MD80 FLT CREW CONDUCTED NIGHT VISUAL APCH AND LANDED ON THE WRONG RWY.

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NIGHT APCH TO LGB WITH VERY STRONG SURFACE WINDS AND TURB LEAD US BEING VECTORED TOWARD LGB ARPT AT NIGHT FOR A VISUAL TO RWY 12 WAS EXPECTED. I HAD DONE AN ARPT LNDG PERFORMANCE ANALYSIS JUST BEFORE TOP OF DSCNT AND BRIEFED THE FO THAT WE ARE GOOD TO LAND ON ANY RWY AT LGB. ATC BROUGHT US IN FROM A DIRECTION WE WEREN'T EXPECTING. (WE HAD BRIEFED FLYING THE LOC RWY 30 CIRCLE TO RWY 12.) INSTEAD APCH BROUGHT US IN AT 1600 FT W OF THE ARPT AND KEPT ASKING US IF WE HAD THE ARPT IN SIGHT. WE BOTH AGREED WE SAW THE ARPT AND DECIDED ON A L TURN AWAY FROM THE ARPT TO GIVE OURSELVES MORE ROOM TO MANEUVER TO A MORE NORMAL DOWNWIND TO BASE. I HAD SET THE FIX PAGE TO GIVE US A DISTANCE TO THE CTR OF THE ARPT AND ALIGNED BOTH OF OUR HSI'S TO THE INBOUND RWY HDG. AS WE TURNED BACK TO THE RWY; WE BOTH SAW THE RWY AND AGREED WE LOOKED PRETTY GOOD VERTICALLY. THE FO HAD THE ACFT CONFIGURED FOR RWY 28 FOR THE STRONG XWIND; AND WE WERE AT TARGET +5; VERT SPD WAS 700 DOWN AND WE WERE WINGS LEVEL ON VASI. WE WERE BOTH VERY BUSY (ME MAKING SURE B/A SET; HDG; AND CALLING 500 FT FOR STABLE; TURNING ON NOSE TAXI LIGHT WHEN CLRED TO LAND; FO COMMENTING ABOUT SEEING VASI'S AND THEM BEING IN THE CORRECT PLACE AND BEING STABLE). AT ABOUT 100 FT I CALLED THE TWR TO CONFIRM WE WERE CLRED TO LAND AND AS I WAS SAYING THAT I SAID RWY 7L BECAUSE THAT WAS WHAT I SAW UNDER THE NOSE (IT DIDN'T REALLY REGISTER TILL ABOUT 20 FT THAT I THOUGHT WE WERE ON RWY 12) TWR HAD CLRED US TO LAND ON THAT RWY (ALBEIT AT VERY LOW ALT) AND WE HAD DONE ALL THE PERFORMANCE FOR ALL THE RWYS. (I REALLY THOUGHT ABOUT GOING AROUND BUT WE WERE ON THE GND ABOUT THAT TIME.) I THINK WE SHOULD LOOK AT OTHER AIRLINES' POLICIES ABOUT LNDG ON RWYS WITHOUT NAVAIDS (ESPECIALLY AT NIGHT). I SEE WHY THEY HAVE THESE RULES. WE THOUGHT WE WERE LINED UP FOR RWY 12 BUT IT WAS RWY 7L AND SUBSEQUENTLY CLRED TO LAND ON RWY 7L. WE HAD LOOKED OVER LNDG PERFORMANCE FOR ALL RWYS SO WE KNEW WE WERE GOOD TO LAND ON ANY RWY. BUT WE WERE SO BUSY WITH THE APCH THAT WE HAD TO ASK IF WE WERE CLRED TO LAND ON RWY 7L. TWR CLRED US TO LAND ON RWY 7L. WE WERE VERY LOW AND REALIZED AT THE LAST MOMENT THAT ALL THE WAY DOWN FINAL WE THOUGHT WE WERE LOOKING AT RWY 12. IT WAS ONLY AT THE LAST MOMENT WE REALIZED IT WAS RWY 7L.