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Nearly-circular Frozen Orbits (FOs) around axisymmetric bodies – or, quasi-circular Periodic Orbits (POs) around non-axisymmetric bodies – are of primary concern in the design of low-altitude survey missions. Here, we study very low-altitude orbits (down to 50 km) in a high-degree and order model of the Martian gravity field. We apply Prony’s Frequency Analysis (FA) to characterize the time variation of their orbital elements by computing accurate quasi-periodic decompositions of the eccentricity and inclination vectors. An efficient, iterative filtering algorithm, previously applied to lunar orbiters, complements the method and is used to accurately compute the locations of POs/FOs, for a wide range of initial conditions. By defining the ’distance’ of any orbit from the family of POs and using the relative amplitudes of the different components of the motion, we can build ’dynamical fate maps’ that graphically depict the survivability of low-eccentricity, low-altitude orbits at every inclination, and can be used for efficient mission planning. While lowering the altitude generally enhances the effect of tesseral and sectorial gravity harmonics, we find this to have less consequence for low altitude Martian satellites, in contrast with the Lunar case. Hence, a high-degree ( ≃ 20 th ) axisymmetric model is adequate for preliminary mission design at moderate altitudes, but should be complemented at low altitudes by the methods described here. All families of POs and their spectral decompositions can be accurately and effectively computed by continuation in arbitrarily complex Martian gravity models, as our filtering algorithm requires only short integration arcs.

We have performed medium resolution numerical simulations over very long times of the stationary turbulent flow that develops from a static constant in time Taylor-Green forcing. By averaging over thousands of large-scale eddy turnover times, we separate the turbulent fluctuations from the inhomogeneous anisotropic mean flow induced by the forcing. We show that the turbulent velocity fluctuations are only slightly more isotropic than the total flow and still display significant deviations from isotropy and homogeneity. Also, the fluctuations and the mean flow are not independent, and their energies are locally anticorrelated. The energy transfer laws of Kolmogorov, Yaglom and Monin and their corresponding finite Reynolds number corrections are also checked for different positions and orientations in the flow, and it is found that Kolmogorov and Yaglom laws are not completely satisfied due to the imperfect return to isotropy and homogeneity of the flow. Monin's relation is verified because it averages dissipation over the different directions and in a volume such that homogeneity is restored, and also only for the total fluid velocity and not for the velocity fluctuations as these do not obey Navier-Stokes equations. These results suggest that the hypothesis of small scale homogeneous and isotropic turbulence should be clarified in the presence of an inhomogeneous anisotropic mean flow induced by forcing. We have performed medium resolution numerical simulations over very long times of the stationary turbulent flow that develops from a static constant in time Taylor-Green forcing. By averaging over thousands of large-scale eddy turnover times, we separate the turbulent fluctuations from the inhomogeneous anisotropic mean flow induced by the forcing. We show that the turbulent velocity fluctuations are only slightly more isotropic than the total flow and still display significant deviations from isotropy and homogeneity. Also, the fluctuations and the mean flow are not independent, and their energies are locally anticorrelated. The energy transfer laws of Kolmogorov, Yaglom and Monin and their corresponding finite Reynolds number corrections are also checked for different positions and orientations in the flow, and it is found that Kolmogorov and Yaglom laws are not completely satisfied due to the imperfect return to isotropy and homogeneity of the flow. Monin's relation is verified because it averages dissipation over the different directions and in a volume such that homogeneity is restored, and also only for the total fluid velocity and not for the velocity fluctuations as these do not obey Navier-Stokes equations. These results suggest that the hypothesis of small scale homogeneous and isotropic turbulence should be clarified in the presence of an inhomogeneous anisotropic mean flow induced by forcing.

We present here a new method for the efficient computation of periodic orbits, which are of particular interest for low-altitude satellite orbits design in high degree/order, non-axisymmetric gravity models. Our method consists of an iterative filtering scheme, that is itself based on ‘Prony’s method’ of frequency analysis, and is independent of the complexity of the gravity model. Applying this method to the case of a low-altitude lunar orbiter, we show that it converges rapidly, in all models and for all values of altitude and initial inclination studied. Thus, as demonstrated below, one could use it to correct the initial conditions of a desired mission orbit — usually defined within the framework of a simplified model (e.g. the ‘ J 2 problem’) — ensuring minimal orbital eccentricity variations and, for very low altitudes, collision avoidance. At the same time, an accurate quasi-periodic decomposition of the orbit is computed, giving a measure of the periodic fluctuations of the orbital parameters.

The generation of large-scale magnetic field in the kinematic regime in the absence of an alpha-effect is investigated by following two different approaches, namely the test-field method and multiscale stability theory relying on the homogenisation technique. We show analytically that the former, applied for the evaluation of magnetic eddy diffusivities, yields results that fully agree with the latter. Our computations of the magnetic eddy diffusivity tensor for the specific instances of the parity-invariant flow-IV of G.O. Roberts and the modified Taylor-Green flow in a suitable range of parameter values confirm the findings of previous studies, and also explain some of their apparent contradictions. The two flows have large symmetry groups; this is used to considerably simplify the eddy diffusivity tensor. Finally, a new analytic result is presented: upon expressing the eddy diffusivity tensor in terms of solutions to auxiliary problems for the adjoint operator, we derive relations between magnetic eddy diffusivity tensors that arise for opposite small-scale flows v(x) and -v(x)., Comment: 29 pp., 19 figures, 42 references

We study the secular dynamics of lunar orbiters, in the framework of high-degree gravity models. To achieve a global view of the dynamics, we apply a frequency analysis (FA) technique which is based on Prony’s method. This allows for an extensive exploration of the eccentricity ( $$e$$ )—inclination ( $$i$$ ) space, based on short-term integrations ( $$\sim $$ 8 months) over relatively high-resolution grids of initial conditions. Different gravity models are considered: 3rd, 7th and 10th degree in the spherical harmonics expansion, with the main perturbations from the Earth being added. Since the dynamics is mostly regular, each orbit is characterised by a few parameters, whose values are given by the spectral decomposition of the orbital elements time series. The resulting frequency and amplitude maps in ( $$e_0,i_0$$ ) are used to identify the dominant perturbations and deduce the “minimum complexity” model necessary to capture the essential features of the long-term dynamics. We find that the 7th degree zonal harmonic ( $$J_7$$ term) is of profound importance at low altitudes as, depending on the initial secular phases, it can lead to collision with the Moon’s surface within a few months. The 3rd-degree non-axisymmetric terms are enough to describe the deviations from the 1 degree-of-freedom zonal problem; their main effect is to modify the equilibrium value of the argument of periselenium, $$\omega $$ , with respect to the “frozen” solution ( $$\omega =\pm 90^{\circ }, \forall \Omega $$ , where $$\Omega $$ is the nodal longitude). Finally, we show that using FA on a fine grid of initial conditions, set around a suitably chosen ‘first guess’, one can compute an accurate approximation of the initial conditions of a periodic orbit.

Guy GOFFETTE, Eloge pour une cuisine de province, poèmes, postface de Jacques Borel, Seyssel, Champ Vallon, 1988, 171 p. La Parole a, dit-on, planté sa tente parmi nous. La Nomadie de Guy Goffette s’y est abritée et, depuis, le poète n’a de cesse. Editeur-typographe, animateur de la splendide revue Triangle, Goffette vient de recevoir le Prix Triennal de Littérature. On s’étonne d’en entendre parler si peu. En matière de poésie, le silence des critiques correspond, il est vrai, à l’hermétism...

A new algorithm for the computation of discrete Legendre transforms is discussed. Classical solutions have a running time proportional toN 2d , whereN is the size of the spatial grid andd is the space dimension. The new algorithm has a running timeO((N log2 N) d ). A general application of this algorithm is to the weak solutions of hyperbolic systems of conservation laws as considered by Lax (1973,Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves, S.I.A.M.). The potential of the method is illustrated on the “adhesion model,” a multi-dimensional version of the Burgers equation, used to study the formation of large-scale structures in cosmology.

A turbulent energy cascade has been recently identified in high‐latitude solar wind data samples by using a Yaglom‐like relation. However, analogous scaling law, suitably modified to take into account compressible fluctuations, has been observed in a much more extended fraction of the same data set recorded by the Ulysses spacecraft. Thus, it seems that large scale density fluctuations, despite their low amplitude, play a major role in the basic scaling properties of turbulence. The compressive turbulent cascade, moreover, seems to be able to supply the energy needed to account for the local heating of the non‐adiabatic solar wind.

Incompressible and isotropic magnetohydrodynamic turbulence in plasmas can be described by an exact relation for the energy flux through the scales. This Yaglom-like scaling law has been recently observed in the solar wind above the solar poles observed by the Ulysses spacecraft, where the turbulence is in an Alfveacutenic state. An analogous phenomenological scaling law, suitably modified to take into account compressible fluctuations, is observed more frequently in the same data set. Large-scale density fluctuations, despite their low amplitude, thus play a crucial role in the basic scaling properties of turbulence. The turbulent cascade rate in the compressive case can, moreover, supply the energy dissipation needed to account for the local heating of the nonadiabatic solar wind.

Dottorato di Ricerca in Fisica, Ciclo XXII, 2009 Università della Calabria

[1] We study the nonuniform solar wind turbulence using high-resolution Ulysses magnetic field data measured at different solar activity level, heliospheric latitudes, and distance. We define several types of solar wind dependent of the coronal region of origin and also of the dynamical behavior of the different streams, namely, “pure” fast wind, fast streams, “pure” slow wind, and slow streams. The turbulent properties of the solar wind types were investigated in terms of their scaling properties and spatial inhomogeneity. A clear trend in the power spectrum of the solar wind magnetic field magnitude is observed: the “pure” fast wind has a slope ∼−1.33 (1/f-like), the fast streams ∼−1.48 (Kraichnan-like), the “pure” slow wind ∼−1.67 (Kolmogorov-like), and the slow streams ∼−1.72. We find that the “pure” fast wind in the polar heliolatitudes is less intermittent than the other types: “pure” slow wind and both slow and fast streams, which is because of the absence of dynamical interactions between streams with different speeds. On the other hand, fast streams are more intermittent than the “pure” fast wind, and slow streams are less intermittent than the “pure” slow winds. A clear radial and latitudinal evolution of the intermittency is observed only for the “pure” fast wind, while in the equatorial plane, the fast streams, the “pure” slow wind, and the slow streams do not show evolution either in heliolatitude or in heliocentric distance.

Journal of Geophysical Research (Space Physics), 114, p. 08101 (2009); International audience

We present the results of CA simulations of a moderately dense lattice gas using an extended version of the FHP model for colored automata. By tracking a tagged particle, we construct its velocity autocorrelation function and we show that the corresponding power spectrum exhibits a low-frequency contribution characteristic of the long-time power law behavior (≈ t-1, in 2D). © 1991., SCOPUS: ar.j, info:eu-repo/semantics/published

The goal of the present paper is the investigation of the final evolution of anisotropic regular structures and turbulence at large Reynolds number in the multidimensional Burgers equation. We show that we have local isotropization at small scales of the velocity and potential fields inside cellular zones. For periodic waves, we have simple decay inside a frozen structure. The global structure at large times is determined by the initial correlations and for short range correlated fields we have isotropization of turbulence. Finally, we consider the final behavior of the field, when the processes of nonlinear beating interactions become frozen, and the evolution of the field is determined only by the linear dissipation.

In this short review we report about recent findings related to two fundamental points in the study of solar wind turbulence: a) the verification of the equivalent of the −4/5 law in the solar wind and b) the estimate of the energy cascade along the spectrum and its comparison with the heating rate necessary to heat the solar wind during its expansion as deduced from in‐situ measurements. As a matter of fact, a Yaglom‐like scaling relation has recently been found in both high‐latitude and in‐ecliptic data samples. However, analogous scaling law, suitably modified to take into account compressible fluctuations, has been observed in a much more extended fraction of the same data set recorded at high latitude. Thus, it seems that large scale density fluctuations, despite their low amplitude, play a major role in the basic scaling properties of turbulence. The compressive turbulent cascade, moreover, seems to be able to supply the energy needed to account for the local heating of the non‐adiabatic solar wind.

The nonlinear dynamics of two-dimensional electrostatic interchange modes in a magnetized plasma is investigated through a simple model that replaces the instability mechanism due to magnetic field curvature by an external source of vorticity and mass. Simulations in a cylindrical domain, with a spatially localized and randomized source at the center of the domain, reveal the eruption of mushroom-shaped bursts that propagate radially and are absorbed by the boundaries. Burst sizes and the interburst waiting times exhibit power-law statistics, which indicates long-range interburst correlations, similar to what has been found in sandpile models for avalanching systems. It is shown from the simulations that the dynamics can be characterized by a Yaglom relation for the third-order mixed moment involving the particle number density as a passive scalar and the E×B drift velocity, and hence that the burst phenomenology can be described within the framework of turbulence theory. Statistical features are qualitat...

Solar wind plasma is known to cool down more slowly while it is blown away from the Sun than expected from an adiabatic spherical expansion. Some source of heating is thus needed to explain the observed temperature radial profile. The presence of a nonlinear turbulent magnetohydrodynamic energy cascade has been recently observed in solar wind plasma. This provides for the first time a direct estimation of the turbulent energy transfer rate, which can contribute to the in situ heating of the wind. The value of such contribution is shown to represent an important fraction ( from 5% to 100%) of the total heating, and is strongly correlated with the wind temperature.