Nonlinear Wave Phenomena in Dense Conglomerate of Flux Tubes

Abstract

Nonlinear wave phenomena in strongly inhomogeneous media have a number of specific features that are important for various physical objects where the parameters of medium change by an order of unity over the scales small compared to the wavelength. Generally, one would expect that the presence of strong inhomogeneities may “cut” the steepening of the wave front, and thus prevent formation of shocks. We shall see that this is not always the case. In this chapter, we address this problem based on properties of sunspots and describe the procedure that allows one to obtain nonlinear equations in the presence of strong inhomogeneities. The approach involves dispersion properties of a system, and dissipative effects. The equation itself takes a form similar to KdV–Bürgers equation and thus describes corresponding scenarios of the system evolution. For example, the predominance of dissipative effects leads to damping of the primary wave at linear stage causing direct heating, or, depending on the interplay between nonlinear and dispersion effects, the process of heating may proceed either through the formation of shocks or through the storing of wave energy in a system of solitons which are later damped away. In any case, the presence of inhomogeneities results in strongly enhanced heating compared to that in homogeneous medium.