file appender that rolls on startup

I'd like a file appender that can roll to a new file on startup.

Example:

• file name myApp.%d {yyyy-MM-dd}

  .%i.log

• if the process lasts the whole day, we get only one log file for that day, called myApp.2010-04-15.0.log
• if the process is restarted, we get multiple files for that day, myApp.2010-04-15.0.log, myApp.2010-04-15.1.log, ...

Currently, I believe that the best we can do with the out-of-the-box appenders/rollers is to either append to or overwrite a single file per day.