Solitary wave propagation in solar flux tubes

2006 ◽  
Vol 13 (3) ◽  
pp. 032902 ◽  
Author(s):  
Robert Erdélyi ◽  
Viktor Fedun
Keyword(s):  
Wave Propagation ◽  
Solitary Wave ◽  
Solar Flux ◽  
Flux Tubes

Statistical properties of the internal solitary wave ensemble

2021 ◽  
Author(s):  
Tatiana Talipova ◽  
Ekaterina Didenkulova ◽  
Anna Kokorina ◽  
Efim Pelinovsky
Keyword(s):  
Wave Propagation ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Internal Solitary Wave ◽  
Statistical Moments ◽  
Nonlinear Propagation ◽  
Positive Sign ◽  
Cubic Nonlinearity ◽  
Gardner Equation ◽  
Water Stratification

<p>Internal solitary wave ensembles are often observed on the ocean shelves. The long internal baroclinic tide is generated by a barotropic tide on the shelf edges, and then transforms into the soliton-like wave packets during the nonlinear propagation to the beach. The tide is a periodic process and the solitary wave ensemble appears on the shelf usually each semi-diurnal period of 12.4 hours. This process is very sensitive to the variation of the tide characteristics and the hydrology.</p><p>We study the propagation of the soliton ensembles numerically in the framework of the spatial form of the Gardner equation (i.e., the Korteweg-de Vries equation with both, quadratic and cubic nonlinearities) assuming horizontally uniform background and applying periodic conditions in time. The water stratification and the local depth are taken similar to the conditions of the north-western Australian shelf, where the stratification admits the existence of solitons but not breathers. The numerical simulation is performed using the Gardner equation with the negative sign of the cubic nonlinearity. For the study of the statistic properties of the solitary waves we use the ensemble of 50 realizations with the same set of 13 solitary waves which are located randomly. The histograms of the wave amplitudes change as the waves travel. The histogram variations become significant after 50 km of the wave propagation. The third (skewness) and the fourth (kurtosis) statistical moments are computed versus the travel distance. It is shown that the both moments decrease by 20% when the solitary wave groups travel for about 150 km.</p><p>A similar simulation is conducted for a variable background within the framework of the variable-coefficient Gardner equation. At some location the water stratification corresponds to the positive sign of the local coefficient of the cubic nonlinearity, and then internal breathers may exist. The wave propagation in horizontally inhomogeneous hydrology leads to the occurrence of complicated patterns of solitons and breathers; in the course of the transformation they can disintegrate or form internal rogue waves. Under these conditions the statistical moments of the wave field are essentially different from case when the breather-like waves cannot occur.</p><p>The research was supported by the RFBR grants No 19-05-00161 (TT and EP) and 19-35-60022 (ED). The Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS” (№ 20-1-3-3-1) is also acknowledged by ED</p>

scholarly journals On the Description of Transverse Wave Propagation Along Thin Magnetic Flux Tubes

2018 ◽  
Vol 58 (7) ◽  
pp. 942-946
Author(s):  
Yu. T. Tsap ◽  
A. V. Stepanov ◽  
Yu. G. Kopylova
Keyword(s):  
Wave Propagation ◽  
Magnetic Flux ◽  
Transverse Wave ◽  
Flux Tubes ◽  
Magnetic Flux Tubes

Generalized momentum method to describe high-frequency solitary wave propagation in systems with varying dispersion

1998 ◽  
Vol 58 (5) ◽  
pp. R5264-R5267 ◽  
Author(s):  
Sergei K. Turitsyn ◽  
Tobias Schaefer ◽  
Vladimir K. Mezentsev
Keyword(s):  
Wave Propagation ◽  
Solitary Wave ◽  
High Frequency ◽  
Generalized Momentum ◽  
Varying Dispersion

Wave Motion of a Nonlinear Elastic Bar Subjected to Axial Excitation

2004 ◽  
Author(s):  
Liming Dai ◽  
Qiang Han
Keyword(s):  
Wave Propagation ◽  
Solitary Wave ◽  
Elastic Wave ◽  
Nonlinear Wave ◽  
Wave Motion ◽  
Initial Conditions ◽  
System Parameters ◽  
Elastic Bar ◽  
Nonlinear Elastic ◽  
Nonlinear Elastic Wave

This research intends to investigate the wave motion in a nonlinear elastic bar with large deflection subjected to an axial external exertion. A nonlinear elastic constitutive relation governs the material of the bar. General form of the nonlinear wave equations governing the wave motion in the bar is derived. With a modified complete approximate method, the asymptotic solution of solitary wave is developed for theoretical and numerical analyses of the wave motion. Various initial conditions and system parameters are considered for investigating the shape and propagation of the nonlinear elastic wave. With the governing equation of the wave motion of the bar and the solution developed, the characteristics of the nonlinear elastic wave of the bar are analyzed theoretically and numerically. Properties of the wave propagation and the effects of the system parameters of the bar and the influences of the initial conditions to the characteristics of the wave motion are investigated in details. Based on the theoretical analysis as well as the numerical simulations, it is found that the nonlinearity of the elastic bar may cause solitary wave in the bar. The velocity of the solitary wave propagating in the bar is related to the initial condition of the wave motion. This exhibits an obvious different characteristic between the nonlinear wave and that of the linear wave of an elastic bar. It is also found in the research that the solitary wave is a pulse wave with stable propagation. If the stability of the wave propagation is destroyed, the solitary wave will no longer exist. The results of the present research may provide guidelines for the wave motion analysis of nonlinear elastic solid elements.

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