A CL60 WING CONTACTED THE GND WHILE ATTEMPTING A GAR DUE TO WINDSHEAR.

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ON NOV/THU/03; WE HAD A PLANNED FLT IN A CL60 FROM TORONTO; CANADA TO PROVIDENCE; RI. I CALLED AND CHKED ON THE WX FOR BOTH LOCATIONS STARTING ABOUT XA00 THAT DAY. I CALLED COMMERCIAL SVC TO RECEIVE WX BRIEFS. ALL WX RPTS FOR PROVIDENCE WERE FORECAST TO BE VFR WITH WINDS 280 DEGS/24 KTS OR 280 DEGS/17 KTS FOR OUR TIME OF ARR. THE LAST CALL TO WX-BRIEF GAVE THE WINDS 310 DEGS/25 KTS GUSTING 35 KTS WITH THE CEILING AROUND 5000 FT AND A NOTAM FOR ILS RWY 23 BEING UNUSABLE OUTSIDE OF 30 DEGS AND DME UNUSABLE OUTSIDE OF 15 DEGS FOR PVD. WE DEPARTED TORONTO AND PROCEEDED TO PROVIDENCE. THE TKOF FROM TORONTO HAD VERY LIGHT CHOP AND THE RIDE TO PROVIDENCE WAS SMOOTH WITH OCCASIONAL LIGHT CHOP. THE FO RECEIVED THE PROVIDENCE ATIS INFO AND WE INCREASED OUR LNDG REF SPD FOR THE WIND GUST. IN THE DSCNT INTO PROVIDENCE; CTR OR APCH REQUESTED THAT WE SLOW FOR AN ACFT LNDG AT PROVIDENCE. WE OBSERVED THE ARPT DSNDING THROUGH 5000 FT. WE CIRCLED L FOR A VISUAL APCH TO RWY 34. THE ACR THAT LANDED BEFORE US RPTED A +/-15 KTS ON THE APCH TO RWY 34. WE ENCOUNTERED +/-10 KTS WITH THE WIND 30 DEGS L OF RWY HEADING. DURING THE APCH TO THE RWY WE ENCOUNTERED MODERATE TURB; BUT CONTROLLABLE. THE FO CALLED OUT REF SPDS; RATE OF DSCNT; AND ALTS AS WE DSNDED. THE LNDG REF SPD CALLS WERE ALL PLUS KTS. I DECIDED TO GO AROUND BECAUSE OF THE TURBULENT CONDITIONS. I ADVANCED THE THROTTLES TO GO AROUND PWR AND ROTATED THE ACFT. SECONDS AFTER THE GAR WAS INITIATED THE PLANE ENCOUNTERED WINDSHEAR AND WITH FULL L AILERON THE PLANE SETTLED DOWN WITH THE R MAIN MAKING CONTACT WITH THE RWY. I CONTINUED TO GO AROUND AND TURNED L DOWNWIND FOR RWY 34 TO STAY IN THE TFC PATTERN. WITH 3 HRS OF FUEL ABOARD THE ACFT; I MADE THE DECISION NOT TO ATTEMPT ANOTHER APCH INTO PVD AND REQUESTED TO PROCEED TO TETERBORO; NJ; FOR LNDG. THIS DECISION WOULD TAKE US S AWAY FROM THE LOW PRESSURE SYS THAT WAS CAUSING THE TURB IN THE PROVIDENCE AREA. ENRTE I REQUESTED WX FROM CTR FOR TETERBORO; NJ; AND BOSTON; MA. I REQUESTED THE FO TO CONTACT THE FBO AT TETERBORO ON THEIR FREQ TO ARRANGE FOR CUSTOMS. WHILE THE FO WAS SPEAKING TO THE FBO AT TETERBORO; ZBW AT SOME POINT IN THE TRIP FROM PROVIDENCE TO TETERBORO; GAVE ME A FREQ AND A TELEPHONE NUMBER TO CALL WHEN I HAD TIME. CTR RPTED THAT A PERSON IN THE PROVIDENCE TWR HAD NOTICED SPARKS ON THE RWY. I ASKED THE FO TO VISUALLY CHK THE CONDITION OF THE R WING. THE FO STATED THAT THE LIGHTS WERE WORKING AND THE WINGLET WAS STABLE. THE ACFT DID NOT HAVE ANY CTL PROBS. WE MADE A SAFE LNDG AT TETERBORO AND WHEN ABLE; INSPECTED THE R WING AND FOUND THAT THE WING HAD MADE GND CONTACT.