I played around with it for a while. Here is what I found:
The (web kit) browser use a database to organize the websql databases. :-)
for chrome it is in (Mac OS X):
~/Library/Application Support/Google/Chrome/Default/databases/Databases.db
You can access this via sqlite3 Databases.db:
Mine looks like:
sqlite> select * from databases;
1|http_slides.html5rocks.com_0|DBTest|HTML5 Database API example|200000
2|http_www.html5rocks.com_0|modernizrtestdb|modernizrtestdb|20000
3|http_www.html5rocks.com_0|Todo|Todo manager|5242880
4|http_experimenting.in_0|mystorage|Web SQL Storage Demo Database|1048576
5|file__0|mystorage|Web SQL Storage Demo Database|1048576
sqlite> .quit
the file ./file__0/5 contains the database for mystorage.
the entries are created when the code does the opendatabase ...
I didn't find a way how to create an entry in this database and give it a path or filname.