If you want Tomcat to automatically rotate/cycle catalina.out with the date then do the following:
Find and edit the file: catalina.sh
change:
CATALINA_OUT="$CATALINA_BASE"/logs/catalina.out
to:
CATALINA_OUT="$CATALINA_BASE"/logs/catalina.`date +%Y-%m-%d`.out
Note:
Be sure you are editing the correct file as many different installs may use their own catalina.sh or even rename it and move it to /etc/init.d. Windows users may have to find work-arounds for the date function.