Solar Physics Division Meeting 2000, June 19-22
Session 1. Helioseismology, Magnetic Fields, Chromosphere and Transition Region
Display, Chair: C. U. Keller, Monday-Thursday, June 19, 2000, 8:00am-6:00pm, Forum Ballroom

[1.01] Dynamics of the Granulation: A Non-Linear Approach

A. Nesis, R. Hammer, M. Roth, H. Schleicher (Kiepenheuer-Institut für Sonnenphysik)

\noindent Observables like Doppler velocity, intensity, and turbulence\,(line broadening) can provide insight into the physics of the granulation -- i.e., into the physics of the upper solar convective layers. So far, measurements of these observables have been processed by means of a power and coherence analysis, which is actually connected with the physical concept of modes in linear theories. The upper solar convective layer, however, is a highly nonlinear dissipative system. According to theoretical considerations, such a system may approach a strange attractor in its phase space with time.\par \vspace{1.mm}

\noindent Based on a series of spectrograms taken at the German VTT on Tenerife in the summer of 1999, we address the granulation attractor and its dimension from an observational point of view. In the three-dimensional phase space spanned by the observables intensity, Doppler velocity, and turbulence, the granulation attractor shows a high level of structuring.\par \vspace{1.mm} \noindent By means of the {\em time-lag} and {\em correlation integral} methods applied to the Doppler velocities we found (i) that the granulation attractor can indeed be described by only three variables and (ii) that its dimension seems to depend on the appearance of enhanced shear flow (shear turbulence) at the granular borders. This means that the dynamical system underlying the {\em large scale} granulation is a {\em low dimension attractor.}\par \vspace{1.mm} \noindent The time-lag and correlation integral methods enable us also to decide between noise and signal: in the case of pure noise the method does not converge. We found that the residual velocity associated with the small {\em sub-granular scales} does converge, however, in higher than 10 embedding dimensions. This implies that for small scale variations the underlying attractor is {\em not} a low dimension one.