### Abstract

Recent experiments on a freely evolving dipolar vortex in a homogeneous shallow ﬂuid layer have clearly shown the existence and evolution of complex three-dimensional 3D ﬂow structures. The present contribution focuses on the 3D structures of a dipolar vortex evolving in a stable shallow two-layer ﬂuid. Experimentally, Stereoscopic Particle Image Velocimetry is used to measure instantaneously all three components of the velocity eld in a horizontal plane and 3D numerical simulations provide the full 3D velocity and vorticity elds over the entire ﬂow domain. Remarkably, the experimental results, supported by the numerical simulations, show to a large extent the same 3D structures and evolution as in the single-layer case. The numerical simulations indicate that the so-called frontal circulation in the two-layer ﬂuid is due to deformations of the internal interface. The 3D ﬂow structures will also affect the distribution of massless passive particles released the free surface. With numerical studies it is shown that these passive particles tend to accumulate or deplete locally where the horizontal velocity eld is not divergence-free. This is in contrast with pure two-dimensional
incompressible ﬂows where the divergence of the velocity eld is zero by denition.

Original language | English |
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Article number | 026314 |

Number of pages | 11 |

Journal | Physical review E: Statistical, nonlinear, and soft matter physics |

Volume | 82 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2010 |

### Keywords

- EWI-19487
- IR-75848
- METIS-276340

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## Cite this

Akkermans, R. A. D., Kamp, L. P. J., Clercx, H. J. H., & van Heijst, G. J. F. (2010). Three-dimensional flow in electromagnetically driven shallow two-layer fluids.

*Physical review E: Statistical, nonlinear, and soft matter physics*,*82*(2), [026314]. https://doi.org/10.1103/PhysRevE.82.026314