Both the Wehrmacht and the Red Army focused heavily on movement in depth on the operational level, especially in offensive operations, and envelopments of entire armies and fronts were common on the Eastern Front. However, I haven't heard of any large envelopent operation being conducted by the Western Allies in Europe. Is this purely coincidence, or perhaps due to the smaller 0scale of the theatre? Or were the western Allies perhaps more traditional in their conduct of operations?
There were at least two major encirclement-type operations by the Allies in western Europe; the Falaise Pocket during the breakout from Normandy, and the Ruhr pocket after crossing the Rhein (the first mostly successful, the second almost entirely). The Allies were entirely willing to try encirclements when the opportunity presented itself.
One factor that may make the tactic seem less prominent in the west was Eisenhower's "broad front" strategy, where he sought to have the Allies advance en masse, in a manner that allowed for maximum mutual support. There were many reasons behind it, and it is still heavily debated today (although making it to the Elbe is a pretty good endorsement of its success.)
I'd think that while the Allies in the Western front didn't have a name for what they did, they did things even better than blitzkrieg or Deep Operations. Today we'd call it combined arms operations. Blitzkrieg worked mostly because it was used against armies not prepared for mobile warfare (France, USSR) or who were simply overwhelmed (Poland). There were Polish and French units who stood up to the Blitzkrieg because their training and leadership let them think outside of the "1918" box. Once the Western Allies landed in France they started using close air support like it had never been used before, artillery support used in support of platoons or companies. While the Germans and Soviets used close air support, they weren't used by calls for fire, they were sent to areas and the pilots attacked what they thought should be attacked, not what the soldiers needed to be attacked at that moment. The Western Allies had roving fighters looking for targets but they also had aircraft on call for support. The Germans did calls for fire but never to the lowest levels the Western Allies allowed. They just weren't as good at arty support as the Western Allies were. And don't forget that after D-Day it became a war on infrastructure and cities too. Canals and shipping were attacked as were cities. Rail heads and marshaling yards struck over and over again. It was a war against mobility and resupply committed by medium bombers and against manufacturing sites by the heavies.