Most of astrophysical objects involve different kinds of plasma flows. Recently it was fully realized that collective phenomena in flows with spatially inhomogeneous velocities (shear flows hereafter referred as SF) are characterized by remarkable, so called "nonmodal" processes, related with non-self-adjointness of linear dynamics of perturbations. Namely, it was found that SF: exchange energy with sound waves (Butler & Farrell 1992); couple different collective modes with one another and lead to their mutual transformations (Chagelishvili et al. 1996); generate nonperiodic, vortical modes of collective behaviour (so called "shear vortices" Rogava et al. 1998) - which eventually may or may not acquire wave-like features; excite beat wave phenomena both in neutral fluids (Rogava & Mahajan 1997) and plasmas (Poedts et al. 1998).
These processes take place not only in neutral fluids (Butler & Farrell 1992; Rogava & Mahajan 1997), standard MHD (Chagelishvili et al. 1996; Rogava et al. 1996; Tatsuno et al. 2001) and electrostatic plasmas (Rogava et al. 1998; Volponi et al. 2000; Mikhailenko et al. 2000), but also in strongly magnetized plasmas with anisotropic pressure (Chagelishvili et al. 1997), electron-positron plasmas (Mahajan et al. 1997) and dusty plasmas (Poedts et al. 2000). The possible role of these phenomena in astrophysical context was immediately realized and a number of astrophysical applications, including pulsar magnetospheric plasmas (Mahajan et al. 1997), solar atmospheric phenomena (Poedts et al. 1998; Rogava et al. 2000) and galactic gaseous disk dynamics (Rogava et al. 1999) appeared within a span of years.
One of the main shortcomings of all these studies, stemming from the very design of nonmodal schemes, is that the description is given in the wave number space (k-space), the knowledge about the appearance of shear-induced phenomena in the real, physical space is lacking. Two more serious limitations of these investigations are related with the neglect of the back reaction of perturbations on the mean flow and with the omission of viscous dissipation effects. However recently a successful effort was made in the direction of spatial visualization of the shear-induced wave transformations (Bodo et al. 2001), became clear that shear-induced processes in SF are quite robust and easily recognizable, even in the presence of quite heavy dissipation.
All these processes were studied predominantly for simple,
plane-parallel flow geometries with linear velocity shear
profiles. However, recently, a new method was developed
(Mahajan & Rogava 1999), which allows a local analysis of the dynamics
of linearized perturbations in SF with arbitrarily complex
geometry and kinematics
.
It was found that a
slight deviation from the plane-parallel mode of motion brings
into the game a variety of new, exotic and asymptotically
persistent modes of collective behavior. Still the systematic
investigation of shear-induced processes in kinematically complex
SF is a challenging task in a state of infancy. The original study
has been limited to two-dimensional flow patterns of neutral
fluids (Mahajan & Rogava 1999).
One begins to wonder whether those astrophysical systems, where kinematically complex modes of plasma motion are definitely present - e.g., astrophysical jets (Ferrari 1998) or solar tornados (Pike & Mason 1998; Velli & Liewer 1999) - might sustain these collective phenomena and what kind of observational consequences could they lead to.
In this paper we consider interaction of a helical flow with Alfvén waves generated within the flow. This problem is actual in plasma physics and plasma astrophysics from experimental/observational, theoretical and numerical points of view.
We are used to observe Alfvén waves, being in interaction with plasma flows, in different astrophysical situations. For example, for the long time it is known that the Sun radiates Alfvén waves: outward propagating Alfvén waves are routinely observed in the solar wind flow at r>0.3 AU (Hollweg 1990). The observations of quasiperiodic pulsed ionospheric flows (PIF) have shown that the PIF are driven and correlated with Alfvénic fluctuations observed in the upstream solar wind (Prikryl et al. 2002). While the observations of the solar transition region (Peter 2001) imply that structuring of the transition region involves closed loops and coronal funnels showing unambiguous evidence for the presence of passing Alfvén waves.
In the theoretical domain the problem of the interaction between
Alfvén waves and ambient flows is quite popular topic of studies
in the wide range of applications including different kinds of
laboratory, geophysical and astrophysical plasma flows. Recent
studies of toroidal flows in axisymmetric tokamaks (van der Holst et al. 2000),
for instance, revealed that these flows generate low-frequency
Alfvén waves. The problem of Alfvén waves sustained by plasma
flows is especially popular in the context of solar physics. It is
argued that chromosphere and transition region flows are primary
energy sources for the fast solar wind; while Alfvén waves,
generated by post-reconnection processes, are continuously
interacting with these flows (Ryutova et al. 2001). In accretion disks
Alfvén waves also seem to be actively interacting with the disk
flow - they are found to be unstable both in high-
(Balbus & Hawley 1991) and low-
(Tagger et al. 1992) disks. Most recently
it was claimed that the Accretion-Ejection Instability
(Tagger & Pellat 1999) can extract accretion energy and angular momentum
from magnetized disk, generate Alfvén waves and "feed" the disk
corona with them (Varnièr & Tagger 2002).
Currently sophisticated numerical codes are developed, which allow to study the propagation of Alfvén waves along an open magnetic flux tube (Saito et al. 2001). These simulations are aimed to clarify mechanisms of the coronal heating and of the formation of solar plasma flow patterns: viz. solar spicules, macrospicules and solar tornadoes. More general numerical tools, like FINESSE and PHOENIX, aimed to study waves and instabilities in different kinds of flows, were very recently developed (Belien et al. 2002). We assume that all these numerical tools could also be used in a number of astrophysical applications involving "parent" flows and "inborn" Alfvén waves interacting with each other.
Most of above-cited studies considered simple (plane-parallel or locally plane-parallel) kinds of flows and the processes were treated by means of usual normal-mode analysis. The purpose of this paper (Paper I) is to study "nonmodal'' evolution of Alfvén waves in swirling flows and to show that these flows may operate as efficient "amplifiers" of Alfvén waves.
In the next section we develop the mathematical formalism and derive general equations governing the evolution of Alfvén waves in helical flows. However, the third section is dedicated to the study of the simpler example of a parallel SF ("pure outflow"). Still, even in this simple case, we find that the amplification of Alfvén waves takes place. The amplification mechanism is linear, transient and can be described by appealingly simple mathematics. The amplification occurs within a relatively brief time interval and it appears as an abrupt, burst-like increase of the wave amplitude. It is tempting to argue that individual acts of wave amplifications, occurring sequentially, may ignite the "chain reaction" of nonmodal cascade amplification of Alfvén waves.
The fourth section of the paper is dedicated to fully helical SF. We show that when SF are helical ("outflow + rotation") there appear new classes of shear instabilities capable of generating high-amplitude Alfvén waves. The presence of differential rotation is crucial for these instabilities and in certain cases the instability is of parametric nature. These instabilities are powerful, often have a "resonant'' nature and are exclusively related with the kinematic complexity of "parent'' shear flows.
The fifth section of the paper contains discussion of the obtained results and of their possible astrophysical applications. We argue that such wave amplification processes may have various astrophysical manifestations including large amplitude Alfvén waves actually observed in the solar atmosphere (Balogh et al. 1995). They could provide the necessary seeding for the development of MHD turbulence in hydromagnetic shear flows. These processes may be present and may lead to perceptible morphological variety and diverse observational appearances in various kinds of "accretion-ejection'' flows: innermost regions of accretion disks, disk-jet transition regions, accretion columns in X-ray pulsars and cataclysmic variables, inner regions of galactic gaseous disks, etc.
This paper will be followed by the second one (Paper II), where we will consider the same flow structure but allow the perturbations to be fully compressible, bringing on-stage another two additional linear MHD wave modes - the slow and fast magnetosonic waves.
Copyright ESO 2003