Two central schemes of finite difference (FD) up to different accuracy orders of space sampling step Dx (Fourth order and Sixth order respectively) were used to study the 1-D nonlinear P-wave propagation in the nonlin...Two central schemes of finite difference (FD) up to different accuracy orders of space sampling step Dx (Fourth order and Sixth order respectively) were used to study the 1-D nonlinear P-wave propagation in the nonlinear solid media by the numerical method. Distinctly different from the case of numerical modeling of linear elastic wave, there may be several difficulties in the numerical treatment to the nonlinear partial differential equation, such as the steep gradients, shocks and unphysical oscillations. All of them are the great obstacles to the stability and conver-gence of numerical calculation. Fortunately, the comparative study on the modeling of nonlinear wave by the two FD schemes presented in the paper can provide us with an easy method to keep the stability and convergence in the calculation field when the product of the absolute value of nonlinear coefficient and the value of u/x are small enough, namely, the value of bu/x is much smaller than 1. Several results are founded in the numerical study of nonlinear P-wave propagation, such as the waveform aberration, the generation and growth of harmonic wave and the energy redistribution among different frequency components. All of them will be more violent when the initial amplitude A0 is larger or the nonlinearity of medium is stronger. Correspondingly, we have found that the nonlinear P-wave propagation velocity will change with different initial frequency f of source wave or the wave velocity c (equal to the P-wave velocity in the same medium without considering nonlinearity).展开更多
In this paper, we develope a timodependent, nonlinear, photochemical-dynamical 2-D model which is composed of 3 models: dynamical gravity wave model, middle atmospheric photochemical model, and airglow layer photochem...In this paper, we develope a timodependent, nonlinear, photochemical-dynamical 2-D model which is composed of 3 models: dynamical gravity wave model, middle atmospheric photochemical model, and airglow layer photochemical model. We use the model to study the effect of the gravity wave propagation on the airglow layer. The comparison between the effects of the different wavelength gravity wave on the airglow emission distributions is made. When the vertical wavelength of the gravity wave is close to or is shorter than the thickness of the airglow layer, the gravity wave can make complex structure of the airglow layer, such as the double and multi-peak structures of the airglow layer. However, the gravity wave that has long vertical wavelength can make large scale perturbation of the airglow emission distribution.展开更多
On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion tha...On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion that the evolution of the amplitude satisfies the variable coefficient Korteweg-de Vries(KdV) equation.展开更多
Nonlinear interactions between the quasi 5-day wave and tides based on meteor radar observation in the Mesosphere and Lower Thermosphere(MLT) at Maui are studied in this paper.Strong sum interaction between quasi 5-da...Nonlinear interactions between the quasi 5-day wave and tides based on meteor radar observation in the Mesosphere and Lower Thermosphere(MLT) at Maui are studied in this paper.Strong sum interaction between quasi 5-day wave and diurnal tide,and evident difference interaction between quasi 5-day wave and semidiurnal tide are observed during the time of attention.However,their difference and sum counterparts are clearly weaker.The secondary waves generated from those interactions beat with the tide and show intense modulation at the period of 5 days which confirms the existence of their interactions.Additionally,correlation coefficients among these waves are calculated to further explore their interactions and find that they can persist for several days although they are highly intermittent.The energy exchange among these waves can be reversible during the observational time.The periods when the significant difference interaction between the quasi 5-day wave and semidiurnal tide occur are much shorter than those when the significant sum interaction between the quasi 5-day wave and diurnal tide occur.Moreover,these two strong interactions can take place simultaneously.In generally,this study provides the proof of nonlinear interactions between quasi 5-day wave and tides which were seldom reported before.展开更多
为解决纯立方刚度非线性能量阱(Nonlinear Energy Sink,NES)在竖直方向工作时,因重力影响造成的激活阈值过高问题,在中心质量块与NES下底座之间引入支撑弹簧单元,从而构造出一种非对称刚度非光滑NES,通过试验研究该NES的动力学响应。对...为解决纯立方刚度非线性能量阱(Nonlinear Energy Sink,NES)在竖直方向工作时,因重力影响造成的激活阈值过高问题,在中心质量块与NES下底座之间引入支撑弹簧单元,从而构造出一种非对称刚度非光滑NES,通过试验研究该NES的动力学响应。对比分析在简谐激励下非光滑NES与纯立方刚度NES的激活阈值差异。分析水平弹簧刚度和中心质量块质量两个参数对NES激活阈值的影响。结果表明,支撑弹簧单元能够有效降低纯立方刚度NES的激活阈值;通过合理控制水平弹簧刚度和质量块质量,可以使非光滑NES更好地应用于不同频带的减振。展开更多
基金Project of Knowledge Innovation Program from Chinese Academy of Sciences (KZCX2-109).
文摘Two central schemes of finite difference (FD) up to different accuracy orders of space sampling step Dx (Fourth order and Sixth order respectively) were used to study the 1-D nonlinear P-wave propagation in the nonlinear solid media by the numerical method. Distinctly different from the case of numerical modeling of linear elastic wave, there may be several difficulties in the numerical treatment to the nonlinear partial differential equation, such as the steep gradients, shocks and unphysical oscillations. All of them are the great obstacles to the stability and conver-gence of numerical calculation. Fortunately, the comparative study on the modeling of nonlinear wave by the two FD schemes presented in the paper can provide us with an easy method to keep the stability and convergence in the calculation field when the product of the absolute value of nonlinear coefficient and the value of u/x are small enough, namely, the value of bu/x is much smaller than 1. Several results are founded in the numerical study of nonlinear P-wave propagation, such as the waveform aberration, the generation and growth of harmonic wave and the energy redistribution among different frequency components. All of them will be more violent when the initial amplitude A0 is larger or the nonlinearity of medium is stronger. Correspondingly, we have found that the nonlinear P-wave propagation velocity will change with different initial frequency f of source wave or the wave velocity c (equal to the P-wave velocity in the same medium without considering nonlinearity).
基金Supported by the National Science Foundation of China (40225011, 40336054)National Research Project (G2000078407)project of CAS (KZCX3-SW-217)International Collaboration Research Team Program of the Chinese Academy of SciencesChina-Russia Joint Research Center on Space Weather,Chinese Academy of Sciences
文摘In this paper, we develope a timodependent, nonlinear, photochemical-dynamical 2-D model which is composed of 3 models: dynamical gravity wave model, middle atmospheric photochemical model, and airglow layer photochemical model. We use the model to study the effect of the gravity wave propagation on the airglow layer. The comparison between the effects of the different wavelength gravity wave on the airglow emission distributions is made. When the vertical wavelength of the gravity wave is close to or is shorter than the thickness of the airglow layer, the gravity wave can make complex structure of the airglow layer, such as the double and multi-peak structures of the airglow layer. However, the gravity wave that has long vertical wavelength can make large scale perturbation of the airglow emission distribution.
基金supported by the Meteorological Special Project of China(GYHY200806005)the National Natural Sciences Foundation of China(40805028,40675039,40575036)the Key Technologies R&D Program of China(2009BAC51B04)
文摘On the basis of the quasi-geostrophic vorticity equation,theoretical research has been down upon the evolution of the amplitude of solitary Rossby waves employing the perturbation method,and come to the conclusion that the evolution of the amplitude satisfies the variable coefficient Korteweg-de Vries(KdV) equation.
基金Supported by the National Natural Science Foundation of China(41174126)the Specialized Fund for Comprehensive Study and Evaluation of the Polar Environment(CHINARE2014-02-03)
文摘Nonlinear interactions between the quasi 5-day wave and tides based on meteor radar observation in the Mesosphere and Lower Thermosphere(MLT) at Maui are studied in this paper.Strong sum interaction between quasi 5-day wave and diurnal tide,and evident difference interaction between quasi 5-day wave and semidiurnal tide are observed during the time of attention.However,their difference and sum counterparts are clearly weaker.The secondary waves generated from those interactions beat with the tide and show intense modulation at the period of 5 days which confirms the existence of their interactions.Additionally,correlation coefficients among these waves are calculated to further explore their interactions and find that they can persist for several days although they are highly intermittent.The energy exchange among these waves can be reversible during the observational time.The periods when the significant difference interaction between the quasi 5-day wave and semidiurnal tide occur are much shorter than those when the significant sum interaction between the quasi 5-day wave and diurnal tide occur.Moreover,these two strong interactions can take place simultaneously.In generally,this study provides the proof of nonlinear interactions between quasi 5-day wave and tides which were seldom reported before.
文摘为解决纯立方刚度非线性能量阱(Nonlinear Energy Sink,NES)在竖直方向工作时,因重力影响造成的激活阈值过高问题,在中心质量块与NES下底座之间引入支撑弹簧单元,从而构造出一种非对称刚度非光滑NES,通过试验研究该NES的动力学响应。对比分析在简谐激励下非光滑NES与纯立方刚度NES的激活阈值差异。分析水平弹簧刚度和中心质量块质量两个参数对NES激活阈值的影响。结果表明,支撑弹簧单元能够有效降低纯立方刚度NES的激活阈值;通过合理控制水平弹簧刚度和质量块质量,可以使非光滑NES更好地应用于不同频带的减振。
