NMAC OCCURS AS ACR B737-200 IS STARTED IN A R TURN DURING INITIAL CLB AND AN F15 FIGHTER CLOSES ON THE R DURING A RWY FLY OVER OR GAR.

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A B737-200; OPERATED BY ACR IN PART 121 SCHEDULED SVC WAS DEPARTING JAX. ON THE FLT DECK; AS FO; I WAS PERFORMING NORMAL PNF DUTIES. TAXI AND TKOF WERE UNEVENTFUL. IMMEDIATELY PRIOR TO OUR TKOF CLRNC; 2 F15 TYPE FIGHTER ACFT MADE A LOW PASS TO RWY 25 AND REMAINED IN CLOSED TFC. OUR TKOF RUN; LIFTOFF; AND CLBOUT FROM RWY 25 WAS NORMAL. DURING OUR CLB (APPROX 600 FT AGL) I HEARD THE ROAR OF JET ENGS. I TURNED TO CHK MY 5 O'CLOCK POS AND SAW THE UNDERSIDE OF AN F15 AT OUR ALT. I ESTIMATE THE RANGE TO BE ON THE ORDER OF 500-1000 FT. RETURNING TO FORWARD SCAN I RPTED THE TFC TO THE CAPT. THE CAPT WAS ESTABLISHED IN APPROX A 15 DEG BANK (IN RESPONSE TO ATC TO TURN R TO A HDG OF 310 DEGS). THE CAPT ARRESTED HIS TURN. I TURNED ONCE AGAIN LOOKING FOR THE TFC; THIS TIME THE F15 AT 4 O'CLOCK; IN APPROX A 70 DEG BANK; IN WHAT APPEARED TO BE FULL AFTERBURNER. HE WAS ACCELERATING RAPIDLY AWAY FROM OUR POS. OUR FLT ATTENDANTS ALSO RPTED HEARING THE ROAR OF THE F15 IN THE MAIN CABIN. 1) WHEN INSTRUCTING THE FIGHTER ACFT; ATC MAY NOT HAVE BEEN SPECIFIC IN REGARD TO OUR POS. 2) THE FIGHTER PLT (HIGH SINGLE PLT WORKLOAD) MAY NOT HAVE SEEN OUR ACFT UNTIL CLOSING RAPIDLY (SHARED USE AIRSPACE?). 3) NO TCASII RA/TA WAS RECEIVED. (F15 NOT SQUAWKING?; EQUIP FAILURE?; EQUIP INHIBIT FUNCTION BELOW 1000 FT AGL?). CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR CALLED BACK WITH THE FOLLOWING INFO. THE PIC WAS FLYING THE ACFT AND WAS VERY CONCERNED WITH THE ISSUES OF THIS EVENT. HE LATER CALLED THE TWR CTLR WHEN THE FLT ARRIVED AT ITS DEST ARPT. THE FO RPTR WAS NOT PRIVY TO WHAT WAS SAID EXCEPT THAT THE TWR CTLR SEEMED; TO THE CAPT; TO BE QUITE UNCONCERNED WITH THE INCIDENT. THE CTLR SAID THAT THIS WAS A 'NORMAL' EVENT. THE CTLR HAD ISSUED A TA TO THE MIL PLTS REGARDING THE B737 ON TKOF AND THAT BOTH MIL ACFT WERE ON A SECOND LOW PASS ON THE GAR FLY-BY. THERE WAS NOT ANY AIR SHOW ACTIVITY GOING ON AT THIS TIME. THE FO SAID THAT THE ROAR OF THE JET ENGS ON THE NMAC WAS INCREDIBLE AND FELT THAT THE PAX MAY HAVE ALSO BEEN ALARMED. HOWEVER; THERE WERE NO ADVERSE COMMENTS BY THE PAX UPON THEIR DEPLANING. SUPPLEMENTAL INFO FROM ACN 362697: SOME WAY MUST BE FOUND TO KEEP HIGH PERFORMANCE FIGHTER ACFT AWAY FROM CIVILIAN ACFT WITH INNOCENT NON COMBAT PAX ABOARD. APPARENTLY; LEGAL SEPARATION MEANS 'NO MERGING OF ACFT.' 1 FT SEPARATION IS AS GOOD AS 1 MI TO ZJX! PARTIES NOTIFIED: JAX TWR BY PHONE; MR Z. ZTL REGION BY PHONE; MR X. DISPATCH; IN PERSON. CHIEF PLT; CAPT Y; IN PERSON AND IN WRITING. FAA PRINCIPAL INSPECTOR; IN PERSON.