Simulation of convectively coupled waves using WRF: a framework for assessing the effects of mesoscales on synoptic scales

The atmospheric variability in the tropics is primarily driven by convective heating. Observations revealed that convection in the tropics is organized into a hierarchy of multiscale convective systems ranging from the individual cloud cells to planetary scale disturbances that are nested within each other like Russian dolls. Current global climate models simulate very poorly these convectively coupled waves due in part to inadequate treatment of organized convection by the underlying cumulus parameterizations. Here, we present idealized simulations of convectively coupled equatorial waves (CCWs) using the weather research and forecast model in a horizontally limited domain consisting of a 4,500 km-wide square centered at the equator at moderate horizontal resolution of 10 km. We attempted and compared various configuration options, including switching on and off the cumulus parameterization (CP) and nesting a fine resolution 3.33 km domain, a 2,000 km-wide square, in the middle of the domain. It turns out that the results without a CP are much superior than those using a CP. While the cases without a CP resulted in a coherent eastward propagating CCW, which has many common features with observed convectively coupled Kelvin waves, the cumulus parameterization tends to destroy both the coherence of the propagating waves, even in the case with a nested domain, and reduces dramatically the variability. A primary demonstration on how such results could be used to show evidence of energy exchange, through momentum transport, between small-scale circulation due to mesoscale convection and the propagating synoptic scale wave will be reported is also presented.     

Parametric solutions of the eigenvalue equation for a convectively cooled slab

The convective cooling of a slab by an ambient fluid under the most general linear and homogeneous boundary conditions is considered. For the roots of the corresponding transcendental eigenvalue equation an explicit formula is written down in a parametric form. The practical consequences of this representation, among them certain “singular solutions” which cannot be obtained by a direct numerical treatment of the original eigenvalue equation, are discussed in detail.     

Generalized Darboux transformation and localized waves in coupled Hirota equations

In this paper, we construct a generalized Darboux transformation to the coupled Hirota equations with high-order nonlinear effects like the third dispersion, self-steepening and inelastic Raman scattering terms. As application, an N$N$th-order localized wave solution on the plane backgrounds with the same spectral parameter is derived through the direct iterative rule. In particular, some semi-rational, multi-parametric localized wave solutions are obtained: (1) vector generalization of the first- and the second-order rogue wave solutions; (2) interactional solutions between a dark–bright soliton and a rogue wave, two dark–bright solitons and a second-order rogue wave; (3) interactional solutions between a breather and a rogue wave, two breathers and a second-order rogue wave. The results further reveal the striking dynamic structures of localized waves in complex coupled systems.     

Identification of thermal material parameters for thermo-mechanically coupled material models

Meccanica - The possibility of accurately identifying thermal material parameters on the basis of a simple tension test is presented, using a parameter identification framework for...     

Thermodynamic models of phase transformations and failure waves

Dynamics and quasi-statics of heterogeneous systems with sharp interfaces are analyzed. We dwell on two particular problems: dynamics of two-layered liquid incompressible planets with phase interfaces and failure fronts in brittle solids. In the former, the dynamics of the interfaces is controlled by the equality or jump in the scalar chemical potential. Similarly, in the latter example, it is controlled by the asymmetric tensorial chemical potential. We made several simplifying assumptions to reduce the system of partial differential equations to the systems of ordinary differential equations. We briefly touch on still existing obstacles.     

Simple waves and small perturbations in magnetizable or polarizable media

The system of equations describing the behavior of the electrically polarizable media in the case of a sufficiently weak magnetic field and the system of equations for magnetizable media in a weak electric field coincide except for the notations. These equations are used for the investigation of Riemann waves and small perturbations for different given dependences of ε and Μ on ρ and T. The case when the velocity of propagation of simple waves takes complex values is considered. Similar investigation has been carried out in [1, 2] in the case where the dependence of Μ on ρ and T is in the form Μ?1/Μ=cρT (Mossoti formula) and μ=1+4πρk(θ-T)/H. The same problems are investigated here for an infinitely conducting magnetizable gas, whose behavior is described by another system of equations reminiscent of the equations of magnetohydrodynamics.     

A coupled level set and volume-of-fluid method for sharp interface simulation of plunging breaking waves

A coupled level set and volume-of-fluid (CLSVOF) method is implemented for the numerical simulations of interfacial flows in ship hydrodynamics. The interface is reconstructed via a piecewise linear interface construction scheme and is advected using a Lagrangian method with a second-order Runge–Kutta scheme for time integration. The level set function is re-distanced based on the reconstructed interface with an efficient re-distance algorithm. This level set re-distance algorithm significantly simplifies the complicated geometric procedure and is especially efficient for three-dimensional (3D) cases. The CLSVOF scheme is incorporated into CFDShip-Iowa version 6, a sharp interface Cartesian grid solver for two-phase incompressible flows with the interface represented by the level set method and the interface jump conditions handled using a ghost fluid methodology. The performance of the CLSVOF method is first evaluated through the numerical benchmark tests with prescribed velocity fields, which shows superior mass conservation property over the level set method. With combination of the flow solver, a gas bubble rising in a viscous liquid and a water drop impact onto a deep water pool are modeled. The computed results are compared with the available numerical and experimental results, and good agreement is obtained. Wave breaking of a steep Stokes wave is also modeled and the results are very close to the available numerical results. Finally, plunging wave breaking over a submerged bump is simulated. The overall wave breaking process and major events are identified from the wave profiles of the simulations, which are qualitatively validated by the complementary experimental data. The flow structures are also compared with the experimental data, and similar flow trends have been observed.     

Hyperbolicity and one-dimensional waves in compressible two-phase flow models

Hyperbolic models for compressible two-phase flows including a conservative symmetric hyperbolic model are reviewed. The basis for a theory of shock waves is developed within the framework of the latter. The analysis of small amplitude discontinuities allows us to conclude that in general there are two types of shocks corresponding to two sound waves. The problem of transition between a pure phase and a mixture (the phase vacuum problem) is analysed. It is proved that for some models the smooth centred wave solution can not provide such a transition. Within the framework of our conservative model there is the possibility of constructing discontinuous solutions which can resolve the phase vacuum problem.PACS: 47.55Kf, 47.40.-xE. Romenski: On leave from Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk 630090, Russia     

传统Spar平台垂荡主共振时非线性耦合响应的研究

考虑瞬时波面影响,建立了Spar平台垂荡-纵摇运动的参数激励耦合运动方程,应用多尺度法导出了波浪频率接近垂荡固有频率时响应方程的一阶摄动解并做数值验证。计算结果显示:当波浪高度达到一定值时,纵摇运动中出现大量的亚谐频率成分;随着波浪高度进一步增大,纵摇运动将出现明显的幅值跳跃现象。研究结果表明,能量渗透现象是纵摇运动失稳的主要原因,波浪激励力矩对于纵摇本身的贡献很小。由于垂荡模态存在能量饱和现象,多余的垂荡能量将会向纵摇模态转移,导致出现大幅值的纵摇运动。     

Asymptotic and numerical models of waves in tunable multi-scale structures

The paper presents asymptotic models and numerical illustrations of periodic systems which possess band gaps and support standing waves at low frequencies. The structures considered here include periodic systems of defects (cracks or resonators of different types). Tuning mechanisms are described to control the position of band gaps in dispersion diagrams.     

On the coupled system performance of transcritical CO2 heat pump and rankine cycle

As one of the natural refrigerants, CO₂ is a potential substitute for synthesized refrigerants with favorable environmental properties. In order to improve the performance of rankine cycle (RankC), the coupled system cycle (CSC) was designed and the performance was analyzed in this paper, which the CSC is combined by the RankC and the transcritical CO₂ heat pump cycle with an expander. Based on thermodynamic principles, the performance analysis platform was designed and the performance analysis was employed. The results show that the average efficiency of the RankC is about 30 %, and the extraction cycle is about 32 %, while the CSC is about 39 %, and the last one is better than the others at the same parameters. With increasing of the boiler feed water temperature, the efficiencies of the three kinds of cycles show increasing trend. With increasing of pressure in conderser–evaporator or outlet temperature of gas cooler, the efficiency of the CSC shows a downward trend. Some fundamental data were obtained for increasing the RankC efficiency by waste heat recovery, and play an active role in improvement the efficiency of power plants.     

Experimental study of coupled two-dimensional models of sliding and spinning friction

An experimental study of coupled models of sliding and spinning friction is carried out. The models are based on Padé approximants of exact integral models. The experimental setup specially designed for the study is described. The experimental procedures are outlined and the results obtained are analyzed.     

Measurement of shock waves velocity in the air plasma of capacitively coupled RF discharge

The velocity of shock wave propagation in the air plasma of stationary capacitively coupled RF discharge at different gas pressure and charged particles concentration has been measured. It is shown, that the velocity of the shock wave increases at the increase of the concentration. Measurement results are brought to the universal dependence. Received 17 August 1998 / Accepted 10 December 1999     

Multidimensional models of traveling waves and nonlinear modes in cylindrical shells

The nonlinear dynamic deformation of a cylindrical shell is modeled taking into account several conjugate vibration modes. Two types of motion are considered: nonlinear normal modes and traveling waves     

On the response of rubbers at high strain rates—I. Simple waves

In this series of papers, we examine the propagation of waves of finite deformation in rubbers through experiments and analysis; in the present paper, Part I, attention is focused on the propagation of one-dimensional waves in strips of natural, latex and synthetic, nitrile rubber. Tensile wave propagation experiments were conducted at high strain rates by holding one end fixed and displacing the other end at a constant velocity. A high-speed video camera was used to monitor the motion and to determine the evolution of strain and particle velocity in rubber strips. Analysis of the response through the theory of finite waves indicated a need for an appropriate constitutive model for rubber; by quantitative matching between the experimental observations and analytical predictions, an appropriate instantaneous elastic response for the rubbers was obtained. This matching process suggested that a simple power-law constitutive model was capable of representing the high strain-rate response for both rubbers used.