Solutions of Conformal Turbulence on a Half Plane

TL;DR

This paper derives exact solutions for conformal turbulence on a half plane, showing how boundary effects influence turbulence behavior and generalize classical Kolmogorov solutions.

Contribution

It provides the first exact solutions of conformal turbulence on a half plane, extending turbulence theory to boundary-influenced scenarios.

Findings

Inertial range develops away from the boundary

Solutions generalize Kolmogorov's solution with boundary effects

Identifies a fixed point for large model parameters

Abstract

Exact solutions of conformal turbulence restricted on a upper half plane are obtained. We show that the inertial range of homogeneous and isotropic turbulence with constant enstrophy flux develops in a distant region from the boundary. Thus in the presence of an anisotropic boundary, these exact solutions of turbulence generalize Kolmogorov's solution consistently and differ from the Polyakov's bulk case which requires a fine tunning of coefficients. The simplest solution in our case is given by the minimal model of $p=2, q=33$ and moreover we find a fixed point of solutions when $p,q$ become large.