Twin-box decks are prone to vortex-induced vibration (VIV) at moderate wind speeds, and previous studies have shown a complex interplay between the flow and the two parallel box girders. OpenFOAM is used to model the aerodynamic and aeroelastic responses of the twin-box deck of the Stonecutters Bridge by means of 3D LES simulations. Two cases are thoroughly analysed under smooth incoming flow: (i) static deck and ii) heave peak amplitude response at VIV excitation. The computational data provided by the CFD simulations have been exploited aiming at better understanding the complex aerodynamic and aeroelastic phenomena taking place. First, spanwise correlation analyses are applied to understand the level of organisation of the forcing flow actions, and identify the regions of the deck affected by different flow structures. Second, three different mode decomposition techniques (POD, SPOD and DMD) are applied to the time-dependent pressure distributions, revealing the pivotal role played by the leeward box in the twin-box deck response under wind action. The modal analyses are of utmost interest in the development of Reduced Order Models (ROM) for the VIV response of twin-box long-span bridges.