  We construct, for the first time to our knowledge, a one-dimensional
stochastic field $\{u(x)\}_{x\in \mathbb{R}}$ which satisfies the following
axioms which are at the core of the phenomenology of turbulence mainly due to
Kolmogorov:
  (i) Homogeneity and isotropy: $u(x) \overset{\mathrm{law}}= -u(x)
\overset{\mathrm{law}}=u(0)$
  (ii) Negative skewness (i.e. the $4/5^{\mbox{\tiny th}}$-law): \\
$\mathbb{E}{(u(x+\ell)-u(x))^3} \sim_{\ell \to 0+} - C \, \ell\,,$ \, for some
constant $C>0$
  (iii) Intermittency:
  $\mathbb{E}{|u(x+\ell)-u(x) |^q} \asymp_{\ell \to 0} |\ell|^{\xi_q}\,,$ for
some non-linear spectrum $q\mapsto \xi_q$
  Since then, it has been a challenging problem to combine axiom (ii) with
axiom (iii) (especially for Hurst indexes of interest in turbulence, namely
$H<1/2$). In order to achieve simultaneously both axioms, we disturb with two
ingredients a underlying fractional Gaussian field of parameter $H\approx \frac
1 3 $. The first ingredient is an independent Gaussian multiplicative chaos
(GMC) of parameter $\gamma$ that mimics the intermittent, i.e. multifractal,
nature of the fluctuations. The second one is a field that correlates in an
intricate way the fractional component and the GMC without additional
parameters, a necessary inter-dependence in order to reproduce the
asymmetrical, i.e. skewed, nature of the probability laws at small scales.
