Lamination and folding in electromagnetically driven flows of specified geometries

Abstract

In this paper, a new characterisation and quantification of lamination are presented. The lamination is identified by tracking material lines and the estimation of the ratio between the length of the material lines within circles and the diameter of the circles. The quantification of the lamination rate relies on the interlaced structure of velocity and the Lagrangian acceleration, which allows the determination of the spatial variation of the Lagrangian angular velocity. Those definitions are illustrated using quasi-steady flows driven by electromagnetic forces using mono- and multi-scale configurations with turbulent-like properties. Both experimental and numerical data are used to compute folding rate intensities and lamination for a large-range length scales. Good agreement is found between grid deformation and the prediction of lamination rate, an agreement further confirmed by the lamination measure. The quantification of lamination is simple and well defined at chosen length-scales. Also, the present form applies to any lines and can be extended to 3D flows. The lamination rate process relies on physical quantities, which scale according to the structures’ length-scales. It is shown that the lamination rate increases with the reduction of the length-scales and in particular it is found that . In turbulent flows, the lamination should then be faster within small coherent structures. This quantification of lamination rate, complemented by a measure of lamination opens new routes for the description and the quantification of mixing in complex and turbulent flows.

Keywords:

• turbulent mixing
• electro- and magneto-hydrodynamic turbulence
• control

Acknowledgements

The authors acknowledge The Royal Society, the EPSRC, Dr. G. Fishpool, S. Bocquet, J.M. Garcia de la Cruz and EPSRC Grant EP/D072034/1.