ﻻ يوجد ملخص باللغة العربية
We discuss the statistical properties of a single vortex line in a perfect fluid. The partition function is calculated up to the end in the thin vortex approximation. It turns out that corresponding theory is renormalizable, and the renormalization law for the core size of the vortex is found. The direction of renormalization group flow makes the thin vortex approximation to be valid for the interest cases and this result does not depend on the choice of infrared regularization. The expressions for some gauge-invariant correlators are obtained to demonstrate the developed formalism at work.
The problem of vortex pair motion in two-dimensional plane radial flow is solved. Under certain conditions for flow parameters, the vortex pair can reverse its motion within a bounded region. The vortex-pair translational velocity decreases or increa
The incompressible three-dimensional Euler equations develop very thin pancake-like regions of increasing vorticity. These regions evolve with the scaling $omega_{max}simell^{-2/3}$ between the vorticity maximum and the pancake thickness, as was obse
The advection of passive tracers in a system of 4 identical point vortices is studied when the motion of the vortices is chaotic. The phenomenon of vortex-pairing has been observed and statistics of the pairing time is computed. The distribution exhi
This paper reviews results from the study of wall-bounded turbulent flows using statistical state dynamics (SSD) that demonstrate the benefits of adopting this perspective for understanding turbulence in wall-bounded shear flows. The SSD approach use
Recent experiments of thin films flowing down a vertical fiber with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. We present a detailed analysis using a full lubrication model that includ