  We analyze the relationship of longitudinal and transverse increment
statistics measured in isotropic small-scale turbulence. This is done by means
of the theory of Markov processes leading to a phenomenological Fokker-Planck
equation for the two increments from which a generalized Karman equation is
derived. We discuss in detail the analysis and show that the estimated equation
can describe the statistics of the turbulent cascade. A remarkably result is
that the main differences between longitudinal and transverse increments can be
explained by a simple rescaling-symmetry, namely the cascade speed of the
transverse increments is 1.5 times faster than that of the longitudinal
increments. Small differences can be found in the skewness and in a higher
order intermittency term. The rescaling symmetry is compatible with the
Kolmogorov constants and the Karman equation and give new insight into the use
of extended self similarity (ESS) for transverse increments. Based on the
results we propose an extended self similarity for the transverse increments
(ESST).
