Magnetohydrodynamic simulations of kelvin-helmholtz generated surface waves and vortices at earth’s magnetopause

When the magnetised solar wind blows across the magnetopause, a process translates shearing momentum into rotational momentum thus driving vortices and magnetopause surface waves (MSWs) along the magnetopause. This process is called the Kelvin-Helmholtz instability (KHI) and it plays a significant role in the viscous-like mass, momentum, and energy transfer from the solar wind into the magnetosphere. It is unclear how the plasma properties and magnetic field orientation of the solar wind influence the different evolutionary stages of the KHI. To unbiasedly analyse evolution, a formal definition of a vortex is needed. As one does not exist, a magnetohydrodynamic vortex identification technique, called $\lambda_\text{MHD}$, is derived which is composed of four parts: vortical momentum, density gradients, compressibility, and rotational magnetic tension. Applying this definition to a local simulation shows different drivers are more important in some stages of the KHI than others. However, the local simulation is a simplification as a realistic magnetopause has a thickness, continuously varying plasma properties, and varying magnetic geometry. Applying $\lambda_\text{MHD}$ to a global MHD simulation of the Sun-Earth interaction tests this and finds that the boundary thickness results in inner- and outer-modes which, as they are in different plasma, evolve differently. It is also shown the magnetic geometry limits the latitudinal extent of the vortices. Finally, there are competing theories surrounding how the KHI influences MSW frequency. These are tested by using dynamic mode decomposition (DMD) - a machine learning technique - on the global simulation. DMD reveals that the KHI generates, amplifies, and advects MSW frequency across the magnetopause. This results in a complex superposition of frequencies at any one local time. When isolating a single frequency, it is shown that MSW wavelength is Doppler-shifted by the accelerating magnetosheath flow. These results have implications for how MSW frequencies and wavelengths are analysed.