Three-dimensional flow in electromagnetically driven shallow two-layer fluids

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 ͑3D͒ 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 field in a horizontal plane and 3D numerical simulations provide the full 3D velocity and vorticity fields 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 at the free surface. With numerical studies it is shown that these passive particles tend to accumulate or deplete locally where the horizontal velocity field is not divergence-free. This is in contrast with pure two-dimensional incompressible flows where the divergence of the velocity field is zero by definition.

Onset of three-dimensionality in electromagnetically driven thin-layer flows

“…One common paradigm for such studies is the electromagnetically driven thin-layer flow, in which a thin layer of conductive fluid is placed in a magnetic field and stirred by the Lorentz forces that arise when a current is passed through the fluid. [8][9][10][11][12][13][14][15][16][17][18][19] Studying twodimensional flow in a three-dimensional laboratory device, however, is necessarily an approximation. A key question for this model system is its faithfulness: how well do thin-layer flows approximate two-dimensionality?…”

Energy spectra and turbulence generation in the wake of magnetic obstacles

“…In great number of industrial applications where the electrically conductive fluids are used (e.g., crystal growth, heat exchangers, latest generation of fusion reactors), heat transfer plays a central role. Generic examples also include fully developed turbulent channel flows subjected to uniform magnetic fields of different orientations (Brouillette and Lykoudis, 6 Reed and Lykoudis, 7 Shimomura, 8 Lee and Choi, 9 Kenjereš et al, 10 Boeck et al 11 ) and electromagnetically driven multiscale isothermal shallow (Rossi et al, 12,13 Lardeau et al, 14 Rossi et al, 15 Akkermans et al, 16 Duran-Matute et al 17 ) or deep (Kenjereš et al 18 ) layers with heat transfer ). The flow of electrically conducting fluids where there is an internal blockage can be generally divided into two categories.…”

Direct experimental visualization of the global Hamiltonian progression of two-dimensional Lagrangian flow topologies from integrable to chaotic state

“…The belt-motor systems (Maxon Motor, Germany) are placed in an external annular region enclosing the flow domain. Two layers of fluid are used to as closely as possible create a 2D flow in the fluid surface: 47 glycerolwater solution (66% by volume) at the bottom layer to dampen bottom-wall friction effects; silicon oil (type AK10000 by Wacker, Germany) at the top layer serving as the fluid of interest. These liquids are immiscible so that the layers remain separated throughout the experiment.…”