I'm just evaluating the H2 database... I downloaded and unpacked the installation and connect to a database at
Are you sure there is no:
file? If not, try this:
$ lsof -p `jps -ml | grep h2 | cut -d' ' -f1` | grep \.h2\.db$
What it does is it look for Java process of H2 console, grabs its PID and lists all open files of that process, filtering by H2 database extension. Of course you can use PID of any other Java process accessing this DB. If it is persisted on the disk, you can't miss it.