Searching for hidden symmetry in passive scalar advected by 2D Navier-Stokes turbulence*

The statistical behavior of a scalar passively advected by a Navier-Stokes flow resulting from a two-dimensional inverse energy cascade is strongly intermittent, displaying anomalous multiscaling [1], which violates Kolmogorov's self-similarity predictions. Recently, the concept of hidden symmetry has been introduced to define a new set of dynamically rescaled (projected) variables for which scale invariance is restored and allowing to calculate  from the projected equation of motion the anomalous scaling of the structure functions. Hidden symmetry has been numerically validated in the context of the shell models [2,3]. In this work we scrutinize its validity for the case of the passive scalar by inspecting the probability distribution function of multipliers, obtained as the ratio of suitably defined scalar increments at two different inertial scales [4]. We also verify the Perron-Frobenius scenario for the anomalous scaling law of structure functions as a consequence of the hidden symmetry. 

[1] Celani et al., Physical review letters 84 (2000).

[2] Mailybaev, Phys. Rev. Fluids 7 (2022).

[3] Thalabard and Mailybaev, arXiv 2402.04198 (2024).

[4] Calascibetta, Biferale, Bonaccorso, Cencini and Mailybaev, Hidden symmetry in passive scalar advected by 2D Navier-Stokes turbulence (in preparation 2024).