I'm not really sure what it is you're asking for here. As another commenter said, ps outputs a list of newline separated entries (using \n, the standard LF character). I even ran some sanity checks to make sure it wasn't using \r\n (CR LF) with the following:
The output of ps aux | grep $USER is consistent with the formatting of ps aux. I also found that ps aux | grep $USER was consistent with ps -fp $(pgrep -d, -u $USER) except that ps -fp $(pgrep -d, -u $USER) shows the header (UID PID PPID C STIME TTY TIME CMD), does not show the processes related to the command (entries of ps aux and grep --color=auto $USER), and does not show grep's keyword matching by highlighting all matches within a line. It is otherwise completely identical.
Can you provide the output that you are getting that is unsatisfactory to you? I don't think I can otherwise understand where the issue is.