How to display already created menus via php?

I found the solution.

I had to do the following

$args = array
(
'theme_location' => $short,
'menu_id' => $short,
'menu_class' => 'menu',
'menu_id'=>$menu_id,
'fallback_cb' => false
 );
wp_nav_menu( $args);

Theme location was the correct attribute.