BNA APCH CTLR SETS UP TWO ARRIVALS ON CROSSING RWYS THAT ARE TIED AT THE INTXN.

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WHILE WORKING LOCAL 1 POS; I WAS GIVEN 2 ACFT ON ILS APCHS TO CROSSING RWYS 20R AND 31. THE SEQUENCE AT WHICH I WAS FED CAUSED THE TWO ACFT TO BE A TIE AT THE INTXN. WHEN THE MILITARY ACFT ATTEMPTED TO CONTACT ME; HE OBVIOUSLY HAD SOME TYPE OF RADIO PROB. I THOUGHT THE T38 WAS GOING TO LAND ANYWAY ON RWY 31 AFTER OVERHEARING HIM ON THE SPEAKER. I SENT THE CRJ AROUND. THE T38 WAS TOLD TO GAR ALSO BY THE DEP CTLR. I WAS NOT AWARE THAT THE T38 WAS TOLD TO GAR. THE T38 PASSED UNDER THE CRJ AT MIDFIELD. IT WAS LATER DETERMINED BY THE FAC; THAT SINCE THE T38 HAD VISUAL ON THE CRJ THAT EVERYTHING WAS OK. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR STATED THAT THE FAC WAS ON A S OP WHICH IS THE REASON DEP CTL WAS WORKING THE T38 ACFT. RPTR SAID THE T38 WAS NEVER ON THE TWR FREQ. HE THINKS THE T38 PLT MAY HAVE BEEN CROSS CHANNELED BECAUSE HE HEARD THE PLT CALL A FEW TIMES BUT COULD NOT ESTABLISH COMS. HE SAID WHEN THE DEP CTLR REESTABLISHED COM WITH THE MILITARY PLT; HE INSTRUCTED THE PLT TO GO AROUND. THE RPTR SAID JUST BEFORE THAT; SINCE HE WAS NOT TALKING TO THE T38; HE THOUGHT IT BEST TO ISSUE TFC AND SEND THE CL65 AROUND. IN ADDITION; THE RPTR SAID THE VIS WAS HAZY.