  The Delta-variance analysis is an efficient tool for measuring the structural
scaling behaviour of interstellar turbulence in astronomical maps. In paper I
we proposed essential improvements to the Delta-variance analysis.
  In this paper we apply the improved Delta-variance analysis to i) a
hydrodynamic turbulence simulation with prominent density and velocity
structures, ii) an observed intensity map of rho Oph with irregular boundaries
and variable uncertainties of the different data points, and iii) a map of the
turbulent velocity structure in the Polaris Flare affected by the intensity
dependence on the centroid velocity determination.
  The tests confirm the extended capabilities of the improved Delta-variance
analysis. Prominent spatial scales were accurately identified and artifacts
from a variable reliability of the data were removed. The analysis of the
hydrodynamic simulations showed that the injection of a turbulent velocity
structure creates the most prominent density structures are produced on a scale
somewhat below the injection scale. The new analysis of a rho Oph continuum map
reveals an intermediate stage in the molecular cloud evolution showing both
signatures of the typical molecular cloud scaling behaviour and the formation
of condensed cores. When analysing the velocity structure of the Polaris Flare
we show that a universal power law connects scales from 0.03 pc to 3 pc.
However, a plateau in the Delta-variance spectrum around 5 pc indicates that
the visible large-scale velocity gradient is not converted directly into a
turbulent cascade.
