Squall on Chanonry Point

We drove out to Chanonry Point on the Moray Firth to see the dolphins. We had to wait whilst a squall blew through. The sea had been flat calm beforehand. Squalls come with very localised strong winds. It occurred to me that the strong wind section must move round as a block under the clouds. How does that happen? I think it will be that squalls are the result of intense convection because they often come with hail or thunder. The strong winds associated might then be the cold air descending. But what interests me is the way that this unit moves through a tranquil space, stirs it up and then leaves it tranquil again. It's a bit like a wave motion, like a carpet ruck being kicked through.