Construction of SDIRK methods with dispersive stability functions

2021 ◽  
Vol 160 ◽  
pp. 265-280
Author(s):  
Giuseppe Izzo ◽  
Zdzislaw Jackiewicz
Keyword(s):  
Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 284
Author(s):  
Evan A. Kalina ◽  
Mrinal K. Biswas ◽  
Jun A. Zhang ◽  
Kathryn M. Newman

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.


1999 ◽  
Vol 09 (12) ◽  
pp. 2315-2320 ◽  
Author(s):  
LOUIS M. PECORA ◽  
THOMAS L. CARROLL

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.


Author(s):  
Da Yang ◽  
Liling Zhu ◽  
Yun Pu

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.


1997 ◽  
Vol 12 (2) ◽  
pp. 81-87
Author(s):  
Erling Murtha-Smith ◽  
Thuyen P. Nguyen

Stability equations are developed for edge joints for Double Layer Grids. Translations are neglected and rotations at each joint are related. Hence, the stiffness matrix reduces to a diagonal matrix of unit bandwidth so each joint becomes an independent substructure. Instability of an edge joint occurs when the minimum principal stiffness coefficient of the joint goes to zero. Using stability functions and the regular geometric relationships of DLG topology, the buckling forces in the members and hence the external load on the system are determined. A simple example in which the members were all of the same length, material and moment of inertia, gives effective length factors for the edge members of between 0.77 to 0.81.


2006 ◽  
Vol 45 (2) ◽  
pp. 341-347 ◽  
Author(s):  
Jonathan E. Pleim

Abstract This note describes a simple scheme for analytical estimation of the surface-layer similarity functions from state variables. What distinguishes this note from the many previous papers on this topic is that this method is specifically targeted for numerical models in which simplicity and economic execution are critical. In addition, it has been in use in a mesoscale meteorological model for several years. For stable conditions, a very simple scheme is presented that compares well to the iterative solution. The stable scheme includes a very stable regime in which the slope of the stability functions is reduced to permit significant fluxes to occur, which is particularly important for numerical models in which decoupling from the surface can be an important problem. For unstable conditions, simple schemes generalized for varying ratios of aerodynamic roughness to thermal roughness (z0/z0h) are less satisfactory. Therefore, a simple scheme has been empirically derived for a fixed z0/z0h ratio, which represents quasi-laminar sublayer resistance.


1995 ◽  
Vol 74 (1-2) ◽  
pp. 113-130 ◽  
Author(s):  
David E. England ◽  
Richard T. McNider
Keyword(s):  

2007 ◽  
Vol 135 (10) ◽  
pp. 3474-3483 ◽  
Author(s):  
Kyung-Ja Ha ◽  
Yu-Kyung Hyun ◽  
Hyun-Mi Oh ◽  
Kyung-Eak Kim ◽  
Larry Mahrt

Abstract The Monin–Obukhov similarity theory and a generalized formulation of the mixing length for the stable boundary layer are evaluated using the Cooperative Atmosphere–Surface Exchange Study-1999 (CASES-99) data. The large-scale wind forcing is classified into weak, intermediate, and strong winds. Although the stability parameter, z/L, is inversely dependent on the mean wind speed, the speed of the large-scale flow includes independent influences on the flux–gradient relationship. The dimensionless mean wind shear is found to obey existing stability functions when z/L is less than unity, particularly for the strong and intermediate wind classes. For weak mean winds and/or strong stability (z/L > 1), this similarity theory breaks down. Deviations from similarity theory are examined in terms of intermittency. A case study of a weak-wind night indicates important modulation of the turbulence flux by mesoscale motions of unknown origin.


2018 ◽  
Vol 97 (3) ◽  
Author(s):  
Andreas Brechtel ◽  
Philipp Gramlich ◽  
Daniel Ritterskamp ◽  
Barbara Drossel ◽  
Thilo Gross

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