A turbine arrangement with a rotor and a stator surrounding the rotor forming a flow path for hot and pressurized combustion gases between the rotor and the stator is provided. The rotor defines a radial direction and a circumferential direction and includes turbine blades extending in the radial direction through the flow path towards the stator. The turbine blades have shrouds located at their tips and the stator includes a wall section along which the shrouds move when the rotor is turning. A supersonic nozzle is located in the wall section and is connected to a cooling fluid provider. The supersonic nozzle provides a supersonic cooling fluid flow towards the shroud. The supersonic nozzle is angled with respect to the radial direction towards the circumferential direction in such an orientation that the supersonic cooling fluid flow has a flow component parallel to the moving direction of the shroud.