A torque converter, including: a cover arranged to receive torque; an impeller including an impeller shell non-rotatably connected to the cover and at least one impeller blade connected to the impeller shell; a turbine including a turbine shell and at least one turbine blade connected to the turbine shell; an output hub connected to the turbine shell and arranged to non-rotatably connect to an input shaft for a transmission; and a turbine clutch including a piston non-rotatably connected to the turbine shell, and for a lock-up mode, axially displaceable to non-rotatably connect the piston and the impeller shell.