  It is well known that the fluid-particle acceleration is intimately related
to the dissipation rate of turbulence, in line with the Kolmogorov assumptions.
On the other hand, various experimental and numerical works have reported as
well its dependence on the kinetic energy, which is generally attributed to
intermittency and non-independence of the small-scale dynamics from large-scale
ones. The analyses given in this paper focus on statistics of the
fluid-particle acceleration conditioned on both the local dissipation rate and
the kinetic energy. It is shown that this quantity presents an exponential
dependence on the kinetic energy with a growth rate independent of the Reynolds
number, in addition to the expected power law behavior with the dissipation
rate. The exponential growth, which clearly departs from the previous
propositions, reflects additional kinematic effects of the flow structures on
the acceleration. Regarding intermittency, to account for the persistence of
the effect of the large-scales on the dissipation rate, it is further proposed
scaling laws for the Reynolds number dependence of the conditional and
unconditional acceleration variance using Barenblatt's incomplete similarity
framework. It is then shown that both these intermittency and kinematic effects
can be combined in a multiplicative cascade process for the acceleration
depending on the kinetic energy and the dissipation rate. On the basis of these
observations, we introduce a vectorial stochastic model for the dynamics of a
tracer in turbulent flows. This model incorporates a fractional log-normal
process for the dissipation rate recently proposed, as well as an additional
hypothesis regarding non-diagonal terms in the diffusion tensor which naturally
leads to the decomposition between tangential and centripetal acceleration.
This model is shown to be in good agreement with direct numerical simulations
and presents the essential characteristics of the Lagrangian turbulence
highlighted in recent years, namely (i) non-Gaussian acceleration, (ii) scale
separation between the norm of the acceleration and its components, (iii)
anomalous scaling law for the Lagrangian velocity spectra, and (iv) negative
skewness of the increments of the mechanical power, reflecting the temporal
irreversibility of the dynamics.
