$arr = array(1,2,3,4);
$file_data = json_encode($res);
$download_filename = '123.json';
$http_user_agent = $_SERVER['HTTP_USER_AGENT'];
header("Content-Type: application/octet-stream");
if (preg_match("/MSIE/", $http_user_agent) ) {
    header('Content-Disposition:  attachment; filename="'.$download_filename.'"');
} elseif (preg_match("/Firefox/", $http_user_agent)) {
    header ('Content-Disposition: attachment; filename*="utf8' . $download_filename . '"' );
} else {
    header('Content-Disposition:  attachment; filename="'.$download_filename.'"');
}
header("Accept-Length: ".strlen($file_data));
echo $file_data;

试了试，谷歌浏览器、火狐浏览器可直接下载；
IE浏览器如果出现如下弹窗：

解决方案：在ie菜单栏的【页面】-->【编码】,选择【自动选择】然后下载试试。

360浏览器也出现这种问题，待测。