NEW DELHI — From the waters of the Philippine Sea this week emerged a partial outline of Washington’s vision for a new Asian maritime-security order that unites democratic powers to contend with a more-assertive and well-armed China.

A U.S. Navy aircraft-carrier strike group along with warships from India and Japan jointly practiced anti-submarine warfare and air-defense and search-and-rescue drills in one of the largest and most complex exercises held by the three countries.