Wake Effects on Drift in Two-Dimensional Inviscid Incompressible Flows

TL;DR

This paper examines how vortex wakes influence particle drift in two-dimensional inviscid flows, revealing complex trajectories and varying drift areas, which improve understanding of hydrodynamic stirring effects.

Contribution

It provides a systematic analysis of wake effects on particle drift in potential flow models, combining numerical and asymptotic methods, and compares wake and wakeless flows.

Findings

Particles follow more complex trajectories with a second loop due to vortex wakes.

Total drift area increases with wake size for large vortex strengths, decreases for small circulation.

Kirchhoff flow model exhibits unbounded total drift area.

Abstract

This investigation analyzes the effect of vortex wakes on the Lagrangian displacement of particles induced by the passage of an obstacle in a two-dimensional incompressible and inviscid fluid. In addition to the trajectories of individual particles, we also study their drift and the corresponding total drift areas in the F\"oppl and Kirchhoff potential flow models. Our findings, which are obtained numerically and in some regimes are also supported by asymptotic analysis, are compared to the wakeless potential flow which serves as a reference. We show that in the presence of the F\"oppl vortex wake some of the particles follow more complicated trajectories featuring a second loop. The appearance of an additional stagnation point in the F\"oppl flow is identified as a source of this effect. It is also demonstrated that, while the total drift area increases with the size of the wake for large vortex strengths, it is actually decreased for small circulation values. On the other hand, the Kirchhoff flow model is shown to have an unbounded total drift area. By providing a systematic account of the wake effects on the drift, the results of this study will allow for more accurate modeling of hydrodynamic stirring.