Bash – With a username passed to a script, find the user’s home directory

I am writing a script that gets called when a user logs in and check if a certain folder exists or is a broken symlink. (This is on a Mac OS X system, but the question is purely bash).

It is not elegant, and it is not working, but right now it looks like this:

#!/bin/bash

# Often users have a messed up cache folder -- one that was redirected
# but now is just a broken symlink.  This script checks to see if
# the cache folder is all right, and if not, deletes it
# so that the system can recreate it.

USERNAME=$3
if [ "$USERNAME" == "" ] ; then
    echo "This script must be run at login!" >&2
    exit 1
fi

DIR="~$USERNAME/Library/Caches"

cd $DIR || rm $DIR && echo "Removed misdirected Cache folder" && exit 0

echo "Cache folder was fine."

The crux of the problem is that the tilde expansion is not working as I'd like.

Let us say that I have a user named george, and that his home folder is /a/path/to/georges_home. If, at a shell, I type:

cd ~george

it takes me to the appropriate directory. If I type:

HOME_DIR=~george
echo $HOME_DIR

It gives me:

/a/path/to/georges_home

However, if I try to use a variable, it does not work:

USERNAME="george"
cd ~$USERNAME
-bash: cd: ~george: No such file or directory

I've tried using quotes and backticks, but can't figure out how to make it expand properly. How do I make this work?

Addendum

I just wanted to post my completed script (really, it isn't as ugly as the work in progress above!) and say that it appears to be working right.

#!/bin/bash

# Often users have a messed up cache folder -- one that was redirected
# but now is just a broken symlink.  This script checks to see if
# the cache folder is all right, and if not, deletes it
# so that the system can recreate it.

#set -x # turn on to help debug

USERNAME=$3 # Casper passes the user name as parameter 3
if [ "$USERNAME" == "" ] ; then
    echo "This script must be run at login!" >&2
    exit 1  # bail out, indicating failure
fi

CACHEDIR=`echo $(eval echo ~$USERNAME/Library/Caches)`

# Show what we've got
ls -ldF "$CACHEDIR"

if [ -d "$CACHEDIR" ] ; then
    # The cache folder either exists or is a working symlink
    # It doesn't really matter, but might as well output a message stating which
    if [ -L "$CACHEDIR" ] ; then
        echo "Working symlink found at $CACHEDIR was not removed."
    else
        echo "Normal directory found at $CACHEDIR was left untouched."
    fi
else
    # We almost certainly have a broken symlink instead of the directory
    if [ -L "$CACHEDIR" ] ; then
        echo "Removing broken symlink at $CACHEDIR."
        rm "$CACHEDIR"
    else
        echo "Abnormality found at $CACHEDIR.  Trying to remove." >&2
        rm -rf "$CACHEDIR"
        exit 2  # mark this as a bad attempt to fix things; it isn't clear if the fix worked
    fi
fi

# exit, indicating that the script ran successfully,
# and that the Cache folder is (almost certainly) now in a good state
exit 0