NMAC WITH A320 AND CHEROKEE ON TKOF.

Narrative

STUDENT PLT IN PIPER CHEROKEE IS ISSUED A L TURN TO 140 DEG HDG AFTER DEP BY CLRNC DELIVERY. RWYS 30R (USED FOR LIGHT ACFT) AND 30L (USED FOR COMMERCIAL JETS) WERE ON SPLIT TWR FREQS. THE STUDENT PLT DEPARTED AHEAD OF US WITH NO OTHER DEP INSTRUCTIONS -- THOUGH THE LCL CTLR WAS SUPPOSED TO ISSUE OTHER INSTRUCTIONS TO AVOID TFC CONFLICT (ACCORDING TO TWR SUPVR). HE WAS NOT ADVISED OF OUR DEP ON THE CLOSELY SPACED PARALLEL RWY EITHER. WE (AN AIRBUS A-320) DEPARTED WITH THE CHEROKEE IN SIGHT. AS WE WERE APCHING HIS ALT; THE CHEROKEE PLT BEGAN HIS L TURN - - DIRECTLY IN OUR FLT PATH. THE FO (PF) PULLED UP AND TURNED R TO AVOID THE CHEROKEE. WE PASSED DIRECTLY OVER HIM. TFC WAS CALLED TO US ONLY MOMENTS PRIOR TO PASSING OVER HIM. BOTH PLTS WERE FOLLOWING ATC INSTRUCTIONS. CLRNC DELIVERY ISSUED INSTRUCTIONS THAT WOULD PUT THE ACFT IN THE DEP PATH OF THE PARALLEL RWY. THE LCL CTLR IS CHARGED WITH ISSUING INSTRUCTIONS TO AVOID THIS CONFLICT; BUT DUE TO HUMAN ERROR ON THE CTLR'S PART; THOSE INSTRUCTIONS WERE NOT ISSUED. THE CAUSE OF THE INCIDENT WAS THE LCL CTLR'S FAILURE TO ISSUE APPROPRIATE DEP INSTRUCTIONS TO THE STUDENT CHEROKEE PLT. EQUALLY AT FAULT IS THE ISSUING OF DEP INSTRUCTIONS BY CLRNC DELIVERY THAT REQUIRED UN-DOING. IN A POST INCIDENT PHONE CALL TO TWR SUPVR; HE INFORMED ME THAT THEY WERE CONSIDERING CHANGING THE CLRNC DELIVERY INSTRUCTIONS TO 'FLY RWY HDG.' HAD THIS BEEN THE POLICY ON THE DAY OF THE INCIDENT; THE CHEROKEE WOULD NOT HAVE TURNED INTO OUR FLT PATH.