Related papers: Conformal Models of Two-Dimensional Turbulence

Simplicity of fundamental physical laws manifests itself in fundamental symmetries. While systems with an infinity of strongly interacting degrees of freedom (in particle physics and critical phenomena) are hard to describe, they often…

We present theory of two-dimensional turbulence excited by an external force in thin fluid films on scales larger than the film thickness. The principal feature of two-dimensional turbulence is the tendency of producing motions of larger…

Two dimensional turbulence has a remarkable tendency to self-organize into large, coherent structures, forming a mean flow. The purpose of this paper is to elucidate how these structures are sustained, and what determines them and the…

A comprehensive introduction to two-dimensional conformal field theory is given.

The two-dimensional ideal fluid and the plasma confined by a strong magnetic field exhibit an intrinsic tendency to organization due to the inverse spectral cascade. In the asymptotic states reached at relaxation the turbulence has vanished…

We present two phenomenological models for 2D turbulence in which the energy spectrum obeys a nonlinear fourth-order and a second-order differential equations respectively. Both equations respect the scaling properties of the original…

The main result of this paper is the construction of a conformally covariant operator in two dimensions acting on scalar fields and containing fourth order derivatives. In this way it is possible to derive a class of Lagrangians invariant…

Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…

Following the previous work of Ferretti and Yang on the role of magnetic fields in the theory of conformal turbulence, we show that non-unitary minimal model solutions to 2-dimensional magnetohydrodynamics (MHD) obtained by dimensional…

The present work studies the isotropic and homogeneous turbulence for incompressible fluids through a specific Lyapunov analysis, assuming that the turbulence is due to the bifurcations associated to the velocity field. The analysis…

We present a conformal theory of a dissipationless relativistic fluid in 2 space-time dimensions. The theory carries with it a representation of the algebra of 2-$D$ area-preserving diffeomorphisms in the target space of the complex scalar…

An ensemble model of turbulence based on states with constant flux in wavenumber space was proposed in [K. Yoshida, Phys. Rev. E, 106, 045106 (2022)]. The justification of this ensemble model relies on the conjecture that almost all states…

We discuss the effects of finite perturbations in fully developed turbulence by introducing a measure of the chaoticity degree associated to a given scale of the velocity field. This allows one to determine the predictability time for…

Two-dimensional turbulence self-organizes through a process of energy accumulation at large scales, forming a coherent flow termed a condensate. We study the condensate in a model with local dynamics, the large-scale quasi-geostrophic…

We study the chaoticity and the predictability of a turbulent flow on the basis of high-resolution direct numerical simulations at different Reynolds numbers. We find that the Lyapunov exponent of turbulence, which measures the exponential…

In this work we construct and analyze continuous hydrodynamic models in one space dimension, which are induced by shell models of turbulence. After Fourier transformation, such continuous models split into an infinite number of uncoupled…

We propose explicit forms for the steady state distributions governing fully developed turbulence in two and three spatial dimensions. We base our proposals on the crucial importance of the area and volume preserving diffeomorphisms in the…

Turbulent cascades characterize the transfer of energy injected by a random force at large scales towards the small scales. In hydrodynamic turbulence, when the Reynolds number is large, the velocity field of the fluid becomes irregular and…

We derive a formula for the entropy of two dimensional incompressible inviscid flow, by determining the volume of the space of vorticity distributions with fixed values for the moments Q_k= \int_w(x)^k d^2 x. This space is approximated by a…

We study shell models that conserve the analogues of energy and enstrophy, hence designed to mimic fluid turbulence in 2D. The main result is that the observed state is well described as a formal statistical equilibrium, closely analogous…