The Perilous Sea by Sherry Thomas

The second volume in the Elemental series – the boys at Eton take a holiday at one boy’s uncle’s estate on the Scottish coast.  One boy, Wintervale, was not able to attend as his mother was not well.  But suddenly, Fairfax and Titus see the boy in a skiff trying desperately to escape from an Atlantis frigate.  When all seems lost, the boy, looks back at the frigate and it is caught in a maelstrom, sucked under by the whirlpool.  He seems completely out of it when he reaches shore and when the prince administers a remedy, he goes into a seizure.  From then on, he has a terrible time walking and has to be helped everywhere.  But worse, Titus now thinks his vision of Iolanthe being the one who will help him succeed in his quest to overthrow Atlantis was wrong and it’s Wintervale instead.

The book is written in two timelines.  In the other timeline, Iolanthe and Titus are in the Sahara desert and don’t remember anything.  However, they’re attacked by agents of Atlantis and fight their way across the desert until allies rescue them.  The book does tie both together at the end.  Which apparently the real showdown that will be explained in book three.