The theory of cosmic ray scattering on pre-existing MHD modes meets data

ABSTRACT We present a comprehensive study about the phenomenological implications of the theory describing Galactic cosmic ray scattering on to magnetosonic and Alfvénic fluctuations in the GeV−PeV domain. We compute a set of diffusion coefficients from first principles, for different values of the Alfvénic Mach number and other relevant parameters associated with both the Galactic halo and the extended disc, taking into account the different damping mechanisms of turbulent fluctuations acting in these environments. We confirm that the scattering rate associated with Alfvénic turbulence is highly suppressed if the anisotropy of the cascade is taken into account. On the other hand, we highlight that magnetosonic modes play a dominant role in Galactic confinement of cosmic rays up to PeV energies. We implement the diffusion coefficients in the numerical framework of the dragon code, and simulate the equilibrium spectrum of different primary and secondary cosmic ray species. We show that, for reasonable choices of the parameters under consideration, all primary and secondary fluxes at high energy (above a rigidity of $\simeq 200 \, \mathrm{GV}$) are correctly reproduced within our framework, in both normalization and slope.

Effects of multi-scale and regular grid geometries on decaying turbulence

The influence of a multi-scale fractal based geometry on the decay of turbulence is investigated by comparing the turbulence produced by a square fractal element grid to that produced by two regular grids with similar physical properties. Comparison of the grid wakes at constant grid Reynolds number, $Re_{M}$, identifies that in the far field both regular grids produce comparable or higher turbulence intensities and local Reynolds numbers, $Re_{\unicode[STIX]{x1D706}}$, than the square fractal element grid. This result is illustrative of a limitation of multi-scale geometries to produce the oft-quoted high levels of turbulence intensity and $Re_{\unicode[STIX]{x1D706}}$. In the far field, the spectra are approximately collapsed at all scales for all three grids at a given $Re_{\unicode[STIX]{x1D706}}$. When a non-equilibrium near field spectrum with $\langle uv\rangle \neq 0$ is compared to a far field spectrum at the same $Re_{\unicode[STIX]{x1D706}}$ but with $\langle uv\rangle \approx 0$, it is shown that their shapes are markedly different and that the non-equilibrium spectrum has a steeper slope, giving the appearance of being nearer $k^{-5/3}$, although there is no theoretical expectation of an inertial range at such locations in the flow. However, when a non-equilibrium spectrum with $\langle uv\rangle \approx 0$ is compared to a far field spectrum at the same $Re_{\unicode[STIX]{x1D706}}$, they are once again collapsed. This is shown to be related to non-zero Reynolds shear stress at scales that penetrate the scaling range for the present experiment, and hence the influence of shear is not limited to the largest scales. These results demonstrate the importance of local properties of the flow on the turbulence spectra at given locations in the inherently inhomogeneous flow found in the non-equilibrium region downstream of grids. In particular, how the presence of local shear stress can fundamentally change the shape of the spectra at scales that can be mistakenly interpreted as an inertial range.

First Observations of Microbaroms with Single Absolute Barometers

The first observations of microbaroms with single absolute barometers are presented and discussed. Microbaroms are pulses of atmospheric infrasound emitted by ocean surface waves. They can propagate over thousands of kilometers through the atmosphere, and they can reach altitudes well into the upper atmosphere before they are refracted down to the earth’s surface. Typical microbarom periods are 5 s, typical wavelengths are 1.5 km, and typical surface amplitudes are 100 mPa (1 μbar). The data presented here were collected during the 2-week period from 26 February through 10 March 2008 in Amherst, Massachusetts, which is located about 150 km away from the Atlantic Ocean. The authors report for the first time, to the best of their knowledge, an f−5 microbarom frequency spectrum, which is consistent with Phillips’s f−5 ocean surface wave equilibrium spectrum.

Observations on the wavenumber spectrum and evolution of an internal wave attractor

Reflecting internal gravity waves in a stratified fluid preserve their frequency and thus their angle with the gravitational direction. At boundaries that are neither horizontal nor vertical, this leads to a focusing or defocusing of the waves. Previous theoretical and experimental work has demonstrated how this can lead to internal wave energy being focused onto ‘wave attractors’ in relatively simple geometries. We present new experimental and theoretical results on the dynamics of wave attractors in a nearly two-dimensional trapezoidal basin. In particular, we demonstrate how a basin-scale mode forced by simple mechanical excitation develops an equilibrium spectrum. We find a balance between focusing of the basin-scale internal wave by reflection from a single sloping boundary and viscous dissipation of the waves with higher wavenumbers. Theoretical predictions using a simple ray-tracing technique are found to agree well with direct experimental observations of the waves. With this we explain the observed behaviour of the wave attractor during the initial development, steady forcing, and the surprising increase of wavenumber during the decay of the wave field after the forcing is terminated.