Try this:
$('textarea').keypress(function (e){
if(e.keyCode == 13){
$('textarea').val($('textarea').val()+"<br />");
}
});
You could try and fiddle with it here
EDIT: I realized this is adding a <br />
at the end only, after some more research, I found this solution:
$('textarea').keypress(function (e){
if(e.keyCode == 13){
e.preventDefault();
this.value = this.value.substring(0, this.selectionStart)+"<br />"+"\n";
}
});
Here is a fiddle for this one
Source (mostly): Insert text into textarea with jQuery
EDIT AGAIN: Looks like the OP wanted the text at the end to also be cleared, so I updated my code accordingly (for other's seeing this: check out the first edit of my relevant fiddle for the case you'd want to keep the remaining text).