Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process an...Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process and provided a theoretical formulation for the recurrence period in 1985 on the basis of the nonlinear cubic Schrodinger equation （NLS）. However, NLS has limitations on the narrow band and the weak nonlinearity. The recurrence period is re-investigated in this paper by using a highly efficient High Order Spectral （HOS） method, which can be applied for the direct phase- resolved simulation of the nonlinear wave train evolution. It is found that the Stiassnie and Shemer＇s formula should be modified in the cases with most unstable initial conditions, which is important for such topics as the generation mechanisms of freak waves. A new recurrence period formula is presented and some new evolution characteristics of the Stokes wave train are also discussed in details.展开更多
Long time series of wave field are experimentally simulated by JONSWAP spectra with random phases in a 2D wave flume. Statistic properties of wave surface, such as significant wave height, skewness and kurtosis, are a...Long time series of wave field are experimentally simulated by JONSWAP spectra with random phases in a 2D wave flume. Statistic properties of wave surface, such as significant wave height, skewness and kurtosis, are analyzed, and the freak wave occurrence probability and its relations with Benjamin-Feir index （BFI） are also investigated. The results show that the skewness and the kurtosis are significantly dependent on the wave steepness, and the kurtosis increases along the flume when BFI is large. The freak waves are observed in random wave groups. They occur more frequently than expected, especially for the wave groups with large BFI.展开更多
We analytically derived the complex Ginzburg-Landau equation from the Liénard form of the discrete FitzHugh Nagumo model by employing the multiple scale expansions in the semidiscrete approximation. The complex G...We analytically derived the complex Ginzburg-Landau equation from the Liénard form of the discrete FitzHugh Nagumo model by employing the multiple scale expansions in the semidiscrete approximation. The complex Ginzburg-Landau equation now governs the dynamics of a pulse propagation along a myelinated nerve fiber where the wave dispersion relation is used to explain the famous phenomena of propagation failure and saltatory conduction. Stability analysis of the pulse soliton solution that mimics the action potential fulfills the Benjamin-Feir criteria for plane wave solutions. Finally, results from our numerical simulations show that as the dissipation along the myelinated axon increases, the nerve impulse broadens and finally degenerates to front solutions.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 41106001)the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20100094110016)+1 种基金the Special Research Funding of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering (Grant No. 2009585812)the Priority Academic Program Development of Jiangsu Higher Education Institutions (Coastal Development and Conservancy)
文摘Owing to the Benjamin-Feir instability, the Stokes wave train experiences a modulation-demodulation process, and presents a recurrence characteristics. Stiassnie and Shemer researched the unstable evolution process and provided a theoretical formulation for the recurrence period in 1985 on the basis of the nonlinear cubic Schrodinger equation （NLS）. However, NLS has limitations on the narrow band and the weak nonlinearity. The recurrence period is re-investigated in this paper by using a highly efficient High Order Spectral （HOS） method, which can be applied for the direct phase- resolved simulation of the nonlinear wave train evolution. It is found that the Stiassnie and Shemer＇s formula should be modified in the cases with most unstable initial conditions, which is important for such topics as the generation mechanisms of freak waves. A new recurrence period formula is presented and some new evolution characteristics of the Stokes wave train are also discussed in details.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51079023 and 51221961)the National Basic Research Program of China(973 Program,Grant Nos.2011CB013703 and 2013CB036101)
文摘Long time series of wave field are experimentally simulated by JONSWAP spectra with random phases in a 2D wave flume. Statistic properties of wave surface, such as significant wave height, skewness and kurtosis, are analyzed, and the freak wave occurrence probability and its relations with Benjamin-Feir index （BFI） are also investigated. The results show that the skewness and the kurtosis are significantly dependent on the wave steepness, and the kurtosis increases along the flume when BFI is large. The freak waves are observed in random wave groups. They occur more frequently than expected, especially for the wave groups with large BFI.
文摘We analytically derived the complex Ginzburg-Landau equation from the Liénard form of the discrete FitzHugh Nagumo model by employing the multiple scale expansions in the semidiscrete approximation. The complex Ginzburg-Landau equation now governs the dynamics of a pulse propagation along a myelinated nerve fiber where the wave dispersion relation is used to explain the famous phenomena of propagation failure and saltatory conduction. Stability analysis of the pulse soliton solution that mimics the action potential fulfills the Benjamin-Feir criteria for plane wave solutions. Finally, results from our numerical simulations show that as the dissipation along the myelinated axon increases, the nerve impulse broadens and finally degenerates to front solutions.
