Our previous studies have produced phenomenological models for turbulence in solar wind plasmas on large-(inertial) magnetohydrodynamic scales, based on observations by the Voyager, Ulysses, and THEMIS missions. Here we consider turbulence in the Earth’s magnetosheath, where timescales are often far shorter than those in the heliosheath, using observations from the currently operating Magnetospheric Multiscale (MMS) mission on much smaller kinetic scales. We employ a standard statistical analysis to obtain energy density spectra for the magnetic field strength and the ion speed at high time resolution. We find a clear breakpoint of the magnetic spectrum exponent from −0.8 to −5/2 near the ion gyrofrequency of 0.25 Hz. In fact, just behind the bow shock and near the magnetopause, the availability of the highest-resolution magnetic field observations enables us also to identify the expected spectral exponent of about −3, which is further followed by steeper spectra with the slopes from −7/2 to −11/2 (−16/3) in the kinetic regime above 20 Hz, possibly resulting from the kinetic Alfvén waves. Because the resolution of the ion plasma parameters is somewhat lower than that for the magnetic field, spectra for the ion velocity can only be resolved near the onset of kinetic scales. On the other hand, deep inside the magnetosheath, where only low-resolution data are available and we are still in the magnetohydrodynamic scale range, we recover the well-known −5/3 Kolmogorov’s spectrum. The obtained results on kinetic scales may be useful for better understanding the physical mechanisms governing turbulence.

We analyse the fractal nature of geomagnetic field northward and eastward horizontal components with 1 min resolution measured by the four stations Belsk, Hel, Sodankylä and Hornsund during the period of 22 August–1 September, when the 26 August 2018 geomagnetic storm appeared. To reveal and to quantitatively describe the fractal scaling of the considered data, three selected methods, structure function scaling, Higuchi, and detrended fluctuation analysis are applied. The obtained results show temporal variation of the fractal dimension of geomagnetic field components, revealing differences between their irregularity (complexity). The values of fractal dimension seem to be sensitive to the physical conditions connected with the interplanetary shock, the coronal mass ejection, the corotating interaction region, and the high-speed stream passage during the storm development. Especially, just after interplanetary shock occurrence, a decrease in the fractal dimension for all stations is observed, not straightforwardly visible in the geomagnetic field components data.

In the present study, we analyze the dynamics of a four-dimensional generalized Lorenz system with one variable describing the profile of the magnetic field induced in a convected magnetized fluid. In particular, we identify the subcritical Hopf bifurcation, at which the dimension of the unstable manifold is increased or reduced by two. Moreover, the new four-dimensional system behavior depending on the control parameters is considered and bidirectional bifurcation structures are revealed. The results show the existence of several windows of nonchaotic variation (windows of order), in particular period-3 windows at the edge of which type I intermittency is observed.