I was reminded of this topic by some of the answers to this question, where it was noted that "typical" measure-preserving transformations are weak-mixing but not strong-mixing for several senses of "typical". As a result, it occurred to me that I do not know of any very natural, explicit examples of transformations which are weakly but not strongly mixing. So,
What are some good examples of measure-preserving transformations which are weak-mixing but not strong-mixing?
To clarify "good": I'm particularly interested in examples where it can be proved in a concise and self-contained manner that weak mixing occurs and strong mixing does not, in examples which arise constructively, and in examples which arise directly from a continuous transformation of a compact metric space (as opposed to abstract measure-theoretic constructions).
Thanks in advance!