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The interaction in the solar wind between two coronal mass ejections (CMEs) is investigated using numerical simulations. We show that the nature of the interaction depends on whether the CME magnetic structures interact, but in all cases the result is an equilisation of the speed of the two CMEs. In the absence of magnetic interaction, the forward shock of the faster trailing CME interacts with the slow leading CME, and accelerates it. When the two CMEs have magnetic fields with the same sense of rotation, magnetic reconnection occurs between the two CMEs, leading to the formation of a single magnetic structure: in the most extreme cases, one CME "eats" the other. When the senses of rotation are opposite, reconnection does not occur, but the CMEs collide in a highly non-elastic manner, again forming a single structure. The possibility of enhanced particle acceleration in such processes is assessed. The presence of strong magnetic reconnection provides excellent opportunities for the acceleration of thermal particles, which then form a seed population for further acceleration at the CME shocks. The presence of a large population of seed particles will thus lead to an overall increase in energetic particle fluxes, as suggested by some observations.

The dynamics of Interplanetary Coronal Mass Ejections (ICMEs) are discussed from the viewpoint of numerical modelling. Hydrodynamic models are shown to give a good zero-order picture of the plasma properties of ICMEs, but they cannot model the important magnetic field effects. Results from MHD simulations are shown for a number of cases of interest. It is demonstrated that the strong interaction of the ICME with the solar wind leads to the ICME and solar wind velocities being close to each other at 1 AU, despite their having very different speeds near the Sun. It is also pointed out that this interaction leads to a distortion of the ICME geometry, making cylindrical symmetry a dubious assumption for the CME field at 1 AU. In the presence of a significant solar wind magnetic field, the magnetic fields of the ICME and solar wind can reconnect with each other, leading to an ICME that has solar wind-like field lines. This effect is especially important when an ICME with the right sense of rotation propagates down the heliospheric current sheet. It is also noted that a lack of knowledge of the coronal magnetic field makes such simulations of little use in space weather forecasts that require knowledge of the ICME magnetic field strength.Key words. Interplanetary physics (interplanetary magnetic fields) Solar physics, astrophysics, and astronomy (flares and mass ejections) Space plasma physics (numerical simulation studies)

In this paper we give a survey of detailed algebraic developments of a solar wind turbulence model. The numerical solution of the coupled system of spectral transfer equations for turbulence composed of Alfvén waves and convective structures or two-dimensional turbulence is prepared. The underlying theory of spectral transfer equations was established by several authors in the early 1990s. The related numerical turbulence model which is elaborated in detail in this paper is based on a rotationally symmetric solar wind model for the background magnetic and flow velocity fields with the full geometry of Parker's spiral which has to be inserted into the transfer equations. Various sources and sinks for turbulent energy are included and appropriately modelled analytically. Spherical expansion terms related to radial gradients of the background velocity fields are considered as far as possible within a rotational symmetric solar wind model, which excludes vorticity effects. Furthermore, nonlinear interaction terms are considered, justified by phenomenological arguments and evaluated by dimensional analysis. Moreover, parametric conversion terms for Alfvén waves and wave-structure interactions are modelled and a generalized spectral flux function for the residual energy eR is introduced. In addition, we compensate the spectra for WKB trends and f -5/3-slopes in order to prepare a convenient form of the equations for numerical treatment. The modelling of source and sink terms includes a special analytical treatment for correlation tensors. This first part presents a summary of the main ideas and the special approximations used for all these terms, together with details on the basic steps of the algebraic calculations. The description of the numerical scheme and a survey of the numerical results of our model, as well as a discussion of the main physical results are contained in a companion paper.

This work follows the paper titled "Spatial transport and spectral transfer of solar wind turbulence composed of Alfvén waves and convective structures I: The theoretical model", and deals with the detailed physics and numerical solution of a two-component solar wind model, consisting of small-scale Alfvén waves and convected structures. In particular, we present numerical results which qualitatively reflect many of the observed features of the radial and spectral evolution of the turbulent energies, the residual energy, the cross-helicity and Alfvén-ratio in high-speed solar wind streams. These features are the following: the formation of a characteristic "inclined eye", which evolves between the energy spectra displayed over the frequency axis and tends to close in the radial development of the spectra, a steepening of all spectra towards Kolmogorov-like f-5/3 spectra, the development of the normalized cross-helicity towards a constant not much less than one and the formation of a "trough" form of the Alfvén ratio with a z-shaped left boundary, By weighting special terms in the equations differently, we can also cast light on the physical role of parametric conversion model terms, wave-structure scattering model terms, nonlinear terms, spherical expansion terms and their effects on the radial evolution of turbulent energies in high-speed solar wind streams.

In this paper we give a survey of detailed algebraic developments of a solar wind turbulence model. The numerical solution of the coupled system of spectral transfer equations for turbulence composed of Alfvén waves and convective structures or two-dimensional turbulence is prepared. The underlying theory of spectral transfer equations was established by several authors in the early 1990s. The related numerical turbulence model which is elaborated in detail in this paper is based on a rotationally symmetric solar wind model for the background magnetic and flow velocity fields with the full geometry of Parker's spiral which has to be inserted into the transfer equations. Various sources and sinks for turbulent energy are included and appropriately modelled analytically. Spherical expansion terms related to radial gradients of the background velocity fields are considered as far as possible within a rotational symmetric solar wind model, which excludes vorticity effects. Furthermore, nonlinear interaction terms are considered, justified by phenomenological arguments and evaluated by dimensional analysis. Moreover, parametric conversion terms for Alfvén waves and wave-structure interactions are modelled and a generalized spectral flux function for the residual energy eR is introduced. In addition, we compensate the spectra for WKB trends and f -5/3-slopes in order to prepare a convenient form of the equations for numerical treatment. The modelling of source and sink terms includes a special analytical treatment for correlation tensors. This first part presents a summary of the main ideas and the special approximations used for all these terms, together with details on the basic steps of the algebraic calculations. The description of the numerical scheme and a survey of the numerical results of our model, as well as a discussion of the main physical results are contained in a companion paper.

This work follows the paper titled "Spatial transport and spectral transfer of solar wind turbulence composed of Alfvén waves and convective structures I: The theoretical model", and deals with the detailed physics and numerical solution of a two-component solar wind model, consisting of small-scale Alfvén waves and convected structures. In particular, we present numerical results which qualitatively reflect many of the observed features of the radial and spectral evolution of the turbulent energies, the residual energy, the cross-helicity and Alfvén-ratio in high-speed solar wind streams. These features are the following: the formation of a characteristic "inclined eye", which evolves between the energy spectra displayed over the frequency axis and tends to close in the radial development of the spectra, a steepening of all spectra towards Kolmogorov-like f-5/3 spectra, the development of the normalized cross-helicity towards a constant not much less than one and the formation of a "trough" form of the Alfvén ratio with a z-shaped left boundary, By weighting special terms in the equations differently, we can also cast light on the physical role of parametric conversion model terms, wave-structure scattering model terms, nonlinear terms, spherical expansion terms and their effects on the radial evolution of turbulent energies in high-speed solar wind streams.