Transition between two-dimensional and three-dimensional MHD turbulence under imposed magnetic field: liquid metal experiment in a rectangular box.
Final Report Abstract
During the course of the project, the following tasks were successfully achieved: 1. Characterization of three-dimensionality and transition to turbulence of an electrically driven vortex pair. 2. Construction of two successive versions of a modular experimental facility with extensive diagnosis techniques to study liquid metal flows in high magnetic fields. 3. Experimental characterization of the mechanisms of the transition to three-dimensionality in a wall bounded array of electrically driven vortices. 4. Discovery of three-dimensional steady MHD vortices. 5. Derivation of an analytical model to explain the appearance of weak three-dimensionality in MHD, which applies to other flows such as rotating flows. Points 2-4 follow the initial layout of the project rather closely while points 1, 5-6 arose partly in the light of important new results obtained in this project and in projects led in parallel to the present one, that were therefore not known when the initial plan was established. Firstly the preliminary experimental setup which was used in 1 was initially planned as a test for the technologies used in the construction of the main setup. However, this early implementation proved to be of sufficiently high quality to enable us to characterize two-dimensional regimes of an electrically driven vortex pair as well as the effects of three-dimensionality in this configuration. We therefore seized this early opportunity to partially achieve one of the main goals of the project and reveal the previously unknown mechanism of transition to turbulence of a wall bounded vortex pair, which wasn’t known in this configuration. We published this work in Phys. Rev. E. Secondly, the first phase of the project, where the flow was electrically forced gave precise answers on the aspects of the transition between two and three-dimensional MHD turbulence which this project aimed at addressing, and which we were able to publish in the prestigious Phys. Rev. Lett. In the process, further questions were raised, in particular on the influence of 3D recirculations, which the mechanical forcing initially planned in the second phase would not have helped to address. It was therefore deemed more important to build the second version of the experiment with the same electrical forcing but to focus on ultrasound velocimetry to be able to diagnose the flow in the bulk. Finally we were able to derive a theoretical model which proves that some of the mechanisms found in the first phase were common to other types of flows such as flows in rotation. This model was published in EPL and broadens the impact of the results found in MHD to a much wider scientific community. In summary, it is fair to say that this project has delivered well above initial expectations. Not only did it allow us to unveil some of the previously unknown mechanisms acting at the transition between two and three-dimensional turbulence in the presence of walls but it made a very clear point that walls are a key component in the 2D-3D transition not only in MHD but also in non-MHD and rotating flows. Two types of three-dimensionalities were distinguished: a strong and a weak one. The strong one involves disruption of 2D structures through instability mechanism and was known from numerical simulations without walls. The first one on the other hand involves mild velocity variations in the third direction and we made clear that it was triggered by the presence of walls through a complex mechanism involving 3D recirculation that is active well beyond the field of MHD. This project has not only brought significant progress in the question of the dimensionality of MHD flows but shown that the problem was more universal and that it could not be realistically be considered without taking boundaries into account. On the top of this scientific achievement, the experimental method which we developed, based on a high number of simultaneous measurements of electric potential offers a way of extensively exploring liquid metal flows which opens vast possibilities for research in the fields of turbulence and vortex dynamics in general.
Publications
- An experiment on MHD Turbulence at low Magnetic Reynolds number. In:
Proceedings of the 6th International Congress on Iindustrial and Aplied Mathematics (ICIAM), Zürich, Switzerland 2007, p. 129.
R Klein, A. Pothérat
- An experiment on the transition between two-dimensional and threedimensional forced MHD Turbulence. In: Proceedings of the 7th International PAMIR conference on fundamental and applied magnetohydrodynamics, Ramatuelle, France 2008, pp. 461–465
R Klein, A. Pothérat
- Numerical Simulations of a Cylinder Wake Under Strong Axial Magnetic
Field. Physics of Fluids (1994-present), Vol. 20. 2008, Issue 1: 017104.
V. Dousset, A. Pothérat
(See online at https://dx.doi.org/10.1063/1.2831153) - Experiment on an elecrically driven, confined vortex pair. Physical Review E, Vol. 79. 2009, Issue 1, 016304.
R. Klein, A. Pothérat, A. Alferjonok
(See online at https://dx.doi.org/10.1103/PhysRevE.79.016304) - Spectral methods based on the least dissipative modes for wall bounded MHD flows. Theoretical and Computational Fluid Dynamics, Vol. 23. 2009, Issue 6, pp. 535-555.
V. Dymkou, A. Pothérat
(See online at https://dx.doi.org/10.1007/s00162-009-0159-9) - Transition between two and three-dimensional MHD flows. In 3rd
international conference on Bifurcations and Instabilitiesin Fluid Dynamics. page 77, Nottingham, UK, 2009.
A. Pothérat, R. Klein, V. Dymkou
- Appearance of Three Dimensionality in Wall-bounded MHD Flows. Physical Review Letters, Vol. 104.2010, Issue 3, 034502.
R. Klein, A. Pothérat
(See online at https://dx.doi.org/10.1103/PhysRevLett.104.034502) - Direct numerical simulations of low-Rm MHD turbulence based on the least dissipative modes. Journal of Fluid Mechanics, Vol. 655. 2010, pp 174- 197.
A. Pothérat, V. Dymkou
(See online at https://dx.doi.org/10.1017/S0022112010000807) - MHD experiments on quasi two dimensional and three-dimensional liquid metal flows. PhD Thesis, Coventry University, UK 2010.
R. Klein
- Transition between two and three-dimensional wall-bounded MHD
flows. In: 8th EUROMECH Fluid Mechanics Conference Bad Reichenhall, 2010.
A. Pothérat, R. Klein, V. Dymkou
- Keynote lecture: Magnetohydrodynamic turbulence at low Rm: The role of boundaries. In: Proceedings of the 8th International PAMIR conference on fundamental and applied magnetohydrodynamics
pages 7–12 Borgo, France 2011.
A. Pothérat
- Appearance of three-dimensionality in a square array of MHD
vortices in a cubic Container. In: 9th EUROMECH Fluid Mechanics Conference Rome, Italy, 2012.
A. Potherat, R. Klein
- Characterisation of the flow around a truncated cylinder in a duct in a spanwise magnetic field. Journal of Fluid Mechanics, Vol. 691. 2012, pp 341- 367.
V. Dousset, A. Pothérat
(See online at https://dx.doi.org/10.1017/jfm.2011.478) - Low Rm MHD turbulence: the role of boundaries. Magnetohydrodynamics, Vol. 48. 2012, No. 1, pp. 13–23.
A. Pothérat
- Three-dimensional effects in quasi-two dimensional flows: Recirculations and Barrel effects. EPL (Europhysics Letters), Vol. 98. 2012, Number 6: 64003.
A. Pothérat
(See online at https://doi.org/10.1209/0295-5075/98/64003) - Why, how and when MHD turbulence at low Rm becomes three-dimensional. Journal of Fluid Mechanics, Vol. 761. 2014, pp 168-205.
A. Pothérat, R. Klein
(See online at https://doi.org/10.1017/jfm.2014.620)
