CVG LCL CTLR DESCRIBED CONFLICT DURING SINGLE RWY OPS WHEN ARR ACFT ELECTED TO GO AROUND AND FAILING TO COMPLY WITH CLRNC; CONFLICTED WITH DEP.

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STRONG GUSTY WINDS FROM WSW FORCED CVG TO USE A SINGLE RWY 27 INSTEAD OF THE PARALLEL RWY 18L/C/R. THERE WERE ABOUT 25-30 ACFT LINED UP FOR DEP AND INBOUNDS WERE IN HOLDING DUE TO AN OVERLOADED FINAL. I WAS THE TWR CTLR AT THE TIME OF THE EVENT. DUE TO THE VOLUME; MINIMUM SPACING WAS BEING USED ON FINAL. AN ARR SPACING OF 3 MI ALLOWED 1 DEP OUT AND 4 MI ALLOWED 2 DEPS; GND SPDS ON FINAL WERE ABOUT 110 KTS. IN A 4 MI SPACE A NON-INVOLVED ACFT DEPARTED AND ACFT #2 WAS THEN CLRED FOR TKOF; RWY 27; TURN L HDG 210 DEGS; IN FRONT OF ACFT #1; NOW ON A 2.5 MI FINAL. ACFT #2 WAS SLOW TO START HIS TKOF ROLL SO ACFT #1 STARTED A GAR ON HIS OWN ON ABOUT A 1 MI FINAL. TWR ISSUED A CLB TO 4000 FT AND A R TURN TO HDG 300 DEGS TO AVOID CONFLICT WITH DEP ACFT. ACFT #1 CLEANED UP THE ACFT; AND ACCELERATED BUT; DID NOT START A CLB OR TURN. ACFT #1 WAS AGAIN ISSUED A CLB AND TURN FURTHER R TO 330 DEGS. BECAUSE OF THE ACCELERATION ACFT #1 WAS NOW OVER TOP OF AND VERY SLIGHTLY AHEAD OF ACFT #2 AT ABOUT 1200 FT AGL AS ACFT #2 WAS LIFTING OFF. ACFT #1 THEN STARTED A L TURN (PUBLISHED MISSED APCH); ACFT #1 WAS THEN TOLD TURN R NOW; HDG 330 DEGS; THEY READ BACK R HDG 030 DEGS; BUT AT LEAST THEY STARTED A R TURN AND THE CONFLICT WAS RESOLVED. ACFT #2 ALSO STARTED A L TURN TO REMOVE THE CONFLICT AT ABOUT THE SAME TIME WHEN HE WAS CLBING OUT OF ABOUT 800 FT AGL. LOOKING BACK NOW; I SHOULD HAVE NOTICED SOONER THAT ACFT #2 WAS NOT STARTING HIS ROLL QUICK ENOUGH AND ABORTED HIM AND SENT ACFT #1 AROUND WITHOUT CONFLICTING TFC. MY ATTN WAS DIVERTED WITH THE PREVIOUS ARR STILL ON MY FREQ AND THE EARLIER DEP STILL ON MY FREQ. HOWEVER; HAD ACFT #2 ROLLED AS EXPECTED OR ACFT #1 TURNED R AFTER EITHER THE FIRST OR SECOND TIME ISSUED; THE CONFLICT WOULD NOT HAVE OCCURRED. I REALIZE A GAR IS A VERY HVY WORKLOAD TIME WHICH IS WHY ONLY A 30 DEG TURN WAS ISSUED TO START. THE GAR ACFT KNEW THE OTHER ACFT WAS ON DEP ROLL ON THE RWY UNDER HIM; THAT IS WHY HE INITIATED THE GAR. WHY HE CHOSE TO IGNORE BOTH MY INSTRUCTIONS AND THE CONFLICTING ACFT UNDER HIM I DO NOT KNOW. I BELIEVE THERE MAY HAVE BEEN A BREAKDOWN IN CREW COMS BTWN THE PF AND THE PNF WHO WAS TALKING ON THE RADIO.