A continuously stratified nonlinear model is set up to study the impact of topographical character on the generation of internal solitary waves over a sill by tidal flow.One of the reasons why almost all of the genera...A continuously stratified nonlinear model is set up to study the impact of topographical character on the generation of internal solitary waves over a sill by tidal flow.One of the reasons why almost all of the generated internal solitary waves propagate westward in the northern South China Sea is explained.The model simulations describe the generation and propagation of internal waves well.When the strength of imposed barotropic tides and the water stratification stay unchanged,the steepness of the sill slope can control both(a) whether or not the waves induced over a sill by tidal flow are linear internal waves or nonlinear internal solitary waves,and(b) the amplitude of the internal solitary waves generated.If the steepness of the sill is asymmetric,the nonlinear internal solitary waves may be induced on the steeper side of the sill.These conclusions are supported by a numerical experiment with a monthly-mean stratification and an actual seafloor topography from the Luzon Strait.展开更多
The propagation and fission process of internal solitary waves （ISWs） with amplitudes of about 170 m are simulated in the northeast of the South China Sea （NSCS） by using the generalized Korteweg-de Vries （KdV） ...The propagation and fission process of internal solitary waves （ISWs） with amplitudes of about 170 m are simulated in the northeast of the South China Sea （NSCS） by using the generalized Korteweg-de Vries （KdV） equation under continuous stratification. More attention is paid to the effects of the ebb and flood background currents on the fission process of ISWs. This kind of background current is provided by the composed results simulated in terms of monthly mean baroclinic circulation and barotropic tidal current. It is found that the obtained relation of the number of fission solitons to the water depth and stratification is roughly in accordance with the fission law derived by Djordjevic and Redekopp in 1978; however, there exists obvious difference between the effects of the ebb and flood background currents on the wave-lengths of fission solitons （defined as the distance between two neighboring peaks of ISWs）. The difference in nonlinearity coefficient a between the ebb and flood background currents is a main cause for the different wave-lengths of fission solitons.展开更多
Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal wav...Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal waves is one of the mechanisms producing internal solitary waves (ISWs), which is different from the generation mechanism in the case where the semidiurnal tidal current flows over topographic drops. In this paper, the model of internal Kelvin wave with continuous stratification is given, and an elementary numerical study of nonlinear evolution of ITWs is made for the SYS, using the generalized KdV model (GKdV model for short) for a continuous stratified ocean, in which the different effects of background barotropic ebb and flood currents are considered. Moreover, the parameterization of vertical turbulent mixing caused by ITWs and ISWs in the SYS is studied, using a parameterization scheme which was applied to numerical experiments on the breaking of ISWs by Vlasenko and Hutter in 2002. It is found that the vertical turbulent mixing caused by internal waves is very strong within the upper layer with depth less than about 30m, and the vertical turbulent mixing caused by ISWs is stronger than that by ITWs.展开更多
This paper is mainly concerned with modeling nonlinear internal waves in the ocean of great depth.The ocean is assumed to be composed of three homogeneous fluid layers of different densities in a stable stratified con...This paper is mainly concerned with modeling nonlinear internal waves in the ocean of great depth.The ocean is assumed to be composed of three homogeneous fluid layers of different densities in a stable stratified configuration.Based on the Ablowitz-Fokas-Musslimani formulation for irrotational flows,strongly nonlinear and weakly nonlinear models are developed for the“shallow-shallow-deep”and“deep-shallow-deep”scenarios.Internal solitary waves are computed using numerical iteration schemes,and their global bifurcation diagrams are obtained by a numerical continuation method and compared for different models.For the“shallow-shallow-deep”case,both mode-1 and mode-2 internal solitary waves can be found,and a pulse broad-ening phenomenon resulting in conjugate flows is observed in the mode-2 branch.While in the“deep-shallow-deep”situation,only mode-2 solitary waves can be obtained.The existence and stability of mode-2 internal solitary waves are confirmed by solving the primitive equations based on the MITgcm model.展开更多
This paper aims to contribute to the literature on the explanatory power of behavior models with heterogeneous agents. The authors present a new nonlinear structural stock market model which is a nonlinear determinist...This paper aims to contribute to the literature on the explanatory power of behavior models with heterogeneous agents. The authors present a new nonlinear structural stock market model which is a nonlinear deterministic process buffeted by dynamic noise. An exogenous noise is introduced to the model with the assumption of IID normal innovations of the fundamental value in order to investigate how noisy dynamics interacts with deterministic process. The market is composed of two typical trader types： the rational fundamentalists and the boundedly rational traders governed by greed and fear. The interaction between noise and deterministic element determines the evolution process of the system as key parameters are changed. The authors find the model is able to generate time series that exhibit dynamical and statistical properties closely resembling those of the S＆：P500 index, such as volatility clustering, fat tails （leptokurtosis）, autocorrelation in square and absolute return, larger amplitude, crashes and bubbles. The authors also investigate the nonlinear dependence structure in our data. The results indicate that the GARCH-type model cannot completely account for all nonlinearity in our simulated market, which is thus consistent with the results from real markets. It seems that the nonlinear structural model is more powerful to give a satisfied explanation to market behavior than the traditional stochastic approach.展开更多
基金Supported by the Knowledge Innovation Program of Chinese Academy of Sciences (No.KZCX1-YW-12-03),(China National Funds for Distinguished Young Scientists)the National High Technology Research and Development Program of China (863 Program) (Nos.2008AA09Z112, 2008AA09A402)+1 种基金the National Natural Science Foundation of China (No.40676021)Chinese Oceanic Association (No.DYXM-115-02-4-02)
文摘A continuously stratified nonlinear model is set up to study the impact of topographical character on the generation of internal solitary waves over a sill by tidal flow.One of the reasons why almost all of the generated internal solitary waves propagate westward in the northern South China Sea is explained.The model simulations describe the generation and propagation of internal waves well.When the strength of imposed barotropic tides and the water stratification stay unchanged,the steepness of the sill slope can control both(a) whether or not the waves induced over a sill by tidal flow are linear internal waves or nonlinear internal solitary waves,and(b) the amplitude of the internal solitary waves generated.If the steepness of the sill is asymmetric,the nonlinear internal solitary waves may be induced on the steeper side of the sill.These conclusions are supported by a numerical experiment with a monthly-mean stratification and an actual seafloor topography from the Luzon Strait.
基金supported by the Key Program of National Natural Science Foundation of China under contract No.41030855
文摘The propagation and fission process of internal solitary waves （ISWs） with amplitudes of about 170 m are simulated in the northeast of the South China Sea （NSCS） by using the generalized Korteweg-de Vries （KdV） equation under continuous stratification. More attention is paid to the effects of the ebb and flood background currents on the fission process of ISWs. This kind of background current is provided by the composed results simulated in terms of monthly mean baroclinic circulation and barotropic tidal current. It is found that the obtained relation of the number of fission solitons to the water depth and stratification is roughly in accordance with the fission law derived by Djordjevic and Redekopp in 1978; however, there exists obvious difference between the effects of the ebb and flood background currents on the wave-lengths of fission solitons （defined as the distance between two neighboring peaks of ISWs）. The difference in nonlinearity coefficient a between the ebb and flood background currents is a main cause for the different wave-lengths of fission solitons.
基金supported by the Key Program of the National Natural Science Foundation of China under contract No.41030855
文摘Many observations show that in the Yellow Sea internal tidal waves (ITWs) possess the remarkable characteristics of internal Kelvin wave, and in the South Yellow Sea (SYS) the nonlinear evolution of internal tidal waves is one of the mechanisms producing internal solitary waves (ISWs), which is different from the generation mechanism in the case where the semidiurnal tidal current flows over topographic drops. In this paper, the model of internal Kelvin wave with continuous stratification is given, and an elementary numerical study of nonlinear evolution of ITWs is made for the SYS, using the generalized KdV model (GKdV model for short) for a continuous stratified ocean, in which the different effects of background barotropic ebb and flood currents are considered. Moreover, the parameterization of vertical turbulent mixing caused by ITWs and ISWs in the SYS is studied, using a parameterization scheme which was applied to numerical experiments on the breaking of ISWs by Vlasenko and Hutter in 2002. It is found that the vertical turbulent mixing caused by internal waves is very strong within the upper layer with depth less than about 30m, and the vertical turbulent mixing caused by ISWs is stronger than that by ITWs.
基金supported by the National Natural Science Foundation of China(Grant Nos.11911530171,11772341,and 42006016)the Key Program of National Natural Science Foundation of China(Grant Nos.12132018,and 91958206)the Natural Science Foundation of Shandong Province(Grant No.ZR2020QD063).
文摘This paper is mainly concerned with modeling nonlinear internal waves in the ocean of great depth.The ocean is assumed to be composed of three homogeneous fluid layers of different densities in a stable stratified configuration.Based on the Ablowitz-Fokas-Musslimani formulation for irrotational flows,strongly nonlinear and weakly nonlinear models are developed for the“shallow-shallow-deep”and“deep-shallow-deep”scenarios.Internal solitary waves are computed using numerical iteration schemes,and their global bifurcation diagrams are obtained by a numerical continuation method and compared for different models.For the“shallow-shallow-deep”case,both mode-1 and mode-2 internal solitary waves can be found,and a pulse broad-ening phenomenon resulting in conjugate flows is observed in the mode-2 branch.While in the“deep-shallow-deep”situation,only mode-2 solitary waves can be obtained.The existence and stability of mode-2 internal solitary waves are confirmed by solving the primitive equations based on the MITgcm model.
基金This research is supported by MEXT Global COE Program （Kyoto University）, National Natural Science Foundation of China under Grant No.71001036 and No. 71171186, Main Direction Program of Chinese Academy of Sciences KACX1-YW-0906, and the Scientific Research Fund of Hunan Provincial Education Department under Grant No. 10A082.
文摘This paper aims to contribute to the literature on the explanatory power of behavior models with heterogeneous agents. The authors present a new nonlinear structural stock market model which is a nonlinear deterministic process buffeted by dynamic noise. An exogenous noise is introduced to the model with the assumption of IID normal innovations of the fundamental value in order to investigate how noisy dynamics interacts with deterministic process. The market is composed of two typical trader types： the rational fundamentalists and the boundedly rational traders governed by greed and fear. The interaction between noise and deterministic element determines the evolution process of the system as key parameters are changed. The authors find the model is able to generate time series that exhibit dynamical and statistical properties closely resembling those of the S＆：P500 index, such as volatility clustering, fat tails （leptokurtosis）, autocorrelation in square and absolute return, larger amplitude, crashes and bubbles. The authors also investigate the nonlinear dependence structure in our data. The results indicate that the GARCH-type model cannot completely account for all nonlinearity in our simulated market, which is thus consistent with the results from real markets. It seems that the nonlinear structural model is more powerful to give a satisfied explanation to market behavior than the traditional stochastic approach.
