G200 FLT CREW INDICATES THEY HAVE THE FIELD IN SIGHT AND ACCEPTS A VISUAL APCH. FLT CREW HAS ANOTHER RWY; ARPT IN SIGHT AND OVERFLIES THEIR INTENDED RWY.

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ENRTE TO DAL ON THE FINGR 3 ARR; WE WERE CLRED TO ROSSE INTXN AND WERE TOLD TO EXPECT RWY 31R. WE PROCEEDED DIRECT TO ROSSE (RWY 31R ILS FAF) AND ATC ASKED PRIOR TO GETTING TO ROSSE TO ADVISE WHEN DAL ARPT IN SIGHT. WE SEARCHED FOR THE ARPT; AND THOUGHT THAT WE HAD IT IN SIGHT AT OUR 12-1 O'CLOCK POS; SO WE ACCEPTED THE VISUAL CLRNC TO RWY 31R. THE CTLR TOLD US TO MAINTAIN A 290 DEG HDG UNTIL WE INTERCEPTED THE RWY 31R FINAL. AT THIS POINT I DISCONNECTED THE AUTOPLT AND PROCEEDED TO THE ASSIGNED HDG. NEXT; ATC ADVISED US THAT WE HAD TFC AT OUR 12-1 O'CLOCK POS; 3 MI -- A B737 GOING TO RWY 31L. WE SEARCHED FOR TFC; THEN I LOOKED BACK AT OUR HSI AND IT SHOWED A FULL R SCALE DEFLECTION; SO I ASKED THE PNF IF THERE WAS A PROB; AT ABOUT THE SAME TIME ATC TOLD US WE WERE OVERFLYING THE ARPT (DAL). THEY COMMANDED US TO MAKE A R TURN TO OVERFLY THE ARPT (DAL) AND DSND TO 2000 FT AND CONTINUE A 270 DEG TURN TO REJOIN FINAL FOR RWY 31R AT DAL. WE DID AS REQUESTED AND LANDED WITH NO FURTHER COMPLICATIONS. SUPPLEMENTAL INFO FROM ACN 685832: I ASKED THE L SEAT FLYING PLT IF HE HAD THE ARPT. HE SAID HE HAD THE ARPT AT ABOUT 1 O'CLOCK POS. I REPLIED 'I DON'T HAVE IT BUT I WILL CALL IT IF YOU DO.' HE SAID 'I HAVE IT.' I CALLED THE ARPT IN SIGHT. I LOOKED TO THE R AND SAW THE APCH END OF THE ARPT JUST AHEAD AND BELOW US. THE TWR CTLR SAID WE WERE OVERFLYING THE ARPT; MAKE A R 360 DEG TURN AND REJOIN THE FINAL. WE PROCEEDED WITHOUT ANY FURTHER COMPLICATIONS.