2010/12/17 by Gregory Falkovich, Falkovich, G., S. Musacchio +1
Economics, Econometrics and Finance · Engineering · Mathematics · #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1012.3868
openalex publication_date 2010/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study statistical properties of turbulent inverse cascades in a class of nonlinear models describing a scalar field transported by a two-dimensional incompressible flow. The class is characterized by a linear relation between the transported field and the velocity, and include several cases of physical interest, such as Navier-Stokes, surface quasi-geostrophic and Charney-Hasegawa-Mima equations. We find that some statistical properties of the inverse turbulent cascades in such systems are conformal invariant. In particular, the zero-isolines of the scalar field are statistically equivalent to conformal invariant curves within the resolution of our numerics. We show that the choice of the conformal class is determined by the properties of a transporting velocity rather than those of a transported field and discover a phase transition when the velocity turns from a large-scale field to a small-scale one.