We investigate the flow of two immiscible, viscous fluids in a rotating Hele-Shaw cell, when one of the fluids is a ferrofluid and an external magnetic field is applied. The interplay between centrifugal and magnetic forces in determining the instability of the fluid-fluid interface is analyzed. The linear stability analysis of the problem shows that a nonuniform, azimuthal magnetic field, appl...

New flows and instabilities are demonstrated for magnetic fluids and by dual analogy to dielectric fluids. If a fluid drop is contained in a thin gap between two glass plates (Hele–Shaw cell) with a simultaneously applied in-plane rotating field and a DC axial field, smooth spirals or an abrupt transformation to many small droplets can occur. A preliminary minimum magnetization and surface ener...

the effect of weak shear thickening and shear thinning on the stability of the taylor-couette flow is explored for a carreau-bird fluid in the narrow-gap limit. the galerkin projection method is used to derive a low-order dynamical system from the conservation of mass and momentum equations. in comparison with the newtonian system, the present equations include additional nonlinear coupling in ...

Perturbations of rotating relativistic stars can be classified by their behavior under parity. For axial perturbations (r-modes), initial data with negative canonical energy is found with angular dependence e for all values of m ≥ 2 and for arbitrarily slow rotation. This implies instability (or marginal stability) of such perturbations for rotating perfect fluids. This low m-instability is str...

We study the three-dimensional Navier--Stokes equations of rotating incompressible viscous fluids with periodic boundary conditions. The asymptotic expansions, as time goes to infinity, are derived in all Gevrey spaces for any Leray-Hopf weak solutions terms oscillating, exponentially decaying functions. results established non-zero rotation speeds, and both cases without zero spatial average s...