Rad Rinie Akkermans

The three-dimensional structure of an electromagnetically generated dipolar vortex in a shallow fluid layer

Many experiments have been performed in electromagnetically driven shallow fluid layers to study quasi-two-dimensional (Q2D) turbulence, the shallowness of the layer commonly is assumed to ensure Q2D dynamics. In this paper, however, we demonstrate that shallow fluid flows exhibit complex three-dimensional (3D) structures. For this purpose we study one of the elementary vortex structures in Q2D turbulence, the dipolar vortex, in a shallow fluid layer. The flow evolution is studied both experimentally and by numerical simulations. Experimentally, stereoscopic particle image velocimetry is used to measure instantaneously all three components of the velocity field in a horizontal plane, and 3D numerical simulations provide the full 3D velocity and vorticity fields over the entire flow domain. It is found that significant and complex 3D structures and vertical motions occur throughout the flow evolution, i.e., during and after the forcing phase. We conclude that the bottom friction is not the main mechanism l...

Intrinsic three-dimensionality in electromagnetically driven shallow flows

The canonical laboratory set-up to study two-dimensional turbulence is the electromagnetically driven shallow one- or two-layer fluid. Stereo-Particle-Image-Velocimetry measurements in such driven shallow flows revealed strong deviations from quasi–two-dimensionality, which are attributed to the inhomogeneity of the magnetic field and, in contrast to what has been believed so far, the impermeability condition at the bottom and top boundaries. These conjectures have been confirmed by numerical simulations of shallow flows without surface deformation, both in one- and two-layer fluids. The flow simulations reveal that the observed three-dimensional structures are in fact intrinsic to flows in shallow fluids because they do not result primarily from shear at a no-slip boundary: they are a direct consequence of the vertical confinement of the flow.

The 3D structure of a dipole in a shallow two-layer fluid

The canonical laboratory setup to study two-dimensional (2D) turbulence is the electromagnetically driven shallow fluid layer. The argument used here is that whenever the vertical length scale is much smaller than the horizontal length scale the flow is presumed to behave in a 2D fashion. However, this assumption disregards the presence of a strong non-uniform magnetic field used to electromagnetically force the flow, a vertical component of the Lorentz force, and, most importantly, it oversimplifies the structure of 3D recirculating flows [1, 2]. The limitations of the single fluid layer setup have been recognized and now the two-layer fluid is commonly used for experimental 2D turbulence research. In this contribution we will study experimentally and numerically the 3D motion inside a two-layer fluid. We will discuss the behaviour of the flow when decreasing the upper fluid layer thickness in steps down from 9 mm to 3.5 mm, the latter being the commonly used upper fluid layer thickness for 2D turbulence experiments. Surprisingly, the flow structures and evolution seen in the two-layer flow are qualitatively the same as in the single-layer flow.