摘要:

The formalism for linear absolute and convective instabilities developed in plasma physics (Briggs, 1964; Bers, 1973) is extended. The conclusion is that any order saddle point as well as any singular point of a frequency as a function of a wavenumber Ω(k) may contribute to instability. Moreover, contributions may come fromk-independent branches of the dispersion relation and from regular nonsaddle points of Ω(k). Accordingly, a variety of algebraic-exponential asymptotic behaviors, in particular, purely algebraic growths and sinusoidal oscillations, of a disturbance is possible. In shear flows and stratified flows instability may also be caused by the singularities associated with critical layers. It is shown that in such flows the asymptotic pattern of a growing disturbance may vary in the direction of the shear and/or stratification. Such variability of pattern may be present only in the presence of instabilities related to the interactions between critical layers and incident amplifying waves. Otherwise the pattern is the same to within a scalar factor.

ISSN:0309-1929    

DOI:10.1080/03091928808208820

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

We consider magnetosonic-gravity waves, in an isothermal atmosphere, under a uniform, horizontal magnetic field, with horizontal wavevector in the plane of gravity and the magnetic field. It is shown (Section 2) that the logarithmic singularity, at the critical level (of type I, i.e. singular layer), only occurs for acoustically evanescent waves, of “large” horizontal wavenumberk>Ω/co, whose frequency Ω<coklies within the continuous spectrum of slow modes; for fast modes, which have a discrete spectrum, in the opposite casek<Ω/co, when a purely acoustic wave could propagate, the “logarithmic singularity” appears as a leading term of a divergent series expansion that cancels it, and the magnetosonic-gravity waves have finite amplitude and phase everywhere (Section 3). The altitudez=zc, corresponding whenk>Ω/coto the critical level (of type I, or singular layer), gives way whenk<Ω/coto a transition layer (or critical level of type II), i.e. a singularity away from the real axis, which determines the regions of convergence of low-altitudez<zcand high-altitudez>zcsolutions (Section 4). The waveform of magnetosonic-gravity waves evolves continuously across the transition layerz=zc, from nearly acoustic-gravity waves far belowz<zc, to compressive Alfvèn type far abovez≫zc, the process of “mode conversion” being illustrated in Figures 1 to 5, for vertical wavesk=0, which are not strongly reflected. Obliquek=0 magnetosonic-gravity waves are strongly reflected at the critical levelz=zc, which is of type III or reflection layer, corresponding to evanescent waves above, and below to the superposition of upward (i.e. incident) plus downward (i.e. reflected) propagating fields.

ISSN:0309-1929    

DOI:10.1080/03091928808208821

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Exploiting the (contravariant) vectorial form for vorticity and magnetic field, and co-(variant) vectorial form for the gradient of a scalar and magnetic potential, and using the geometric Lie derivative operator, conservation of various analogues of potential vorticity are discussed for a barotropic non-dissipative electrically-conducting fluid. These analogues include the potential magnetic field, helicity, magnetic helicity, and cross helicity, together with some higher order quantities. It is noted that the volume conservation of potential vorticity continues to hold in the presence of arbitrary dissipation. However, of the analogue quantities derived for the non-dissipative system, only potential magnetic field and cross helicity have invariant integrals in the presence of dissipation. We conclude that only they are true analogues of potential vorticity. Finally, a straightforward generalisation of the method for tensorial relationships is noted.

ISSN:0309-1929    

DOI:10.1080/03091928808208822

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor

摘要:

Magnetic fields induced by non-radial compressible flows (vr≡ 0, ∇·v≢ 0) in spherical conductors are shown to decay, or at least be incapable of indefinite amplification. The results herein supplement previously established antidynamo results for purely toroidal flows (vr≡ ∇·v≡ 0), with the allowance of compressibility necessitating new proofs with different senses of field decay. The poloidal field variabler·Bdecays in a global sense with an undetermined decay rate. A pointwise bound is established that limits the ultimate strength of the toroidal field scalar T, and shows that if the poloidal field is negligible and the conductivity uniform then the toroidal field decays to zero at no slower than the poloidal free-decay rate π2.

ISSN:0309-1929    

DOI:10.1080/03091928808208823

出版商:Taylor & Francis Group    

年代:1988

数据来源: Taylor