Enhancement of the Benjamin-Feir instability with dissipation

It is shown that there is an overlooked mechanism whereby some kinds of dissipation can enhance the Benjamin-Feir instability of water waves. This observation is new, and although it is counterintuitive, it is due to the fact that the Benjamin-Feir instability involves the collision of modes with opposite energy sign (relative to the carrier wave), and it is the negative energy perturbations which are enhanced.Comment: 15 pages, 2 figures To download more papers, go to http://www.cmla.ens-cachan.fr/~dias. Physics of Fluids (2007) to appea

Magnetoelliptic Instabilities

We consider the stability of a configuration consisting of a vertical magnetic field in a planar flow on elliptical streamlines in ideal hydromagnetics. In the absence of a magnetic field the elliptical flow is universally unstable (the ``elliptical instability''). We find this universal instability persists in the presence of magnetic fields of arbitrary strength, although the growthrate decreases somewhat. We also find further instabilities due to the presence of the magnetic field. One of these, a destabilization of Alfven waves, requires the magnetic parameter to exceed a certain critical value. A second, involving a mixing of hydrodynamic and magnetic modes, occurs for all magnetic-field strengths. These instabilities may be important in tidally distorted or otherwise elliptical disks. A disk of finite thickness is stable if the magnetic fieldstrength exceeds a critical value, similar to the fieldstrength which suppresses the magnetorotational instability.Comment: Accepted for publication in Astrophysical Journa

On over-reflection and generation of Gravito-Alfven waves in solar-type stars

The dynamics of linear perturbations is studied in magnetized plasma shear flows with a constant shearing rate and with gravity-induced stratification. The general set of linearized equations is derived and the two-dimensional case is considered in detail. The Boussinesq approximation is used in order to examine relatively small-scale perturbations of low-frequency modes: Gravito-Alfven waves (GAW) and Entropy Mode (EM) perturbations. It is shown that for flows with arbitrary shearing rate there exists a finite time interval of non-adiabatic evolution of the perturbations. The non-adiabatic behavior manifests itself in a twofold way, viz. by the over-reflection of the GAWs and by the generation of GAWs from EM perturbations. It is shown that these phenomena act as efficient transformers of the equilibrium flow energy into the energy of the perturbations for moderate and high shearing rate solar plasma flows. Efficient generation of GAW by EM takes place for shearing rates about an order of magnitude smaller than necessary for development of a shear instability. The latter fact could have important consequences for the problem of angular momentum redistribution within the Sun and solar-type stars.Comment: 20 pages (preprint format), 4 figures; to appear in The Astrophysical Journal (August 1, 2007, v664, N2 issue

Growing hydrodynamic modes in Keplerian accretion disks during secondary perturbations: Elliptical vortex effects

The origin of hydrodynamic turbulence, and in particular of an anomalously enhanced angular momentum transport, in accretion disks is still an unsolved problem. This is especially important for cold disk systems which are practically neutral in charge and therefore turbulence can not be of magnetohydrodynamic origin. While the flow must exhibit some instability and then turbulence in support of the transfer of mass inward and angular momentum outward, according to the linear perturbation theory, in absence of magnetohydrodynamic effects, it should always be stable. We demonstrate that the three-dimensional secondary disturbance to the primarily perturbed disk, consisting of elliptical vortices, gives significantly large hydrodynamic growth in such a system and hence may suggest a transition to an ultimately turbulent state. This result is essentially applicable to accretion disks around quiescent cataclysmic variables, in proto-planetary and star-forming disks, the outer region of disks in active galactic nuclei, where the gas is significantly cold and thus the magnetic Reynolds number is smaller than 10^4.Comment: 21 pages including 4 figures, aastex format; Accepted for publication in The Astrophysical Journa

Microwave control electrodes for scalable, parallel, single-qubit operations in a surface-electrode ion trap

We propose a surface ion trap design incorporating microwave control electrodes for near-field single-qubit control. The electrodes are arranged so as to provide arbitrary frequency, amplitude and polarization control of the microwave field in one trap zone, while a similar set of electrodes is used to null the residual microwave field in a neighbouring zone. The geometry is chosen to reduce the residual field to the 0.5% level without nulling fields; with nulling, the crosstalk may be kept close to the 0.01% level for realistic microwave amplitude and phase drift. Using standard photolithography and electroplating techniques, we have fabricated a proof-of-principle electrode array with two trapping zones. We discuss requirements for the microwave drive system and prospects for scalability to a large two-dimensional trap array.Comment: 8 pages, 6 figure

Quadratic invariants for discrete clusters of weakly interacting waves

We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix with entries 1, −1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N − M* ≥ N − M, where M* is the number of linearly independent rows in Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney–Hasegawa–Mima wave model, and by showing a classification of small (up to three-triad) clusters

The Magnetohydrodynamic Kelvin-Helmholtz Instability: A Three-Dimensional Study of Nonlinear Evolution

We investigate through high resolution 3D simulations the nonlinear evolution of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz instability. We confirm in 3D flows the conclusion from our 2D work that even apparently weak magnetic fields embedded in Kelvin-Helmholtz unstable plasma flows can be fundamentally important to nonlinear evolution of the instability. In fact, that statement is strengthened in 3D by this work, because it shows how field line bundles can be stretched and twisted in 3D as the quasi-2D Cat's Eye vortex forms out of the hydrodynamical motions. In our simulations twisting of the field may increase the maximum field strength by more than a factor of two over the 2D effect. If, by these developments, the Alfv\'en Mach number of flows around the Cat's Eye drops to unity or less, our simulations suggest magnetic stresses will eventually destroy the Cat's Eye and cause the plasma flow to self-organize into a relatively smooth and apparently stable flow that retains memory of the original shear. For our flow configurations the regime in 3D for such reorganization is $4\lesssim M_{Ax} \lesssim 50$, expressed in terms of the Alfv\'en Mach number of the original velocity transition and the initial Alfv\'en speed projected to the flow plan. For weaker fields the instability remains essentially hydrodynamic in early stages, and the Cat's Eye is destroyed by the hydrodynamic secondary instabilities of a 3D nature. Then, the flows evolve into chaotic structures that approach decaying isotropic turbulence. In this stage, there is considerable enhancement to the magnetic energy due to stretching, twisting, and turbulent amplification, which is retained long afterwards. The magnetic energy eventually catches up to the kinetic energy, and the nature of flows become magnetohydrodynamic.Comment: 11 pages, 12 figures in degraded jpg format (2 in color), paper with original quality figures available via ftp at ftp://ftp.msi.umn.edu/pub/users/twj/mhdkh3dd.ps.gz or ftp://canopus.chungnam.ac.kr/ryu/mhdkh3dd.ps.gz, to appear in The Astrophysical Journa