Wind power [was never] taken seriously in the ancient world [...] though Hero of Alexandria described a windmill connected to an air pump designed to blow an organ, there is no evidence for the existence of any rotary windmills before the tenth century CE.
- Ancient Technology, pg 17.
Mechanical knowledge had a long way to go in antiquity, but my understanding is that the Romans and Hellenistic Greeks made limited but significant use of water power for mills, clocks, and more rarely, automatons. My question here is pretty straightforward: Are there any clear reasons why wind power was never used, especially considering that watermills require a constant and fairly heavy flow of moving water? (Not that you can set up a windmill just anywhere, but it's surprising to me they don't appear as an alternative in areas without strong rivers.)
For this question please take antiquity to mean the Mediterranean and Near Eastern world from the end of the Bronze Age in 1200 BC up to the decline of Rome around 500 AD.