Inertial perturbations to inertialess magnetohydrodynamic and rotating flows

Inertial perturbations to two types of inertialess, steady flows of viscous, incompressible fluids in variable-area rectangular ducts with small divergences are studied. The first type is magnetohydrodynamic flow; there are strong transverse magnetic fields, the fluids are electrically conducting, and the walls of the ducts are rotating rapidly about axes perpendicular to their centerline. On the basis of the asymptotic solutions for the intertialess flows, small-inertia asymptotic expansions are constructed to include the largest possible inertial disturbances that have been neglected in the inertialess approximation. For infinitely long ducts, inertial perturbations are found to decay faster with distance than the inertialess solutions in all the flow subregions for both types of flow and for all divergences considered. For the magnetohydrodynamic flows, the ratio of the first inertial perturbations to the corresponding inertialess solutions are found to decay more slowly as the divergence of the duct becomes smaller; while for the rotating flows, the reverse is true. Solutions for the first-order terms in the small-inertia asymptotic expansions are found in every flow-carrying subregion of the duct. These solutions can be used as correction terms to the inertialess solutions when inertial effects are small but significant