The interaction between cold atmospheric pressure plasma and liquids is receiving increasing attention for various applications. In particular, the use of plasma-treated liquids (PTL) for biomedical applications is of growing importance, in particular for sterilization and cancer treatment. However, insight into the underlying mechanisms of plasma-liquid interactions is still scarce. Here, we present a 2D fluid dynamics model for the interaction between a plasma jet and liquid water. Our results indicate that the formed reactive species originate from either the gas phase (with further solvation) or are formed at the liquid interface. A clear increase in the aqueous density of H2O2, HNO2/NO2- and NO3- is observed as a function of time, while the densities of O3, HO2/O2- and ONOOH/ONOO- are found to quickly reach a maximum due to chemical reactions in solution. The trends observed in our model correlate well with experimental observations from the literature.