F. T. Gratton

Viscous-type processes in the solar wind-magnetosphere interaction

A debate of long standing concerns the role viscous interactions play in magnetospheric dynamics. Is it minor or is it central to, e.g., drive the low latitude boundary layer on closed field lines and account for the substantial level of wave activity seen on the flanks? Newer data and theoretical considerations leave little doubt that viscous coupling is important. The Kelvin-Helmholtz instability is a major protagonist in fostering momentum transfer. Closer studies of the state of the flank magnetosphere will help to resolve the issue.

Is the magnetopause Rayleigh‐Taylor unstable sometimes?

At the terrestrial magnetopause the dense magnetosheath flowing around the magnetosphere interfaces with the normally much more tenuous magnetospheric plasma. Temporal variations in the solar wind dynamic pressure cause the magnetopause to be in continuous motion. When it decelerates and rebounds sunward after a strong and rapid drop in the solar wind dynamic pressure, we have a situation of a heavy-over-light plasma in an effective gravitational field. In this paper we investigate theoretically the conditions under which this configuration may become Rayleigh-Taylor (RT) unstable. The motion of the magnetopause is studied using a gas-dynamic model which takes into account forces arising from hypersonic flow past an object of prescribed shape. Thus the effect of the magnetic field near the magnetopause is not included. For sufficiently large and rapid dynamic pressure variations we obtain accelerations ≥ 1kms−2 lasting for periods of the order of 1–2 min. We discuss the possible instability of both global (λ ≫ Δ, thickness of the magnetopause) and internal (λ < Δ) modes, taking into account the stabilizing effects of (1) magnetic shear across the magnetopause and (2) viscosity of the magnetosheath plasma. We find that both modes are stable when the magnetic shear across the magnetopause is large. When the magnetosheath field points strongly northward, however, we find that both modes may be RT unstable. Among the effects of RT instability on the magnetopause and its environs are (1) large distortions of the magnetic field lines, (2) localized compressions of the magnetospheric magnetic field, (3) increased magnetopause thickness, and (4) reduced average density gradient across the magnetopause. (Since we only concentrate here on the linear stage of the development of the instability, no mass transfer into the magnetosphere is included.) These are all, in principle, observable effects, though the rapid motion of the magnetopause would require a fortuitous spacecraft-magnetopause configuration for them to be actually seen in single-spacecraft data. This work may be considered as a contribution to the current research on the structure and physics of the low-shear magnetopause.

On the multispacecraft determination of periodic surface wave phase speeds and wavelengths

Observations of surface waves on the magnetopause indicate a wide range of phase velocities and wavelengths. Their multispacecraft analysis allows a more precise determination of wave characteristics than ever before and reveal shortcomings of approximations to the phase speed that take a predetermined fraction of the magnetosheath speed or the average flow velocity in the boundary layer. We show that time lags between two or more spacecraft can give a qualitative upper estimate, and we confirm the unreliability of flow approximations often used by analyzing a few cases. Using two‐point distant magnetic field observations and spectral analysis of the tailward magnetic field component, we propose an alternative method to estimate the wavelength and phase speed at a single spacecraft from a statistical fit to the data at the other site.

A Vortical Dawn Flank Boundary Layer for Near-Radial IMF: Wind Observations on 24 October 2001

We present an example of a boundary layer tailward of the dawn terminator which is entirely populated by rolled-up flow vortices. Observations were made by Wind on 24 October 2001 as the spacecraft moved across the region at X ∼−13 RE. Interplanetary conditions were steady with a near-radial interplanetary magnetic field (IMF). Approximately 15 vortices were observed over the 1.5 h duration of Winds crossing, each lasting ∼5 min. The rolling up is inferred from the presence of a hot tenuous plasma being accelerated to speeds higher than in the adjoining magnetosheath, a circumstance which has been shown to be a reliable signature of this in single-spacecraft observations. A blob of cold dense plasma was entrained in each vortex, at whose leading edge abrupt polarity changes of field and velocity components at current sheets were regularly observed. In the frame of the average boundary layer velocity, the dense blobs were moving predominantly sunward and their scale size along X was ∼7.4 RE. Inquiring into the generation mechanism of the vortices, we analyze the stability of the boundary layer to sheared flows using compressible magnetohydrodynamic Kelvin-Helmholtz theory with continuous profiles for the physical quantities. We input parameters from (i) the exact theory of magnetosheath flow under aligned solar wind field and flow vectors near the terminator and (ii) the Wind data. It is shown that the configuration is indeed Kelvin-Helmholtz (KH) unstable. This is the first reported example of KH-unstable waves at the magnetopause under a radial IMF.

Kelvin-Helmholtz Multi-Spacecraft Studies at the Earth's Magnetopause Boundaries

The Kelvin-Helmholtz (KH) instability can operate in various situations in the solar wind, but at the boundaries of planetary obstacles, for example the Earths magnetopause, it is most amenable to investigation. Reliable estimates of wave characteristics are essential for comparison with theoretical and numerical models and for understanding the non-linear development of KH waves and their role in the plasma entry into the magnetosphere. After discussing their typical conditions of appearance in KH unstable domains at the magnetopause, both theoretically and observationally, we outline recent results of multi-spacecraft analysis with Cluster giving accurate, albeit spatially limited, determination of surface wave characteristics. Those characteristics (wavelength and propagation direction), close to the terminator on the nightside, are likely to be prescribed by the 3-D geometry and the bending of field lines developed by the KH waves, rather than by the magnitude and the direction of the magnetosheath or background flow. An unprecedented number of satellites provides now the opportunity to extend the analysis of source regions of KH waves and their domains of development.

On the MHD Boundary of Kelvin-Helmholtz Stability Diagram at Large Wavelengths

Working within the domain of inviscid incompressible MHD theory, we found that a tangential discontinuity (TD) separating two uniform regions of different density, velocity and magnetic field may be Kelvin-Helmholtz (KH) stable and yet a study of a transition between the same constant regions given by a continuous velocity profile shows the presence of the instability with significant growth rates. Since the cause of the instability stems from the velocity gradient, and since a TD may be considered as the ultimate limit of such gradient, the statement comes as a surprise. In fact, a long wavelength (‚) boundary for the KH instability does not exist in ordinary liquids being instead a consequence of the presence of magnetic shear, a possibility that has passed unnoticed in the literature. It is shown that KH modes of a magnetic field configuration with constant direction do not have the long ‚ boundary. A theoretical explanation of this feature and examples of the violation of the TD stability condition are given using a model that can be solved in closed form. Stability diagrams in the (kd, MA) plane are given (where kd = 2…d=‚, 2d is the velocity gradient length scale, and MA is the Alfv´ Mach number) that show both the well-known limit at small ‚s and the boundary for large but finite ‚s noted here. Consequences of this issue are relevant for stability studies of the dayside magnetopause as the stability condition for a TD should be used with care in data analysis work.

Compressible Kelvin-Helmholtz instability at the terrestrial magnetopause

The compressible magnetohydrodynamic Kelvin-Helmholtz instability occurs in two varieties, one that can be called incompressible as it exists in the limit of vanishing compressibility (primary instability), while the other exists only when compressibility is included in the model (secondary instability). In previous work we developed techniques to investigate the stability of a surface of discontinuity between two different uniform ows. Our treatment includes arbitrary jumps of the velocity and magnetic fields as well as of density and temperature, with no restriction on the wave vector of the modes. Then it allows stability analyses of complex configurations not previously studied in detail. Here we apply our methods to investigate the stability of various typical situations occurring at different regions of the front side, and the near anks of the magnetopause. The physical conditions of the vector and scalar fields that characterize the equilibrium interface at the positions considered are obtained both from experimental data and from results of simulation codes of the magnetosheath available in the literature. We give particular attention to the compressible modes in configurations in which the incompressible modes are stabilized by the magnetic shear. For configurations of the front of the magnetopause, which have small relative velocities, we find that the incompressible MHD model gives reliable estimates of their stability, and compressibility effects do not introduce significant changes. However, at the anks of the magnetopause the occurrence of the secondary instability and the shift of the boundary of the primary instability play an important role. Consequently, configurations that are stable if compressibility is neglected turn out to be unstable when it is considered and the stability properties are quite sensitive on the values of the parameters. Then compressibility should be taken into account when assessing the stability properties of these configurations, since the estimates based on incompressible MHD may be misleading. A careful analysis is required in each case, since no simple rule of thumb can be given.

Velocity shear instability and plasma billows at the Earth's magnetic boundary

The Kelvin-Helmoltz instability (KH) with formation of vortices appears in a wide variety of terrestrial, interplanetary, and astrophysical contexts. We study a series of iterated rolled-up coherent plasma structures (15) that flow in the equatorial Earths boundary layer (BL), observed on October 24, 2001. The data were recorded during a 1.5 hour-long Wind crossing of the BL at the dawn magnetospheric flank, tailward of the terminator (X≈−13 RE). The interplanetary magnetic field (IMF) was radially directed, almost antiparallel to the magnetosheath (MS) flow. This configuration is expected to be adverse to the KH instability because of the collinearity of field and flow, and the high compressibility of the MS. We analyze the BL stability with compressible MHD theory using continuous profiles for the physical quantities. Upstream, at near Earth sites, we input parameters derived from an exact MHD solution for collinear flows. Further downtail at Wind position we input measured parameters. The BL is found KH unstable in spite of unfavorable features of the external flow. On the experimental side, the passage of vortices is inferred from the presence of low density - hot plasma being accelerated to speeds higher than that of the contiguous MS. It is further supported by the peculiar correlation of relative motions (in the bulk velocity frame): cold-dense plasma drifts sunward, while hot-tenuous plasma moves tailward. This event differs from many other studies that reported BL vortices under strongly northward IMF orientations. This is a case of KH vortices observed under an almost radial IMF, with implicit significance for the more common Parkers spiral fields, and the problem of plasma entry in the magnetosphere.

The stability of the pristine magnetopause

Abstract A MHD theory of combined Kelvin–Helmholtz (KH) and Rayleigh–Taylor (RT) instabilities for a transition layer with two different scale lengths (Δ and δ for the variation of velocity/magnetic fields and density, respectively) is presented. The study is motivated by reports of magnetopauses with no low latitude boundary layer, in which a sharp density drop over a distance δ⪡Δ is observed (“pristine” magnetopauses (J. Geophys. Res. 101 (1996) 49). The theory ignores compressibility effects and applies to subsonic regions of the dayside magnetopause. The RT effect is included to account for temporary periods of acceleration of the magnetopause, caused by sudden changes of the solar wind dynamic pressure. For small wavelengths λ, such that δ⪡λ⪡Δ, a WKB solution shows that the velocity gradient operates, together with magnetic tensions, to attenuate or even stabilize the Rayleigh–Taylor instability within a certain wavelength range. An exact dispersion relation for flute modes, valid for all λ, in the form of a fourth order polynomial for the complex frequency ω, is obtained from a model with a constant velocity gradient, dV/dy within Δ, and with δ→0. Flute modes are possible because of the existence of bands of very small magnetic shear on the dayside magnetopause (J. Geophys. Res. 103 (1998) 6703). The exact solution allows for a study of the change of the action of the velocity gradient with λ from the long-λ range where dV/dy is KH destabilizing to the short-λ range where dV/dy produces a stabilizing effect. Both, the WKB approximation and the well known tangential discontinuity model (Δ→0) are recovered as limiting cases of the exact solution. Properties of the KH and RT instabilities, for different density ratios on either side of the magnetopause, are described. For flute modes, at very small λ the RT instability grows faster and becomes the dominant effect. However, it is shown that the growth rate remains bounded at a finite value as λ→0, when a theory with a finite δ model is considered. To study configurations with finite, arbitrary, δ/Δ ratios, the MHD perturbation equations are solved numerically, using hyperbolic tangent functions for both the density and velocity transitions across the magnetopause. To examine the influence of different δ/Δ ratios on the growth rates of KH and RT, calculations are performed for different δ/Δ, with and without acceleration, and for two different density ratios. It is found that the general features exhibited by the constant dV/dy model, are confirmed by these numerical solutions. The stability of pristine magnetopauses, and the possibility of observing some theoretical predictions during magnetopause crossings in ongoing missions, are discussed.

Reply to comment by H. Hasegawa on "Evolution of Kelvin-Helmholtz activity on the dusk flank magnetopause"

We demonstrate, on experimental grounds, that the justifications for the comment by Hasegawa [2009], hereinafter H09, on work done by Foullon et al. [2008], hereinafter F08, are not well founded.