  To answer the question whether a cascade of energy exists or not in
turbulence, we propose a set of correlation functions able to test if there is
an irreversible transfert of energy, step by step, from large to small
structures. These tests are applied to real Eulerian data of a turbulent
velocity flow, taken in the wind grid tunnel of Modane, and also to a prototype
model equation for wave turbulence. First we demonstrate the irreversible
character of the flow by using multi-time correlation function at a given point
of space. Moreover the unexpected behavior of the test function leads us to
connect irreversibility and finite time singularities (intermittency). Secondly
we show that turbulent cascade exists, and is a dynamical process, by using a
test function depending on time and frequency. The cascade shows up only in the
inertial domain where the kinetic energy is transferred more rapidly (on
average) from the wavenumber $k_{1}$ to $k_{2}$ than from $k_{1}$ to $k'_{2}$
larger than $k_{2}$.
