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In this paper, we present a numerical investigation into the influence of electric and magnetic fields on the dynamics of a suspended liquid film that carries an electric current. A nonuniform magnetic field is considered utilizing a disk-shaped magnet located above the two-dimensional fluid. Electric and magnetic forces exerted on the fluid induce a new dynamical features. We perform a numerical study of the dynamics of such two-dimensional fluid system commonly named Liquid Film Motor. The presence of the nonuniform external magnetic field causes changes in the fluid’s behavior. Specifically, the previously symmetric vortex becomes asymmetric under the influence of the magnetic field. In this dynamic behavior, as the external magnetic field increases, the center of the vortex shifts in a direction perpendicular to the electric current passing through the fluid film. The unique combination of electric and magnetic field allows to manipulate the motion of the vortex without resorting to traditional mechanical methods. This finding implies that the motion of the vortex can be directed and controlled by adjusting the strength of the external magnetic field, without the need for direct contact with the fluid or mechanical tools. [ABSTRACT FROM AUTHOR]

Unstable flows in the runner of water turbines, such as reverse flow, vorticity and flow direction transition, are the main factors causing increased losses and decreased efficiency, and changing the geometry structure in the downstream of the runner is an important means of mitigating these instabilities. The different flow fields downstream of runners induced by different locking nut structures are numerically calculated and verified by experimental results. The flow states are evaluated in terms of characteristic quantities such as pressure gradient, swirling flow, reverse flow, and vorticity. The results show a non-negligible effect of the locking nut, which leads to a more uniform pressure distribution, increases the descending speed of the reverse flow rate, and reduces the volume and strength of the vortex. The small locking nut significantly weakens the pressure gradient, reduces the top reverse flow zone, and decreases the vortex volume at the blade flow passage outlet and the size of the downstream disturbance vortex. The extended lock nut reduces the growth rate of the vortex generation rate and the size of the partial vortex, but increases the range of the high-pressure zone, causing the bottom reverse flow and increasing the vortex. [ABSTRACT FROM AUTHOR]

The paper proposes a theory of similarity of quasi-geostrophic vortices against the background of large-scale flows. This information is useful when planning laboratory and numerical experiments to study mesoscale and submesoscale vortex dynamics of vortices interacting with currents. Special attention is paid to studying geometric similarity of phenomena. It is revealed that the complete set of dimensionless similarity numbers of baroclinic vortices includes four dimensionless parameters: the dimensionless intensity of the vortex, the geometric similarity of the background flow (the ratio of the relative vorticity to the deformation coefficient of the background flow), the coefficient of horizontal stretching of the vortex core, and the coefficient of vertical oblateness of the vortex core coinciding with the Burger number. To describe the similarity of barotropic vortices against the background of barotropic flows, the number of necessary dimensionless parameters is reduced by one number: the coefficient of vertical oblateness of the vortex core is eliminated from consideration. When studying axisymmetric vortices or vortex structures close to axisymmetric, another geometric parameter of the vortex is eliminated from consideration—the coefficient of horizontal stretching of the vortex core. As a result, the maximum possible set of similarity parameters includes four dimensionless numbers, and the minimum is two. [ABSTRACT FROM AUTHOR]