Observational investigations of Earth's bow shock have highlighted distinct variations in turbulence characteristics when comparing fluctuations in the shock transition with those in the upstream and downstream plasma regions. To gain a more focused understanding in each of these areas, we have examined a range of local 2D and 3D hybrid simulations, using kinetic ions and fluid electrons. Each simulation has been chosen to cover a range of shock geometries, from quasi-parallel to quasi-perpendicular and high to low Mach number. In-situ observations, such as those from the Magnetospheric Multiscale (MMS) mission, are often unable to fully disentangle spatial and temporal effects. This is particularly evident in the shock transition and the magnetosheath, where, for example, whistler waves may have speeds comparable to the bulk flow and thus locally violate Taylor’s hypothesis for kinetic-scale fluctuations. Simulations overcome these limitations, enabling us to model the evolution of turbulence in the shock transition and further downstream. We characterize the turbulent fluctuations using the following three methods: Firstly, we examine the magnetic spectral indices spanning the inertial range and extending into the ion range as they change across the shock. Secondly, we investigate intermittency by means of the scale-dependent kurtosis. Lastly, we quantify the correlation lengths as measured across the shock, offering insights into the physical dimensions of fluctuations at scales smaller than the shock width. We will discuss the application of these measures to simulations in understanding the kinetic-scale behaviour of turbulence at Earth's bow shock.

Turbulent plasmas such as the solar wind and magnetosheath exhibit an energy cascade which is present across a broad range of scales, from the stirring scale at which energy is injected, down to the smallest scales where energy is dissipated through processes such as reconnection and wave-particle interactions. Recent observations of Earth's bow shock reveal a disordered or turbulent transition region which exhibits features of turbulent dissipation, such as reconnecting current sheets. We have used observations from Magnetospheric Multiscale (MMS) over four separate bow shock crossings of varying θBn to characterise turbulence in the shock transition region and how it evolves towards the magnetosheath. We observe the magnetic spectrum evolving by fitting power laws over many short intervals and find that the power-law index in the shock transition region is separable from that of the upstream and downstream plasma, for both quasi-perpendicular and quasi-parallel shocks. Across the shock, we see a change in the breakpoint location between inertial and ion power-law slopes. We also observe the evolution of scale-independent kurtosis of magnetic fluctuations across the shock, finding a reduction of high kurtosis intervals downstream of the shock, which is more apparent in the quasi-perpendicular case. Finally, we adapt a method for calculating correlation length to include a high-pass filter, allowing estimates for changes in correlation length across Earth's bow shock. In a quasi-perpendicular shock, we find the correlation length to be significantly smaller in the magnetosheath than in the solar wind, however the opposite can occur for quasi-parallel shocks.