Film cooling is a common technique to manage turbine vane and blade thermal environment. Optimizing its cooling efficiency is furthermore an active research topic which goes in hand with a strong knowledge of the flow associated with a cooling hole. The following paper aims at developing deeper understanding of the flow physics associated with a standard cooling hole and helping guide future cooling optimization strategies. For this purpose, large eddy simulations (LESs) of the 7-7-7 fan-shaped cooling hole are performed and the flow inside the cooling hole is studied and discussed. Use of mathematical techniques such as the fast Fourier transforms (FFTs) and dynamic mode decomposition (DMD) is done to quantitatively access the flow modal structure inside the hole based on the LES unsteady predictions. Using these techniques, distinct vortex features inside the cooling hole are captured. These features mainly coincide with the roll-up of the internal shear layer formed at the interface of the separation region at the hole-inlet. The topology of these vortex features is discussed in detail and it is also shown how the expansion of the cross section in case of shaped holes aids in breaking down these vortices. Indeed upon escaping, these large-scale features are known to not be always beneficial to film cooling effectiveness.