006–autumn 2007) of mainly southerly circulations inducing warm weather, when the absolute record of the maximum temperature was registered. The important snowfalls and snowdrifts, leading to a consistent snow layer (up to 100 cm), produced serious transport and electricity supply perturbations. Since this atypical local weather event was not correctly represented by the operational numerical forecasts, several cross-comparison numerical simulations were performed to analyze the relative role of the coupler/coupling models and to compare two ways of process-scale uncertainties mitigation: optimizing the forecast range and performing ensemble forecast through the perturbation of the lateral boundary conditions. The results underline, for this case, the importance of physical parametrization package on the first place and secondary, the importance of the model horizontal resolution. The resolution increase is beneficial only in the local process representation; on larger scale it may either improve or decrease the accuracy effect, depending on the specified nudging between large-scale and small-scale information. The event capture is likely to be favored by two elements: a more appropriate time-scale of the event's physics and the quality of the transmitted large-scale information. Concerning the time scale, the statistics on skill as a function of forecast range are shown to be a useful tool in order to increase the accuracy of the numerical simulations. Ensembles forecasting versus resolution increase experiments indicate, for such atypical events, an interesting supply in the forecast accuracy through the ensemble method when applied to correct the minimum skill of the deterministic forecast.

scholarly journals Fast mixing mechanism of two vortex–current filaments

1999 ◽  
Vol 62 (5) ◽  
pp. 493-511 ◽  
Author(s):  
YUICHI YATSUYANAGI ◽  
TADATSUGU HATORI ◽  
TOMOKAZU KATO
Keyword(s):  
Lyapunov Exponent ◽  
Numerical Simulations ◽  
Strong Interaction ◽  
Time Scale ◽  
Diffusion Region ◽  
Reconnection Rate ◽  
Reconnection Process ◽  
Ideal Mhd ◽  
Current Filaments ◽  
Overlapping Region

We demonstrate fast mixing of vortex–current filaments by means of numerical simulations of collision (strong interaction) between two straight filaments. The two filaments mutually approach, collide, and are rapidly tangled with each other. In fact, the instantaneous Lyapunov exponent shows that the dynamics becomes chaotic. Then there appear many small regions where the two filaments overlap. We consider each overlapping region to be equivalent to the traditional resistive diffusion region. We assume that the overall ‘reconnection rate’ of the two filaments is proportional to the product of the traditional (non-chaotic) resistive reconnection rate and the normalized overlapping volume. The overlapping volume rapidly increases on the time scale of ideal MHD. When many overlapping regions are produced, the overall reconnection probability, i.e. the sum of the probabilities of reconnection in every overlapping region, should be increased compared with that of the single overlapping region. Thus the overall reconnection rate becomes sufficiently large, although the basic reconnection process in each overlapping region is resistive and slow. We conclude that the fast mixing due to chaos may enhance the conventional resistive reconnection. We call this process ‘chaotic reconnection’.

scholarly journals The Secular Resonances in the Solar System

1994 ◽  
Vol 160 ◽  
pp. 189-204
Author(s):  
Christiane Froeschle ◽  
Alessandro Morbidelli
Keyword(s):  
Solar System ◽  
Secular Resonance ◽  
Small Bodies ◽  
Fourth Degree ◽  
Secular Resonances ◽  
Mean Motion Resonances ◽  
Non Linear ◽  
Resonant Dynamics ◽  
Dynamical Nature ◽  
Element Algorithm

In the last three years new studies on secular resonances have been done. The second–order and fourth–degree secular perturbation theory of Milani and Knežević allowed to point out the effect of mean motion resonances on the location of the linear and non linear secular resonances. Moreover this theory improved the knowledge of the exact location of the g = g6 (i.e. ν6) resonance at low inclination. Morbidelli and Henrard revisited the semi–numerical method of Williams, taking into account the quadratic terms in the perturbing masses. They computed not only the location of secular resonances, but also provided a global description of the resonant dynamics in the main secular resonances namely g = g5 (i.e. ν5), g = g6 (i.e. ν6) and s = s6 (i.e. ν16). The resonant proper element algorithm developed by Morbidelli allows to identify the dynamical nature of resonant objects, and is a powerful tool to study the mechanisms of meteorite transport to the inner Solar System. Purely numerical experiments have been done, which show: (i) the complexity of the dynamics when two resonances overlap; (ii) the efficiency of successive crossings of non linear resonances in pumping up the inclination of small bodies; (iii) the efficiency of the secular resonance ν6 as a source of meteorites up to 2.4 AU.

On the emergence of non-classical decay regimes in multiscale/fractal generated isotropic turbulence

2014 ◽  
Vol 756 ◽  
pp. 816-843 ◽  
Author(s):  
Marcello Meldi ◽  
Hugo Lejemble ◽  
Pierre Sagaut
Keyword(s):  
Energy Spectrum ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Time Scale ◽  
Isotropic Turbulence ◽  
Initial Kinetic Energy ◽  
Grid Turbulence ◽  
Production Term ◽  
Turbulence Decay ◽  
Turbulence Production

AbstractThe present paper addresses the issue of finding key parameters that may lead to the occurrence of non-classical decay regimes for fractal/multiscale generated grid turbulence. To this aim, a database of numerical simulations has been generated by the use of the eddy-damped quasi-normal Markovian (EDQNM) model. The turbulence production in the wake of the fractal/multiscale grid is modelled via a turbulence production term based on the forcing term developed for direct numerical simulations (DNS) purposes and the dynamics of self-similar wakes. The sensitivity of the numerical results to the simulation parameters has been investigated successively. The analysis is based on the observation of both the time evolution of the turbulent energy spectrum $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}E(k,t)$ and the decay of the flow statistical quantities, such as the turbulent kinetic energy $\mathcal{K}(t)$ and the energy dissipation rate $\varepsilon (t)$. A satisfactory agreement with existing experimental data published by different research teams is observed. In particular, it is observed that the key parameter that governs the nature of turbulence decay is $\alpha ={d/U_{\infty }}\, {(\varepsilon (0)/\mathcal{K}(0))}={d/L(0)} \, {(\sqrt{\mathcal{K}(0)}/U_{\infty })}$ (with $d$ the bar diameter and $U_{\infty }$ the upstream uniform velocity), which measures the ratio of the time scale largest grid bar $d/U_{\infty }$ to the turbulent time scale $\mathcal{K}(0)/\varepsilon (0)$. Two asymptotic behaviours for $\alpha \rightarrow + \infty $ and $\alpha \rightarrow 0$ are identified: (i) a fast algebraic decay law regime for rapidly decaying production terms, due to strongly modified initial kinetic energy spectrum and (ii) a real exponential decay regime associated with strong, very slowly decaying production terms. The present observations are in full agreement with conclusions drawn from recent fractal grid experiments, and it provides a physical scenario for occurrence of anomalous decay regime which encompasses previous hypotheses.

DYNAMIC RELAXATION OF FINANCIAL INDICES

2009 ◽  
Vol 23 (24) ◽  
pp. 2889-2897 ◽  
Author(s):  
J. SHEN ◽  
B. ZHENG ◽  
H. LIN ◽  
T. QIU
Keyword(s):  
Numerical Simulations ◽  
Dynamic Behavior ◽  
Power Law ◽  
Time Scale ◽  
Price Change ◽  
Dynamic Relaxation ◽  
Before And After ◽  
Financial Indices ◽  
Daily Time

The dynamic relaxation of the German DAX both before and after a large price-change is investigated. The dynamic behavior is characterized by a power law. At the minutely time scale, the exponent p governing the power-law behavior takes a same value before and after the large price change, while at the daily time scale, it is different. Numerical simulations of an interacting EZ herding model are performed for comparison.

scholarly journals Strong wave–mean-flow coupling in baroclinic acoustic streaming

2018 ◽  
Vol 858 ◽  
pp. 536-564 ◽  
Author(s):  
Guillaume Michel ◽  
Gregory P. Chini
Keyword(s):  
Acoustic Wave ◽  
Numerical Simulations ◽  
Time Scale ◽  
Acoustic Streaming ◽  
Computational Cost ◽  
Fast Wave ◽  
Mean Flow ◽  
Strong Wave ◽  
Flow Coupling ◽  
Streaming Flow

The interaction of an acoustic wave with a stratified fluid can drive strong streaming flows owing to the baroclinic production of fluctuating vorticity, as recently demonstrated by Chini et al. (J. Fluid Mech., 744, 2014, pp. 329–351). In the present investigation, a set of wave/mean-flow interaction equations is derived that governs the coupled dynamics of a standing acoustic-wave mode of characteristic (small) amplitude $\unicode[STIX]{x1D716}$ and the streaming flow it drives in a thin channel with walls maintained at differing temperatures. Unlike classical Rayleigh streaming, the resulting mean flow arises at $O(\unicode[STIX]{x1D716})$ rather than at $O(\unicode[STIX]{x1D716}^{2})$. Consequently, fully two-way coupling between the waves and the mean flow is possible: the streaming is sufficiently strong to induce $O(1)$ rearrangements of the imposed background temperature and density fields, which modifies the spatial structure and frequency of the acoustic mode on the streaming time scale. A novel Wentzel–Kramers–Brillouin–Jeffreys analysis is developed to average over the fast wave dynamics, enabling the coupled system to be integrated strictly on the slow time scale of the streaming flow. Analytical solutions of the reduced system are derived for weak wave forcing and are shown to reproduce results from prior direct numerical simulations (DNS) of the compressible Navier–Stokes and heat equations with remarkable accuracy. Moreover, numerical simulations of the reduced system are performed in the regime of strong wave/mean-flow coupling for a fraction of the computational cost of the corresponding DNS. These simulations shed light on the potential for baroclinic acoustic streaming to be used as an effective means to enhance heat transfer.

scholarly journals On secular resonances of small bodies in the planetary systems

2006 ◽  
Vol 2 (S236) ◽  
pp. 77-84
Author(s):  
Jianghui Ji ◽  
L. Liu ◽  
G. Y. Li
Keyword(s):  
Solar System ◽  
Planetary System ◽  
Planetary Systems ◽  
Giant Planets ◽  
Small Bodies ◽  
Secular Resonances ◽  
Mean Motion Resonances ◽  
The Earth ◽  
Habitable Zones ◽  
Earth Like Planets

AbstractWe investigate the secular resonances for massless small bodies and Earth-like planets in several planetary systems. We further compare the results with those of Solar System. For example, in the GJ 876 planetary system, we show that the secular resonances ν1 and ν2 (respectively, resulting from the inner and outer giant planets) can excite the eccentricities of the Earth-like planets with orbits 0.21≤ a <0.50 AU and eject them out of the system in a short timescale. However, in a dynamical sense, the potential zones for the existence of Earth-like planets are in the area 0.50≤ a ≤1.00 AU, and there exist all stable orbits last up to 105 yr with low eccentricities. For other systems, e.g., 47 UMa, we also show that the Habitable Zones for Earth-like planets are related to both secular resonances and mean motion resonances in the systems.

Numerical study of vertical dispersion by stratified turbulence

2009 ◽  
Vol 631 ◽  
pp. 149-163 ◽  
Author(s):  
G. BRETHOUWER ◽  
E. LINDBORG
Keyword(s):  
Potential Energy ◽  
Numerical Simulations ◽  
Turbulent Flows ◽  
Time Scale ◽  
Numerical Study ◽  
Turnover Time ◽  
Particle Dispersion ◽  
Stratified Turbulence ◽  
The Mean ◽  
Simulation Results

Numerical simulations are carried out to investigate vertical fluid particle dispersion in uniformly stratified stationary turbulent flows. The results are compared with the analysis of Lindborg & Brethouwer (J. Fluid Mech., vol. 614, 2008, pp. 303–314), who derived long- and short-time relations for the mean square vertical displacement 〈δz〉 of fluid particles. Several direct numerical simulations (DNSs) with different degrees of stratification and different buoyancy Reynolds numbers are carried out to test the long-time relation 〈δz2〉 = 2ϵPt/N2. Here, ϵP is the mean dissipation of turbulent potential energy; N is the Brunt–Väisälä frequency; and t is time. The DNSs show good agreement with this relation, with a weak dependence on the buoyancy Reynolds number. Simulations with hyperviscosity are carried out to test the relation 〈δz2〉 = (1+πCPL)2ϵPt/N2, which should be valid for shorter time scales in the range N−1 ≪ t ≪ T, where T is the turbulent eddy turnover time. The results of the hyperviscosity simulations come closer to this prediction with CPL about 3 with increasing stratification. However, even in the simulation with the strongest stratification the growth of 〈δz2〉 is somewhat slower than linear in this regime. Based on the simulation results it is argued that the time scale determining the evolution of 〈δz2〉 is the eddy turnover time, T, rather than the buoyancy time scale N−1, as suggested in previous studies. The simulation results are also consistent with the prediction of Lindborg & Brethouwer (2008) that the nearly flat plateau of 〈δz2〉 observed at t ~ T should scale as 4EP/N2, where EP is the mean turbulent potential energy.

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