Study of instabilities and transitions for a family of quasi-two-dimensional magnetohydrodynamic flows based on a parametrical model

In this study, flow phenomena associated with inflectional and boundary-layer instabilities, as well as a mixed instability mode in quasi-two-dimensional magnetohydrodynamic flows in a rectangular duct are accessed with the help of a parametrical model, where the basic velocity profile with near-wall jets and associated points of inflection are produced by imposing an external flow-opposing force. By varying this force, various instability modes and transition scenarios are reproduced. First, linear stability analysis is performed and then nonlinear effects are studied using direct numerical simulation for Hartmann numbers 100 and 200 and Reynolds numbers from 1800 to 5000. A special attention is paid to the location of the inflection point with respect to the duct wall. A more complex flow dynamics, including various vortex-wall and vortex-vortex interactions, and even negative turbulence production are observed and analyzed as the inflection point approaches the wall. The analysis of obtained results and their comparison with relevant data for magnetohydrodynamic duct flows gain an insight into what is typically called "jet instability," including linear and nonlinear mechanisms.