  The geometrical structure is among the most fundamental ingredients in
understanding complex systems. Is there any systematic approach in defining
structures quantitatively, rather than illustratively? If yes, what are the
basic principles to follow? By introducing the concept of extremal points at
different scale levels, a multi-level dissipation element approach has been
developed to define structures at different scale levels, in accordance with
the concept of structure hierarchy. Each dissipation element can be
characterized by the length scale and the scalar variance inside. Using the
two-dimensional fractal Brownian motion as a benchmark case, the conditional
mean of the scalar difference with respect to the length scale shows clearly a
power law and the scaling exponent is in agreement with the Hurst number. For
the 3D turbulence velocity component, the 1/3 scaling law can be represented.
These results indicate the important linkage between the turbulence physics and
ow structure, if well posed and defined. In principle, the multi-level
dissipation element idea is generally applicable in analyzing other multiscale
complex systems as well.
