Quasi-2D Vortex Structures in Turbulent Flows: a Lagranjian Model with Fractal Effects

Abstract

This paper presents a physically motivated model of quasi-two-dimensional vortex structures in turbulent flows. The theory of quasi-two-dimensional turbulence explains many phenomena in geophysical hydrodynamics, since due to the rapid rotation of the Earth, large-scale movements of the atmosphere and ocean almost two-dimensional. Quasi-2D turbulence is approximately two-dimensional and is described by equations containing additional terms. Such additions allow us to take into account weak three-dimensional effects that arise in real conditions, for example, in the atmosphere or ocean. We consider the basic equations for the velocity and pressure fields using the Lagrangian frame and incorporating centrifugal and Coriolis forces, as well as fractal disturbances on the vortex surface. Numerical simulations implemented in MatLab reproduce classical vortex behavior and reveal the influence of fractal corrections on field asymmetry. The model aligns well with existing experimental data and offers a foundation for analyzing energy transport and vortex interactions in stratified or thin-layered turbulent systems.

Keywords: quasi- two-dimensional turbulence, fractal boundary, Lagrangian frame, streamfunction, vortex elements, numerical simulations.