Well, that would depend on a couple of definitions a priori: what defines a civilization and at which point should we say that a new civilization is born?
To my knowledge, several authors have done impressive work on these issues, but there has been some disagreement on exactly how many distinct civilizations can we say to have developped in world history. In my view this also defines the next question. It seems that much of what shapes a civilization is confined with its cultural and religious paradigm, but a change per se does not necessarily mean a new civilization has emerged. Take the west for example: when did it start? I guess there are several hypothesis, but the most accepted must be around 800 AD, when Charlemagne and the Pope established their alliance, that is, when the roles of both religious and secular power were cleared and separated, and at the same time Christianity was emerging from what became known as Dark Ages. So we might say that at the core of the West's identity lays an idea of separation of Church and State, although the kind I mentionbed above is a very primitive one, and we had to wait 1000 years for it to fully consolidate, at which point we stop calling Christianity to the West and start calling it the West.
Obviously new civilizations either descend directly from one or more earlier ones (like the west descends from the classical roman and greek civilizations and also the canaanite or hebrew one, a melting pot in which the cultural background of the germanic peoples, perhaps not a civilization on its own merit, also entered), or they evolve from earlier tribal pre-civilizations.
So, in the West's case, imo, there was definitly a collapse of an earlier civilization, but followed by a long gestation period in a which a new stabe world was erected. But that world didn't stay stactic after that, on the contrary. Though most scholars would agree that the civilization of William the Conqueror, or St. Francis of Assissi, or Dante Alighieri, or Leonardo da Vinci, or Louis XIV, or Napoleon Bonaparte, or Thomas Jefferson, or Karl Marx, or Charles Darwin, or Winston Churchill is always the same, and the same as ours, I doubt they would recognise it themselves, had they met each other for a chat in the after life. So, in my mind civilizations are very dinamic, even those that don't seem to be so turbulent as the west. There surely seem to have been periods when the west was about to be destroyed (the mongol, arabian or turk hordes), or split (the Reformation, WWII and the Cold War), etc.
Yet it stood, and stood because people felt there was something that united them and separated them from the alien worlds elsewhere, although, as we've seen with the recent cartoon crisis, we no longer seem to know what thing is that.
So I belive that what you call "smooth transition" depends very much in the context. How long is a smooth transition? 2 generations? 2 centuries? A 1000 years? I'm not an expert in neither of this, but it seems that North Africa, particulary earlier strongholds of (pre)West, like nowadays Lybia and Tunisia, made a quick transition to Islam. In fact Islam seems to be much better at expanding itself faster than the West, which took ages to bring Norther Europe, Scandinavia and the western slavic peoples to its family, and never quite achieved that with Russia. But in these cases, we're talking about a pre-existing civilization expanding its borders, not of a birth of a civilization proper. When we shift an entire region from one earsed civilization to a new born one, things are much more complex. But if you regard Byzantium or Orthodoxy as a different civilization from both West and Classical greco-roman, and I think it's perfectly legitimate to do so, the transition was much caler than in the former western roman empire. It was indeed faster and smoother, but that may be connected with political fragmentation. For the time that it took Byzantine civilization to emerge, there was always a universal empire, a civilization-state. That was never the case with the West, that until very recently was for a 1000 years in a period of warring states, and although they're no longer warrier, they're not unified either, despite the EU or NATO, which may be in future, the prototypes of such a unified empire.
To conclude, I think most civilization shifts and births have turmoil or conquest at its genesis, but that's not a universal rule and it can be obtained in a much easier bargain, especially if there is a previous unified culture, empire, and especially the notion of a common alien foe.
