Viscous flow regimes in unit square: Part 4. Vorticity dynamics from monopoles to multipoles

TL;DR

This paper numerically investigates the vorticity dynamics in viscous flows within a unit square, exploring various initial conditions and revealing complex phenomena like vortex merging and spiral formation.

Contribution

It introduces a numerical iterative method to solve the vorticity equation for diverse initial vorticity distributions, advancing understanding of flow behaviors from monopoles to multipoles.

Findings

Observation of vortex roll-ups and merging

Identification of spiral structure formation

Diverse flow phenomena from different initial conditions

Abstract

The initial-boundary value problem of the vorticity equation has been solved numerically by an iterative method. A variety of initial vorticity distributions is specified. All of them can be described by simple mathematical functions: there are a vorticity source-sink pair, circular shears out of a localised monopole, a cat's-eye topology and a few flows originating from single or multiple vortices. Our computational results show diverse flow phenomena, such as roll-ups of shear layers, vortex merging or impingement, as well as birth of spiral structures.