scholarly journals A general formula for the stability functions of a group of implicit advanced step-point (IAS) methods

2007 ◽  
Vol 46 (1-2) ◽  
pp. 214-224 ◽  
Author(s):  
G. Psihoyios
Keyword(s):  
General Formula ◽  
Stability Functions ◽  
The Stability

scholarly journals Sensitivity of an Idealized Tropical Cyclone to the Configuration of the Global Forecast System–Eddy Diffusivity Mass Flux Planetary Boundary Layer Scheme

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 284
Author(s):  
Evan A. Kalina ◽  
Mrinal K. Biswas ◽  
Jun A. Zhang ◽  
Kathryn M. Newman
Keyword(s):  
Boundary Layer ◽  
Planetary Boundary Layer ◽  
Weather Prediction ◽  
Intensity Change ◽  
Rapid Intensification ◽  
Forecast System ◽  
Stability Functions ◽  
Non Local ◽  
The Stability ◽  
Heat And Moisture

The intensity and structure of simulated tropical cyclones (TCs) are known to be sensitive to the planetary boundary layer (PBL) parameterization in numerical weather prediction models. In this paper, we use an idealized version of the Hurricane Weather Research and Forecast system (HWRF) with constant sea-surface temperature (SST) to examine how the configuration of the PBL scheme used in the operational HWRF affects TC intensity change (including rapid intensification) and structure. The configuration changes explored in this study include disabling non-local vertical mixing, changing the coefficients in the stability functions for momentum and heat, and directly modifying the Prandtl number (Pr), which controls the ratio of momentum to heat and moisture exchange in the PBL. Relative to the control simulation, disabling non-local mixing produced a ~15% larger storm that intensified more gradually, while changing the coefficient values used in the stability functions had little effect. Varying Pr within the PBL had the greatest impact, with the largest Pr (~1.6 versus ~0.8) associated with more rapid intensification (~38 versus 29 m s−1 per day) but a 5–10 m s−1 weaker intensity after the initial period of strengthening. This seemingly paradoxical result is likely due to a decrease in the radius of maximum wind (~15 versus 20 km), but smaller enthalpy fluxes, in simulated storms with larger Pr. These results underscore the importance of measuring the vertical eddy diffusivities of momentum, heat, and moisture under high-wind, open-ocean conditions to reduce uncertainty in Pr in the TC PBL.

MASTER STABILITY FUNCTIONS FOR SYNCHRONIZED COUPLED SYSTEMS

1999 ◽  
Vol 09 (12) ◽  
pp. 2315-2320 ◽  
Author(s):  
LOUIS M. PECORA ◽  
THOMAS L. CARROLL
Keyword(s):  
Simple Form ◽  
Coupled Systems ◽  
Stability Function ◽  
Coupled Oscillator ◽  
Synchronous State ◽  
Master Stability Function ◽  
Stability Functions ◽  
The Stability

We show that many coupled oscillator array configurations considered in the literature can be put into a simple form so that determining the stability of the synchronous state can be done by a master stability function which solves, once and for all, the problem of synchronous stability for many couplings of that oscillator.

Model and Stability of the Traffic Flow Consisting of Heterogeneous Drivers

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Da Yang ◽  
Liling Zhu ◽  
Yun Pu
Keyword(s):  
Traffic Flow ◽  
Heterogeneous Traffic ◽  
Model Parameters ◽  
Optimal Velocity ◽  
Stability Functions ◽  
Car Following Model ◽  
Traffic Wave ◽  
The Stability ◽  
Different Characteristics ◽  
Stationary Velocity

Although traffic flow has attracted a great amount of attention in past decades, few of the studies focused on heterogeneous traffic flow consisting of different types of drivers or vehicles. This paper attempts to investigate the model and stability analysis of the heterogeneous traffic flow, including drivers with different characteristics. The two critical characteristics of drivers, sensitivity and cautiousness, are taken into account, which produce four types of drivers: the sensitive and cautious driver (S-C), the sensitive and incautious driver (S-IC), the insensitive and cautious driver (IS-C), and the insensitive and incautious driver (IS-IC). The homogeneous optimal velocity car-following model is developed into a heterogeneous form to describe the heterogeneous traffic flow, including the four types of drivers. The stability criterion of the heterogeneous traffic flow is derived, which shows that the proportions of the four types of drivers and their stability functions only relating to model parameters are two critical factors to affect the stability. Numerical simulations are also conducted to verify the derived stability condition and further explore the influences of the driver characteristics on the heterogeneous traffic flow. The simulations reveal that the IS-IC drivers are always the most unstable drivers, the S-C drivers are always the most stable drivers, and the stability effects of the IS-C and the S-IC drivers depend on the stationary velocity. The simulations also indicate that a wider extent of the driver heterogeneity can attenuate the traffic wave.

Is There a Relation Between Synchronization Stability and Bifurcation Type?

2020 ◽  
Vol 30 (08) ◽  
pp. 2050123
Author(s):  
Zahra Faghani ◽  
Zhen Wang ◽  
Fatemeh Parastesh ◽  
Sajad Jafari ◽  
Matjaž Perc
Keyword(s):  
Complex Networks ◽  
Nonlinear Dynamical Systems ◽  
General Relation ◽  
Dynamical Behavior ◽  
Stability Function ◽  
Nonlinear Dynamical ◽  
Practical Applications ◽  
Stability Functions ◽  
Stability And Bifurcation ◽  
The Stability

Synchronization in complex networks is an evergreen subject with many practical applications across the natural and social sciences. The stability of synchronization is thereby crucial for determining whether the dynamical behavior is stable or not. The master stability function is commonly used to that effect. In this paper, we study whether there is a relation between the stability of synchronization and the proximity to certain bifurcation types. We consider four different nonlinear dynamical systems, and we determine their master stability functions in dependence on key bifurcation parameters. We also calculate the corresponding bifurcation diagrams. By means of systematic comparisons, we show that, although there are some variations in the master stability functions in dependence on bifurcation proximity and type, there is in fact no general relation between synchronization stability and bifurcation type. This has important implication for the restrained generalizability of findings concerning synchronization in complex networks for one type of node dynamics to others.

scholarly journals A Framework for Assessing Water Security and the Water–Energy–Food Nexus—The Case of Finland

2019 ◽  
Vol 11 (10) ◽  
pp. 2900 ◽  
Author(s):  
Mika Marttunen ◽  
Jyri Mustajoki ◽  
Suvi Sojamo ◽  
Lauri Ahopelto ◽  
Marko Keskinen
Keyword(s):  
Environmental Sustainability ◽  
Water Environment ◽  
Water Security ◽  
Well Being ◽  
The State ◽  
Security Assessment ◽  
Stability Functions ◽  
State Of Water ◽  
The Stability ◽  
Water Issues

Water security demands guaranteeing economic, social and environmental sustainability and simultaneously addressing the diversity of risks and threats related to water. Various frameworks have been suggested to support water security assessment. They are typically based on indexes enabling national comparisons; these may, however, oversimplify complex and often contested water issues. We developed a structured and systemic way to assess water security and its future trends via a participatory process. The framework establishes a criteria hierarchy for water security, consisting of four main themes: the state of the water environment; human health and well-being; the sustainability of livelihoods; and the stability, functions and responsibility of society. The framework further enables the analysis of relationships between the water security criteria as well as between water, energy and food security. The framework was applied to a national water security assessment of Finland in 2018 and 2030. Our experience indicates that using the framework collaboratively with stakeholders provides a meaningful way to improve understanding and to facilitate discussion about the state of water security and the actions needed for its improvement.

Evaluating turbulent length scales from local MOST extension with different stability functions in first order closures for stably stratified boundary layer

2021 ◽  
Author(s):  
Andrey Debolskiy ◽  
Evgeny Mortikov ◽  
Andrey Glazunov ◽  
Christof Lüpkes
Keyword(s):  
Boundary Layer ◽  
Asymptotic Behavior ◽  
Surface Layer ◽  
Similarity Theory ◽  
Functional Dependence ◽  
Stability Parameter ◽  
Turbulent Length Scale ◽  
First Order ◽  
Stability Functions ◽  
The Stability

<p>According to the Monin-Obukhov similarity theory (MOST), in the stratified surface layer of the atmosphere, the mean vertical velocity and scalars gradients are related to the turbulent fluxes of these quantities and to the distance z from the surface in a universal manner. The stability parameter ζ=z/L, where L is the Obukhov turbulent length scale, is the only dimensionless parameter that determines the flux-gradient relationships. This imposes a dependency of the dimensionless velocity and buoyancy gradients on ζ in form of universal nondimensional stability functions for  the surface layer. Over the decades a number of them were proposed and derived mostly from extensive field campaigns of measurements in the ABL. The stability functions differ from each other by both open coefficients and functional dependence on  ζ.  They have a limited range of applicability, which is often extended by incorporating the assumption about their asymptotic behavior.</p><p>           A generalization of MOST by considering the dependence of the dimensionless gradients on the local stability parameter z/Λ  in the framework of first order closures allows the extension of  the universal stability functions from the surface layer to most of the ABL. However, because of applicability constraints, differences in the asymptotic behavior and in other implied assumptions, it is not immediately obvious, which set of stability functions will perform best. In this study we analyze a set of stability functions which are implemented in a uniform manner into a one-dimensional first-order closure.  The latter applies a turbulent mixing length with generalized local MOST scaling which fits to a surface schemes employing corresponding functions for consistency. We use two numerical experiment setups accompanied with LES data for validation which correspond to the weakly stable GABLES1 case and to LES simulations of the very stable ABL based on measurements at the Antarctic station DOME-C (van der Linden et al. 2019). We also focus on the sensitivity of the 1D model results to coarser grids with respect to both the used  surface flux schemes and  the ABL turbulence closures since their are meant to be used in climate models because of numerical efficiency.</p><p>Authors want to aknowledge partial funding by Russian Foundation for Basic Research (RFBR project N 20-05-00776), sensitivity analysis and closure development were performed with support  of Russian Science Foundation (RSF No 20-17-00190). Steven van der Linden for providing LES data of DOME-C based experiments.</p><p>References:</p><p>van der Linden S.J. et al. Large-Eddy Simulations of the Steady Wintertime Antarctic Boundary Layer // Boundary Layer Meteorology 173.2 (2019): 165-192.</p>

Sign in / Sign up

Export Citation Format

Share Document