Using the nonlinear geometrical acoustics method in the problem of moreton and EUV wave propagation in the solar corona

Propagation of shock related Moreton and EUV waves in the solar atmosphere is simulated by the nonlinear geometrical acoustics method. This method is based on the ray approximation and takes account of nonlinear wave features: dependence of the wave velocity on its amplitude, nonlinear dissipation of wave energy in the shock front, and the increase in its duration with time. The paper describes ways of applying this method to solve the propagation problem of a blast magnetohydrodynamic shock wave. Results of analytical modeling of EUV and Moreton waves in the spherically symmetric and isothermal solar corona are also presented. The calculations demonstrate deceleration of these waves and an increase in their duration. The calculation results of the kinematics of the EUV wave observed on the Sun on January 17, 2010 are presented as an example.     

固体介质中非线性波的能量初探

本文从能源问题与勘探问题的密切关系出发,提出进行深入的非线性波研究的必要性——进一步提供可靠而详实的地质资料,以解决实际地质问题.说明了非线性科学与非线性波动的关系和特点,非线性波动是非线性科学的一个重要的分支,而地球本身的特点也决定了非线性科学是解决地质问题的重要基础.回顾了波动理论的研究历程及当今国内外非线性研究的进展情况.通过上述认识,提出了非线性波动问题中能量的重要性,然后分别从震源与冲击波的形成,界面处的能量分配,介质中能量的衰减,波的相互作用四个方面讨论了非线性波的能量问题.通过对能量问题的讨论,进一步讨论了影响非线性波能量的因素.从能量的角度出发,探讨了以后进行固体中非线性波研究的重点.最后对非线性波在地学应用中的可能性进行了探讨.     

Nonlinear waves on a coupled density front

Abstract

It is shown that the inclusion of the nonlinear terms in the equations of motion of a coupled density front of zero potential vorticity results in wave solutions which merely propagate with time. The linear theory, on the other hand, predicts an exponential temporal growth. The nonlinear equation admits steady solutions representing standing waves whereas if the nonlinear terms are omitted no steady solutions exist. The general initial value problem is difficult to solve numerically since the linear problem is ill posed.

In addition we prove that the general similarity solution of the nonlinear equation tends to zero for large times, at any point in space, regardless of the initial condition.     

Wave Processes in Inhomogeneous Nonlinear-Dissipative Media

Several problems for nonlinear localized wave processes are analysed. Wave solutions of the kink type, concentrated in the vicinity of some curve l, are considered. Both the solution and the curve l are unknown. It is shown that the determination of l may be realized without knowledge of the solution. For one class of problems, a variational principle for finding l, similar to the Fermat principle, is obtained. Types of waves are found which exist due to the inhomogeneity of the medium or due to the initial front curvature only.     

On the RH relations across weak and strong shocks in van der Waals gases

The Rankine–Hugoniot (RH) jump relations for normal shock waves in van der Waals fluids have been studied in order to improve a theoretical understanding of those shock related phenomena as observed in a real atmosphere which cannot be accounted for by the ideal gas model. The RH jump relations for the pressure, density, particle velocity, temperature, speed of sound, adiabatic compressibility and change-in-entropy across the shock front have been analysed in terms of the non-idealness parameter of the gas, downstream Mach number and adiabatic index of the gas. Further, as the strength of shock waves may range from weak to strong, the convenient forms of RH jump relations for weak and strong shock waves have been discussed, simultaneously. Finally, the effects on the flow-field behind the shock front have been explored due to the non-idealness parameter of the gas, downstream Mach number and adiabatic index of the gas.     

Upstream whistler-mode waves at planetary bow shocks: A brief review

Upstream whistler-mode waves appear to be present in front of all collisionless shocks. Because the whistler-mode group velocity exceeds its phase velocity over the frequency range in which the phase velocity increases with frequency, interesting alterations of polarization and frequency spectrum occur in the observer's reference frame. Landau resonance also plays a role in the wave properties. The source of these waves is the shock but the mechanism for wave generation is not yet understood.     

Atmospheric gravity wave excitation through sum nonresonant interaction

Applying a fully nonlinear numerical scheme, sum nonresonant interaction of gravity waves is studied. The process of new wave excitation clearly exhibits that sum nonresonant interaction not only can happen in the atmosphere, but also has a considerable energy exchange magnitude, which is comparable to that of resonant interaction. The interacting waves have almost steady wavelengths and obey the dispersion relation of gravity waves, which differs from the results in the weak interaction theory. Despite the lack of the resonant condition restriction, nonresonant interactions depend on the detuning degrees of interactions.     

山区剧动高速滑坡超前气浪的动力学机理

针对高速滑坡超前气浪灾害的动力学问题,建立了滑坡体沿坡面滑动的二维模型;采用动网格技术,数值仿真了高速滑坡超前冲击气浪的流场特征,分析了其形成的动力学机理。计算结果表明：随着滑坡体下滑速度增大,在滑坡体前缘上方和滑坡体后方出现的涡流逐渐加强,速度也逐渐变大;滑坡体下滑速度越大,在滑坡体正前方不同高度处的气浪速度越大,气浪所影响的距离越远,所造成的破坏也越大。在滑坡体正前方出现高压区,并且随着滑坡体下滑速度增大,滑坡体前方的压力变化也增大,压力的急剧增大也导致气浪速度变大。高速滑坡引发的,中击气浪在前方100m范围内产生12级以上的大风,破坏力极大。此研究将为超前气浪灾害的防治提供科学依据。     

中层耗散大气中Rossby波包的非线性相互作用理论

采用弱非线性近似得出中层耗散大气连续谱Ｒｏｓｓｂｙ波包的非线性时空演化方程，讨论了Ｒｏｓｓｂｙ波包的三波相互作用问题．数值计算表明，耗散和非线性的共同效应决定了Ｒｏｓｓｂｙ波包的演变．当一个Ｒｏｓｓｂｙ波包通过大气传播时，它的振幅若超过某个阈值，空间尺度分别比它大和比它小的两个次级Ｒｏｓｓｂｙ波包的振幅会随时间增长．特别当这两个次级波包同时随时空变化时，仅当主波的振幅超过一个更大的阈值，且其群速度介于两次级波包的群速度之间时，两次级波包的振幅才会随时空同时增长，即出现绝对不稳定现象，耗散和３个波包的频率失配都会增大不稳定的阈值．     

Nearshore Tsunami Inundation Model Validation: Toward Sediment Transport Applications

Model predictions from a numerical model, Delft3D, based on the nonlinear shallow water equations are compared with analytical results and laboratory observations from seven tsunami-like benchmark experiments, and with field observations from the 26 December 2004 Indian Ocean tsunami. The model accurately predicts the magnitude and timing of the measured water levels and flow velocities, as well as the magnitude of the maximum inundation distance and run-up, for both breaking and non-breaking waves. The shock-capturing numerical scheme employed describes well the total decrease in wave height due to breaking, but does not reproduce the observed shoaling near the break point. The maximum water levels observed onshore near Kuala Meurisi, Sumatra, following the 26 December 2004 tsunami are well predicted given the uncertainty in the model setup. The good agreement between the model predictions and the analytical results and observations demonstrates that the numerical solution and wetting and drying methods employed are appropriate for modeling tsunami inundation for breaking and non-breaking long waves. Extension of the model to include sediment transport may be appropriate for long, non-breaking tsunami waves. Using available sediment transport formulations, the sediment deposit thickness at Kuala Meurisi is predicted generally within a factor of 2.     

Transport of suspended sediment under the dam‐break flow on an inclined plane bed of arbitrary slope

The problem of transport of suspended sediment after the break of a dam on an inclined bed is considered. To that end we use the shallow‐water approximation for arbitrary, constant slopes of the bottom, taking into consideration the effect of friction. The numerical technique and the frictional model are validated by comparison with available experimental data and asymptotic analytical solutions, with special attention to the numerical solution near the wetting front. The transport of suspended sediment down the inclined bed is obtained and discussed as a function of the slope of the bed for different values of the parameters characterizing the sediment and its transport properties. For sufficiently large times we always find the formation of roll waves near the water front, which affects the transport of sediments significantly. These strong oscillations are accurately computed with the numerical method used. The relative importance of the bed load (to the suspended load) sediment transport is also discussed as a function of the size of the sediment particles and the slope of the bed for different models on the initiation of sediment suspension from bed load. We also check the dilute sediment approach and characterize the conditions for its failure. Finally, the results of the present simplified model are intended to be used as tests of more complex numerical models. Copyright © 2007 John Wiley & Sons, Ltd.     

重力波包在中层大气温度波导中传播的数值模拟

给出了重力波在中层大气温度波导中的反对称形式导制传播的线性理论模型,并采用二维非线性的数值模型对重力波波包在中层大气温度波导中的传播和演变过程进行了模拟研究.模拟的结果表明,下层大气激发的重力波能量进入波导区域后被俘获形成导制传播.重力波在波导内不停地来回反射,垂直方向的自由传播受到限制,能量在波导内沿着水平方向传输,模拟得到的波参数与理论值相近.重力波包在温度波导中传播时伴随着能量泄漏,且能量泄漏的速率随时间变缓,最终总有部分能量被限制在波导区域.重力波在水平方向上传播几百公里后,依然维持着良好的波结构,同时数值模拟也给出了重力波在波导区域内能量密度的时空分布.     

Ponderomotive effects in magnetospheric hydromagnetic waves

The ponderomotive force (PMF) is a ubiquitous nonlinear wave effect arising in plasma physics when applied wave fields or plasma parameters have significant spatial gradients. Some basic properties of the PMF are described as they relate to ULF hydromagnetic waves in the magnetosphere. Examples are given of recent results obtained using both analytical and numerical techniques for waves from the lowest frequencies (determined by the dimensions of the magnetosphere) up to the vicinity of the ion cyclotron frequency. These results include the possibilities that the PMF may transport plasma over large distances in the magnetosphere, and that the PMF may energize magnetospheric ions significantly. In particular the PMF may play a role in transporting and energizing O⁺ ions from the ionosphere into the body of the magnetosphere. The PMF can also generate nonlinear coupling between the slow magnetosonic mode and the other hydromagnetic modes. This should lead to limitation of density enhancements and, notably in the case of standing Alfvén waves, to spatial harmonic generation, secularly growing frequency shifts, and saturation of driven wave fields. Some implications of these results for the magnetosphere are discussed.Based on an invited review given in IAGA Symposium 3.07, Nonlinear and Kinetic Effects in ULF Waves, at the IUGG XXI General Assembly, Boulder, Colorado, July 2-14, 1995.     

Deformation autowaves in fault zones

Empirical data on the spatiotemporal migration of recent deformation processes in fault zones are presented. Direct geodesic measurements reveal two types of waves, the interfault and intrafault waves. The velocity of the interfault wave is two-threefold higher than that of the intrafault wave. The phenomenological model describing the formation of autowave deformation processes is developed. The obtained nonlinear diffusion equation for the displacements of the Earth’s surface is shown to be structurally similar to the well-known Kolmogorov-Petrovsky-Piskunov equation derived in the population wave theory. Satisfactory agreement between the suggested model and the geodetic measurements is demonstrated. The concept of a pseudowave is discussed, and a way to expand the developed approaches to the spatiotemporal migration of earthquakes is discussed.     

垂直无碰撞激波中多离子波动和He2+加热

应用一维混合模拟方法数值研究了高Alfven－Mach数垂直无碰撞激波中He²⁺的运动及其加热机制．结果表明，在激波面处将会产生向下游传播的多离子波动，它对He²⁺加热有着重要影响．He²⁺的加热过程可能包含两个阶段，由于质子温度各向异性激发的质子回旋波和镜波先使He²⁺加热，而He²⁺与多离子波动相互作用进一步使He²⁺加热到更高的温度．     

On steady and travelling waves over bottom topography in the model of homogeneous flow in a beta-plane channel

Abstract

A spectral low-order model is proposed in order to investigate some effects of bottom corrugation on the dynamics of forced and free Rossby waves. The analysis of the interaction between the waves and the topographic modes in the linear version of the model shows that the natural frequencies lie between the corresponding Rossby wave frequencies for a flat bottom and those applying in the “topographic limit” when the beta-effect is zero. There is a possibility of standing or eastward-travelling free waves when the integrated topograhic effect exceeds the planetary beta-effect.

The nonlinear interactions between forced waves in the presence of topography and the beta-effect give rise to a steady dynamical mode correlated to the topographic mode. The periodic solution that includes this steady wave is stable when the forcing field moves to the West with relatively large phase speed. The energy of this solution may be transferred to the steady zonal shear flow if the spatial scale of this zonal mode exceeds the scale of the directly forced large-scale dynamical mode.     

Geostrophic vs magneto-geostrophic adjustment and nonlinear magneto-inertia-gravity waves in rotating shallow water magnetohydrodynamics

The evolution of localised jets and periodic nonlinear waves in rotating shallow water magnetohydrodynamics (rotating SWMHD) and standard rotating shallow water model (RSW) is compared within the framework of translationally-invariant 1.5-dimensional configurations, which are traditionally used in geophysical fluid dynamics for studying geostrophic adjustment and frontogenesis. Such configurations also allow for exact nonlinear wave solutions in both models. A theory of the magneto-geostrophic adjustment, i.e. adjustment of an arbitrary initial configuration to a state of magneto-geostrophic equilibrium in RSWMHD, is developed and confirmed by numerical simulations with a finite-volume well-balanced code. The code is resolving all kinds of waves in the model and corresponding weak solutions equally well. It is benchmarked by reproducing exact solutions – steady essentially nonlinear Alfvèn and mixed magneto-inertia-gravity waves – and used to demonstrate robustness of these solutions with respect to localised along-wave perturbations. It is also shown how the results on adjustment can be extended to the fully 2-dimensional case.     

Coupled simulation of transient bed evolution in alluvial channels

Abstract

In dealing with the transient sediment transport problem, the commonly used uncoupled model may not be suitable. The uncoupling technique is intended to separate the physical coupling phenomenon of water flow and sediment transport into two independent processes. Very often, as a result, severe numerical oscillation and solution instability problems appear in the simulation of transient sediment transport in alluvial channels. The coupled model, which simultaneously solves water flow continuity, momentum and sediment continuity equations, gives fewer numerical oscillation and solution instability problems. In this article, a coupled model using a matrix double-sweep method to solve the system of nonlinear algebraic equations has been developed. Several test runs designed on the basis of a schematic model have been performed. The numerical oscillation and solution instability problems have been investigated through a comparison with those obtained from an uncoupled model. Based on the proposed case studies, it can be concluded that, for transient bed evolution, the performance of the coupled model is much better than that of the uncoupled model. The numerical oscillation is reduced and the solution is more stable. This newly developed coupled model was also applied to the Cho-Shui River in Taiwan. This application study implied that the effect of the peaky flood wave propagation on the bed evolution could be simulated better by the coupled model than by the uncoupled model.     

地球弓激波前的低频磁流体波

一、引言 在地球弓激波前存在着低频磁流体波。这种低频磁流体波是太阳风在地球弓激波上的反射粒子和太阳风粒子之间相互作用产生的。根据人造卫星的观测资料可以得到,在地球弓激波前,Pc3-4脉动频率范围内的低频磁流体波的主频率和行星际磁场强度     

A model for nonlinear wave interactions

Phenomena associated with weakly nonlinear waves are encountered in optics, plasma physics, and geophysics. Specific applications in oceanography include ocean surface waves, internal gravity waves, Rossby waves, and interactions between these wave systems. Techniques for studying these phenomena include direct numerical integration, Boltzmann-like transport equations, and Langevin transient response functions. A simple model, called thetest wave model, is described and used to illustrate comparison of these methods.