Abstract:
We investigate the magnetodynamic oscillations of a bounded annular cylinder filled with a highly dense liquid (tar) under the influence of a spatially varying magnetic field. The governing eigenvalue relation is derived, rigorously analyzed, and interpreted within a physical framework. Several well-established stability criteria from different models emerge as limiting cases and are systematically examined. The analysis covers both axisymmetric and nonaxisymmetric perturbation modes, offering a comprehensive understanding of the system's stability characteristics. The results indicate that the magnetic field exerts a stabilizing effect, while surface tension plays a dual role—suppressing short-wavelength perturbations but amplifying long-wavelength ones. This research has broad implications across engineering and industrial domains, including optimizing electrical generator performance, advancing plasma control techniques, and improving the understanding of magnetically influenced fluid dynamics. Moreover, its findings extend to diverse applications, from aerodynamics (such as airflow over wings) to pipeline design, offering new insights into complex magnetic systems within applied physics, electrical engineering, and magnetism.
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