CARJ CREW HAD CVG APCH CTL ISSUE A 'LOW ALT ALERT' ON 2 SEPARATE APCHS; WHILE FLYING THE LUK LOC (BACK COURSE) TO RWY 3R APCH. THE ACFT WAS 500 FT ABOVE THE PUBLISHED MDA ALT.

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EXECUTING THE LOC BACK COURSE RWY 3R AT LUK. ON THE FIRST APCH; WE GOT POOR VECTORS ALONG WITH LOTS OF WIND AND TURB; BUT WAS STABILIZED PRIOR TO FAF. THE STEP-DOWN TO MDA WAS PERFORMED AND 500 FT ABOVE MDA; THE CTLR ISSUED A LOW ALT ALERT. WE STOPPED THE DSCNT AND A FEW SECONDS LATER; DID THE MISSED. WE THEN WERE VECTORED FOR A SECOND APCH WHICH HAD BETTER VECTORS AND HAVING A BETTER IDEA OF THE WIND AND TURB WAS STABILIZED FURTHER OUT. AT THAT FAF WE STARTED THE STEP-DOWN TO MDA. AGAIN; THE CTLR ISSUED A LOW ALT ALERT 500 FT ABOVE MDA. AGAIN WE STOPPED OUR DSCNT AND A FEW SECONDS LATER PERFORMED THE MISSED. ON BOTH THE APCHS; THE CREW COULD NOT DETERMINE WHY THE LOW ALT ALERTS WERE ISSUED. WE DECIDED TO DIVERT TO CVG AND TRY AND FIGURE OUT WHAT HAPPENED. THE NEXT DAY; I SPOKE WITH LUK TWR PERSONNEL. THEY ADVISED ME THAT IT IS TYPICAL FOR ACFT TO BE ISSUED THE ALERTS (90% OF ACFT) BECAUSE OF THE WAY THE RADAR AND TERRAIN IS SITUATED. I AM CURRENTLY WORKING WITH THE MGR AT CVG APCH CTL AT THE REQUEST OF THE LUK TWR MGR. IT SEEMS THAT THE TWR MGR HAS HAD AN ONGOING DIALOG CONCERNING THIS ISSUE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: ARPT WIND WAS 045 DEGS AT 40 KTS. THIS REQUIRED AN APCH TO RWY 3R. THE CREW FLEW 2 APCHS AND GOT THE LOW ALT ALERT AT THE SAME ALT BOTH TIMES. THE WARNING WAS RECEIVED AT 1740 FT MSL OR 500 FT ABOVE THE PUBLISHED MDA OF 1240 FT MSL.