C172 flight instructor reports prop strike and wing tip damage when student attempts to turn off the runway after landing in strong gusty winds.

Narrative

I am a full time flight instructor. I was giving instrument instruction to student in the local area. Upon returning to the airport; we executed the VOR approach to a landing. It had been a relatively gusty day with forecast winds 270-300 degrees; 15-25 KTS with occasional gusts to 30 KTS. I had made a previous flight that day and had not encountered any winds greater than 15-25 KTS. As best as I can recollect; the ATIS was reporting 300 degrees at 14 KTS gusting to 24 KTS. While on final approach; the Local Controller gave us at least 3 wind checks; none of which were greater than 27 KTS; although he did mention that since he had come on duty he had seen 1 gust of 37 KTS. As we arrived over the runway; the wind had shifted down the runway to 270 degrees and looking at the windsock I estimated 25 KTS. I assisted my student with the landing which was quite uneventful. After coming to a complete stop on the runway; we retracted the flaps and I reminded him that on own downwind turn off the runway we would continue to hold full right aileron and we would be adding full forward elevator as the winds now seemed to be swinging back toward 300 degrees. As we began the turn off the runway (left turn taxiway heading approximately 160 degrees) we had only turned from 270 degrees to about 230 degrees the right wing (with full right aileron) suddenly rose abruptly to the point that the left wingtip hit the ground and the propeller was impacting the runway. I immediately pulled the mixture to idle cutoff and the airplane came to a stop on a heading of about 220 degrees. The Tower called for the airport vehicles and we eventually got the aircraft towed back to its tie-down. I've been flying for 35 years and never seen anything like it. I have flown in winds in excess of what we had that night without experiencing any loss of control. I can only guess that we must have experienced a gust in excess of 50 KTS although the Tower didn't report any readings of that velocity.