  Features of the turbulent cascade are investigated for various datasets from
three different turbulent flows. The analysis is focused on the question as to
whether developed turbulent flows show universal small scale features. To
answer this question, 2-point statistics and joint multi-scale statistics of
longitudinal velocity increments are analysed. Evidence of the Markov property
for the turbulent cascade is shown, which corresponds to a 3-point closure that
reduces the joint multi-scale statistics to simple conditional probability
density functions (cPDF). The cPDF are described by the Fokker-Planck equation
in scale and its Kramers-Moyal coefficients (KMCs). KMCs are obtained by a
self-consistent optimisation procedure from the measured data and result in a
Fokker-Planck equation for each dataset. The knowledge of these stochastic
cascade equations enables to make use of the concepts of non-equilibrium
thermodynamics and thus to determine the entropy production along individual
cascade trajectories. In addition to this new concept, it is shown that the
local entropy production is nearly perfectly balanced for all datasets by the
integral fluctuation theorem (IFT). Thus the validity of the IFT can be taken
as a new law of the turbulent cascade and at the same time independently
confirms that the physics of the turbulent cascade is a memoryless Markov
process in scale. IFT is taken as a new tool to prove the optimal functional
form of the Fokker-Planck equations and subsequently to investigate the
question of universality of small scale turbulence. The results of our analysis
show that the turbulent cascade contains universal and non-universal features.
We identify small scale intermittency as a universality breaking feature. We
conclude that specific turbulent flows have their own particular multi-scale
cascade, with other words their own stochastic fingerprint.
