Shelf areas represent a critical transition zone between the terrestrial area and the deep ocean. These marine areas attract particulate attention due to high human activity there and its vulnerability to natural hazards. The coastal zones and deep ocean evolve in time as one entity. However, there is still substantial gap in understanding of the deep signal fate in the coastal areas. Making progress on this largely depends on the accurate representation of the physical environment in a coupled coastal-open ocean system. In current work, we present newly developed FESOM-C numerical solution and its application to the North Sea hydrodynamics under climate change pressure. FESOM-C is a coastal branch of the global Finite Element (VolumE) Sea-ice Ocean Model FESOM. It was developed to focus on smaller scales than FESOM and on physical and dynamical processes commonly not accounted in largescale models. FESOM-C numerical core is created in a way to provide most efficient exchange of fluxes between coastal and global solutions. The model performance was evaluated based on hydrodynamics simulations for the southeastern part of the North Sea. The simulation results cover the period from January 2010 to December 2014 and show good agreement with data from autonomous observation stations, ferries and glider expeditions. We also made an analysis of the river tracers, which determines the temporal and spatial dynamics of zones affected by the different freshwater sources. The continuing sea level rise suggests significant changes in shelf hydrodynamics. Based on numerical simulations we present the sensitivity study of the North Sea dynamics to the changes of the sea level at the open boundary. The particular attention was paid to the changes in the tidal residual circulation, which largely defines the biogeochemical transport in the coastal zones.