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AS-600-03 Resolution on Change in Academic Senate Grants Review Committee Membership (Bylaws Section I.7.a)
Eliminates an administrative position on the Grants Review Committee
Paradox of inductionless magnetorotational instability in a Taylor-Couette flow with a helical magnetic field
We consider the magnetorotational instability (MRI) of a hydrodynamically
stable Taylor-Couette flow with a helical external magnetic field in the
inductionless approximation defined by a zero magnetic Prandtl number
(\Pm=0). This leads to a considerable simplification of the problem
eventually containing only hydrodynamic variables. First, we point out that the
energy of any perturbation growing in the presence of magnetic field has to
grow faster without the field. This is a paradox because the base flow is
stable without the magnetic while it is unstable in the presence of a helical
magnetic field without being modified by the latter as it has been found
recently by Hollerbach and Rudiger [Phys. Rev. Lett. 95, 124501 (2005)]. We
revisit this problem by using a Chebyshev collocation method to calculate the
eigenvalue spectrum of the linearized problem. In this way, we confirm that MRI
with helical magnetic field indeed works in the inductionless limit where the
destabilization effect appears as an effective shift of the Rayleigh line.
Second, we integrate the linearized equations in time to study the transient
behavior of small amplitude perturbations, thus showing that the energy
arguments are correct as well. However, there is no real contradiction between
both facts. The linear stability theory predicts the asymptotic development of
an arbitrary small-amplitude perturbation, while the energy stability theory
yields the instant growth rate of any particular perturbation, but it does not
account for the evolution of this perturbation.Comment: 4 pages, 3 figures, submitted to Phys. Rev.
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