Optimal energy amplification of rotating magnetohydrodynamic channel flows

The stability behaviors of rotating magnetohydrodynamic channel flows have broad relevance to various applications, particularly in microfluidic systems, such as lab-on-a-chip platforms used in engineering and biomedical devices. We extend the work Sengupta and Ghosh, “Linear stability of a rotating channel flow subjected to a static magnetic field,” Phys. Fluids 34, 054116 (2022) by adopting the non-modal stability approach to examine the stability of an incompressible fluid flow under the influence of spanwise system rotation and a static transverse magnetic field. Transforming the perturbed Navier–Stokes equations into the Orr–Sommerfeld framework, unlike modal analysis, we investigate short-time energy instabilities and explore the underlying mechanisms responsible for transient energy amplification by applying the Chebyshev spectral collocation method. We analyze how the non-normality of spanwise rotation controls the energy instability at low Reynolds numbers over short time intervals. At low Hartmann numbers, significant transient energy amplification occurs due to the combined effects of inertial and Coriolis forces. However, when the magnetic field becomes sufficiently strong, the transient energy growth is effectively suppressed by electromagnetic damping. The optimal initial perturbation and its corresponding response, as determined by our analysis, exhibit roll-cell structures in the form of secondary vortices, whose size progressively decreases with increasing Hartmann number. We further estimate the influence of external harmonic forcing by evaluating the resolvent norm and the numerical range associated with the modified stability operator.