the $$ variable is a process id, which does not change within a currently running process (i.e. execution of your code)

If you want a different file name for each iteration, you could construct one using the $i variable, as well as the $$. Don't forget to close the file after you're done!

i.e.

for my $i (0..@array1-1) {
    open (OUT,">$$.out$i", or die "Ooops...!";
    print OUT ">$array1[$i]>$array2[$i]\n\n\n";
    close OUT;
}
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