MySQL: Cloning a MySQL database on the same MySql instance

I would like to write a script which copies my current database `sitedb1` to `sitedb2` on the same mysql database instance. I know I can dump the sitedb1 to a sql script: mysqldump -u root -p sitedb1 >~/db_name.sql and then import it to `sitedb2`. Is there an easier way, without dumping the first database to a sql file?