Oracle Database Migration using Oracle SQL Developer
why do you need windows at all? you even do not need sql developer.


shutdown the source database
scp datafiles(.dbf .ctl)
scp files in ORACLE_HOME/dbs (like initSID.ora, spfileSID.ora, and also password file)
you should also create dirs for diagnostic_dest (where alert.log is placed)
amend /etc/oratab
set the right SID
start the database


PS: this assumes that the Oracle version (including fixpack) is exactly the same.