A method for drilling a wellbore includes drilling the wellbore by injecting drilling fluid into a top of a tubular string disposed in the wellbore at a first flow rate and rotating a drill bit. The tubular string includes: the drill bit disposed on a bottom thereof, tubular joints connected together, a longitudinal bore therethrough, a port through a wall thereof, and a sleeve operable between an open position where the port is exposed to the bore and a closed position where a wall of the sleeve is disposed between the port and the bore. The method further includes moving the sleeve to the open position; and injecting drilling fluid into the port at a second flow rate while adding a tubular joint(s) to the tubular string. The injection of drilling fluid into the tubular string is continuously maintained between drilling and adding the joint(s).