Non linear evolution of Alfvén wave in the solar atmosphere

We investigate the non-linear evolution of Alfvén waves in the solar atmosphere and wind, from the photosphere out to the Earth’s orbit. Photosphere and chromosphere are modeled as isothermal layers in static equilibrium, connecting across the transition region with a corona and wind. Nonlinear coupling between waves propagating in opposite directions is modeled by a phenomenological term containing an integral turbulent length scale. Spectrum modifications remain similar to what is found in a linear analysis and some characteristic features - i.e. oscillations at higher frequencies- persist despite nonlinear interactions

Propagation and dissipation of Alfvén waves in stellar atmospheres permeated by isothermal winds

We investigate the nonlinear evolution of Alfvén waves in a radially stratified isothermal atmosphere with wind, from the atmospheric base out to the Alfvénic point. Nonlinear interactions, triggered by wave reflection due to the atmospheric gradients, are assumed to occur mainly in directions perpendicular to the mean radial magnetic field. The nonlinear coupling between waves propagating in opposite directions is modeled by a phenomenological term, containing an integral turbulent length scale, which acts as a dissipative coefficient for waves of a given frequency. Although the wind acceleration profile is not determined self-consistently one may estimate the dissipation rate inside the layer and follow the evolution of an initial frequency spectrum. Reflection of low frequency waves drives dissipation across the whole spectrum, and steeper gradients, i.e. lower coronal temperatures, enhance the dissipation rate. Moreover, when reasonable wave amplitudes are considered, waves of all frequencies damp at the same rate and the spectrum is not modified substantially during propagation. Therefore the sub-Alfvénic coronal layer acts differently when waves interact nonlinearly, no longer behaving as a frequency dependent filter once reflection-generated nonlinear interactions are included, at least within the classes of models discussed here

What can we infer about the underlying physics from burst distributions observed in an RMHD simulation ?

We determine that the sizes of bursts in mean-square current density in a reduced magnetohydrodynamic (RMHD)simulation follow power-law probability density function (PDF). The PDFs for burst durations and waiting time between bursts are clearly not exponential and could also be power-law. This suffices to distinguish their behaviour from the original Bak et al. sandpile model which had exponential waiting time PDFs. However, it is not sufficient to distinguish between turbulence, some other SOC-like models, and other red noise sources.Comment: In press, Planetary and Space Science. Proceedings of a session at European Geophysical Society General Assembly, Nice, 200

The third-order law for increments in magnetohydrodynamic turbulence with constant shear

We extend the theory for third-order structure functions in homogeneous incompressible magnetohydrodynamic (MHD) turbulence to the case in which a constant velocity shear is present. A generalization is found of the usual relation [Politano and Pouquet, Phys. Rev. E, 57 21 (1998)] between third-order structure functions and the dissipation rate in steady inertial range turbulence, in which the shear plays a crucial role. In particular, the presence of shear leads to a third-order law which is not simply proportional to the relative separation. Possible implications for laboratory and space plasmas are discussed

Hearing silent voices: talk and silence as data in 'Skills for Life' classrooms

This paper examines how innovative social-constructivist pedagogies in adult numeracy education are generating new types of naturalistic linguistic data which enable students? previously silent voices to be heard. However, it also argues that some students' voices are still silent, and that these silences can be regarded as data which is as illuminating as episodes of talk. The new pedagogies, recently extended from school mathematics to adult numeracy, provide opportunities for adult students to work together to solve mathematical problems in classrooms formerly characterised by individualised learning in near silence. Audio-data collected in such classrooms is used to demonstrate how students' discussions offer previously unavailable insights into their experiences of learning. Informal numeracy practices, usually carried out 'invisibly' in one's head, are rendered audible as students 'think aloud', and their hitherto unheard voices give glimpses of their relationships with each other, with learning, and with the wider social structures of curriculum and accreditation. In particular, the rich and diverse linguistic repertoire through which they reflect and maintain these relationships offers a challenge to the discourses of deficit which predominate in this sector. Conversely, however, the voices of some participating students are absent from the data, and their silence is key to revealing new forms of inequality that may emerge from social-constructivist pedagogies. Thus the paper concludes by arguing that silence should not be regarded as an absence of data, but as data in itself. This is illustrated by a reflective account of the author's research journey in learning to 'hear' these silences, and contrasts perceptions of participants who might be expected to be silent (in this case a deaf student) with those whose silences were unanticipated. The limitations and affordances of collecting audio-data versus video-data are discussed in relation to this aspect of the study

Properties of mass-loading shocks, 2. Magnetohydrodynamics

The one-dimensional magnetohydrodynamics of shocked flows subjected to significant mass loading are considered. Recent observations at comets Giacobini-Zinner and Halley suggest that simple nonreacting MHD is an inappropriate description for active cometary bow shocks. The thickness of the observed cometary shock implies that mass loading represents an important dynamical process within the shock itself, thereby requiring that the Rankine-Hugoniot condition for the mass flux possess a source term. In a formal sense, this renders mass-loading shocks qualitatively similar to combustion shocks, except that mass loading induces the shocked flow to shear. Nevertheless, a large class of stable shocks exist, identified by means of the Lax conditions appropriate to MHD. Thus mass-loading shocks represent a new and interesting class of shocks, which, although found frequently in the solar system, both at the head of comets and, under suitable conditions, upsteam of weakly magnetized and nonmagnetized planets, has not been discussed in any detail. Owing to the shearing of the flow, mass-loading shocks can behave like switch-on shocks regardless of the magnitude of the plasma beta. Thus the behavior of the magnetic field in mass-loading shocks is significantly different from that occurring in nonreacting classical MHD shocks. It is demonstrated that there exist two types of mass-loading fronts for which no classical MHD analogue exists, these being the fast and slow compound mass-loading shocks. These shocks are characterized by an initial deceleration of the fluid flow to either the fast or the slow magnetosonic speed followed by an isentropic expansion to the final decelerated downstream state. Thus these transitions take the flow from a supersonic to a supersonic, although decelerated, downstream state, unlike shocks which occur in classical MHD or gasdynamics. It is possible that such structures have been observed during the Giotto-Halley encounter, and a brief discussion of the appropriate Halley parameters is therefore given, together with a short discussion of the determination of the shock normal from observations. A further interesting new form of mass-loading shock is the “slow-intermediate” shock, a stable shock which possesses many of the properties of intermediate MHD shocks yet which propagates like a slow mode MHD shock. An important property of mass-loading shocks is the large parameter regime (compared with classical MHD) which does not admit simple or stable transitions from a given upstream to a downstream state. This suggests that it is often necessary to construct compound structures consisting of shocks, slip waves, rarefactions, and fast and slow compound waves in order to connect given upstream and downstream states. Thus the Riemann problem is significantly different from that of classical MHD

Mass-loading and parallel magnetized shocks

Recent observations at comets Giacobini-Zinner and Halley suggest that simple non-reacting gas dynamics or MHD is an inappropriate description for the bow shock. The thickness of the observed (sub)shock implies that mass-loading is an important dynamical process within the shock itself, thereby requiring that the Rankine-Hugoniot conditions possess source terms. This leads to shocks with properties similar to those of combustion shocks. We consider parallel magnetized shocks subjected to mass-loading, describe some properties which distinguish them from classical MHD parallel shocks, and establish the existence of a new kind of MHD compound shock. These results will be of importance both to observations and numerical simulations of the comet-solar wind interaction