  The inertial subrange of turbulent scales is commonly reflected by a power
law signature in ensemble statistics such as the energy spectrum and structure
functions - both in theory and from observations. Despite promising findings on
the topic of fractal geometries in turbulence, there is no accepted image for
the physical flow features corresponding to this statistical signature in the
inertial subrange. The present study uses boundary layer turbulence
measurements to evaluate the self-similar geometric properties of velocity
isosurfaces and investigate their influence on statistics for the velocity
signal. The fractal dimension of streamwise velocity isosurfaces, indicating
statistical self-similarity in the size of "wrinkles" along each isosurface, is
shown to be constant only within the inertial subrange of scales. For the
transition between the inertial subrange and production range, it is inferred
that the largest wrinkles become increasingly confined by the overall size of
large-scale coherent velocity regions such as uniform momentum zones. The
self-similarity of isosurfaces yields power law trends in subsequent
one-dimensional statistics. For instance, the theoretical 2/3 power law
exponent for the structure function can be recovered by considering the
collective behavior of numerous isosurface level sets. The results suggest that
the physical presence of inertial subrange eddies is manifested in the
self-similar wrinkles of isosurfaces.
