Absolute versus convective helical magnetorotational instabilities in Taylor-Couette flows

Abstract

We study magnetic Taylor-Couette flow in a system having nondimensional radii $r_i=1$ and $r_o=2$, and periodic in the axial direction with wavelengths $h\ge 100$. The rotation ratio of the inner and outer cylinders is adjusted to be slightly in the Rayleigh-stable regime, where magnetic fields are required to destabilize the flow, in this case triggering the axisymmetric helical magnetorotational instability (HMRI). Two choices of imposed magnetic field are considered, both having the same azimuthal component $B_{\varphi }=r^{-1}$, but differing axial components. The first choice has $B_z=0.1$, and yields the familiar HMRI, consisting of unidirectionally traveling waves. The second choice has $B_z\approx 0.1\sin (2\pi z/h)$, and yields HMRI waves that travel in opposite directions depending on the sign of $B_z$. The first configuration corresponds to a convective instability, the second to an absolute instability. The two variants behave very similarly regarding both linear onset as well as nonlinear equilibration.

submitted to Fluid Dyn Res

References in corpus (5)

• High Reynolds number Taylor-Couette turbulence
• Experimental evidence for magnetorotational instability in a helical magnetic field
• Observation of magnetocoriolis waves in a liquid metal Taylor-Couette experiment
• Observation of a Free-Shercliff-Layer Instability in Cylindrical Geometry
• Absolute versus convective helical magnetorotational instability in a Taylor-Couette flow

Cited by in corpus (2)

• Stability and instability of hydromagnetic Taylor-Couette flows
• Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow