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We construct, for the first time to our knowledge, a one-dimensionalstochastic field $\{u(x)\}_{x\in \mathbb{R}}$ which satisfies the followingaxioms which are at the core of the phenomenology of turbulence mainly due toKolmogorov:  (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 someconstant $C>0$  (iii) Intermittency:  $\mathbb{E}{|u(x+\ell)-u(x) |^q} \asymp_{\ell \to 0} |\ell|^{\xi_q}\,,$ forsome non-linear spectrum $q\mapsto \xi_q$  Since then, it has been a challenging problem to combine axiom (ii) withaxiom (iii) (especially for Hurst indexes of interest in turbulence, namely$H<1/2$). In order to achieve simultaneously both axioms, we disturb with twoingredients a underlying fractional Gaussian field of parameter $H\approx \frac1 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 anintricate way the fractional component and the GMC without additionalparameters, a necessary inter-dependence in order to reproduce theasymmetrical, i.e. skewed, nature of the probability laws at small scales.

On a skewed and multifractal uni-dimensional random field, as a probabilistic representation of Kolmogorov's views on turbulence