On nonlinear theory for atmospheric gravity waves

Atmospheric gravity waves play a significant role in numerical weather and climate prediction. Especially, waves with rather short wavelengths, which are omnipresent and influence predictions, remain spatially unresolved by the numerical simulations, such that they need to be parametrized, i.e. represented somehow by resolved quantities.

In order to improve weather and climate forecasting, my work aims to enhance gravity wave parametrizations by focusing on nonlinear effects. Nonlinear wave dynamics may lead to counterintuitive properties that are not available in linear theory. For instance, the group velocity, as defined usually by the derivative of the dispersion relation, may not coincide with the wave’s actual envelope velocity. Also, stability properties may change notably. Nonlinear traveling wave packets, e.g., turn out to be unconditionally prone to modulational instabilities.

For my investigations, I use numerical methods such as finite volume schemes with operator splitting and analytical techniques like linear stability analysis in combination with Fredholm operator theory.