Wake Effects on Drift in Two-Dimensional Inviscid Incompressible Flows

摘要

This investigation analyzes the effect of vortex wakes on the Lagrangiandisplacement of particles induced by the passage of an obstacle in atwo-dimensional incompressible and inviscid fluid. In addition to thetrajectories of individual particles, we also study their drift and thecorresponding total drift areas in the F\"oppl and Kirchhoff potential flowmodels. Our findings, which are obtained numerically and in some regimes arealso supported by asymptotic analysis, are compared to the wakeless potentialflow which serves as a reference. We show that in the presence of the F\"opplvortex wake some of the particles follow more complicated trajectoriesfeaturing a second loop. The appearance of an additional stagnation point inthe F\"oppl flow is identified as a source of this effect. It is alsodemonstrated that, while the total drift area increases with the size of thewake for large vortex strengths, it is actually decreased for small circulationvalues. On the other hand, the Kirchhoff flow model is shown to have anunbounded total drift area. By providing a systematic account of the wakeeffects on the drift, the results of this study will allow for more accuratemodeling of hydrodynamic stirring.