FOLLOWING WINDSHEAR ENCOUNTER ON APPROACH; MEDIUM LARGE TRANSPORT ACFT DIVERTS TO ANOTHER AIRPORT AND MUST DECLARE A FUEL EMERGENCY DUE TO NO ALTERNATE FUEL BOARDED.

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FLT WAS DISPATCHED TO ZZZ WITH 13.9 FUEL WITH A PLANNED ARR FUEL OF 6.9. WX IN ZZZ RPTED WINDS 120 DEGS AT 7 KTS; VISIBILITY 10 MI; FEW CLOUDS AT 5500 FT; 11000 FT BROKEN; TEMP 11/-1; ALTIMETER 29.76; RWY XX AND RWY XY WERE IN USE. I BRIEFED THE APCH FOR RWY XX WITH THE ANTICIPATION OF A VISUAL APCH. TFC IN THE AREA WAS COMPANY AHEAD OF US AND ANOTHER BEHIND US ARRIVING INTO ZZZ. APPROX 25-30 MI OUT FROM ZZZ VOR; APCH CTL TOLD US TO PLAN TO HOLD AT ZZZ VOR AS PUBLISHED ON THE APCH TO RWY XX. COMPANY AHEAD OF US EXPERIENCED WINDSHEAR ON APCH; EXECUTED A GAR; RPTED +/-20 KTS; AND WAS TOLD TO ENTER HOLD. THEY THEN TRIED THE APCH AGAIN AND LANDED ON RWY XX STILL RPTING WINDS +/-20 KTS. APCH CTL ANNOUNCED THEIR EQUIP ON THE FIELD RPTED +/-20 KTS ALL AROUND THE FIELD. AT THAT TIME; WE WERE GIVEN A HDG FOR VECTORS TO FINAL APCH AND WX WAS BEGINNING TO BUILD NEAR THE ARPT. I BEGAN A VISUAL APCH TO RWY XX AND ONCE REACHING 600 FT; ENTERED TURB AND WINDSHEAR +40 KTS. EXECUTED WINDSHEAR RECOVERY; GIVEN A L DOWNWIND TURN; AND EXPERIENCED SEVERE TURB ON THE CLBOUT. AT THAT TIME; I NOTIFIED OPS AND DISPATCH WE WERE DIVERTING AND NEEDED AN ALTERNATE IMMEDIATELY WITH FUEL 5.8. DISPATCH RESPONDED OUR ALTERNATE WOULD BE ZZZ1. I DECLARED EMER FUEL; BRIEFED THE APCH INTO ZZZ1 FROM THE ALTERNATE MANUAL PACKAGE; OBTAINED ARPT AND WX INFO. THE TWR WAS CLOSED AT THE TIME OF ARR AND WE LANDED WITH 2.3 FUEL. THE FLT ATTENDANTS AND PAX WERE BRIEFED AS TO WHAT HAPPENED AND TOLD THEM WE WOULD REFUEL AND DEPART SHORTLY. DEPARTED ZZZ1 RWY XX WINDS 200 DEGS AT 8 KTS; VISIBILITY 10 MI; TEMP 14/7; ALTIMETER 29.77; FUEL 12.8 (3.0) BURN; AND GIVEN ZZZ2 AS AN ALTERNATE 4.0 BURN; INTO ZZZ. LANDED IN ZZZ ON RWY XX; DEPLANED; AND DEADHEADED BACK. THE COM WITH OPS AND DISPATCH WAS VERY DIFFICULT. I SHOULD HAVE QUESTIONED DISPATCH ABOUT THE BIG PICTURE IN REGARDS TO THE WX FOR A MORE SUITABLE ALTERNATE. I TRUSTED DISPATCH WITH THEIR DECISION; HAVING MORE INFO ON THE WX.