CE-560XL Captain reported experiencing a violent shudder in the air frame possibly associated with a wake turbulence encounter in descent through FL360; and after landing discovered the upper cowl was missing from the left engine.

Narrative

While descending from FL390 to FL350 we encountered a violent shudder of the aircraft; we both looked at each other and I wrote it off to wake turbulence. We were in trail with a heavy aircraft (type and distance ahead of us unknown). We were switched to next facility and continued to FL270 crossing BRNDN intersection. We reviewed our assigned STAR and were cleared to descend along this track to 6000. During this time we had no unusual engine or abnormal flight characteristics with the aircraft. It wasn't until downwind that we observed the heavy jet as they turned base to final. We discussed how to operate if asked for traffic and airport for visual APCH. we were turned for base and eventually cleared for visual APCH.After landing we taxied to the FBO and ATC did not mention that anything appeared abnormal on aircraft. Once parked the FBO line personnel meet aircraft; I opened door to get out with my fuel order in mind and the statement was you're not going anywhere. I was baffled and said something like 'what; why' he said look. I looked at left engine and the upper cowl was missing; now I was mystified.I took some pictures; forwarded them. Started the process of grounding the aircraft. We know where and when this event occurred plus what we felt.What could have been a bad ending; turned into a failed mission.There are many lessons learned; but the most important one was a safe completion for both my SIC and myself.