Display secondary menu of parent or self (if top level)

I have created a menu in WordPress that has two levels. On each page I want to show the secondary menu for the parent or the self (if it is top level).

Here is an example of the menu structure:

• Parent 1

• Child 1
• Child 2

• Parent 2

• Child 3
• Child 4

If I am on “Child 2”, I should see “Child 1” and “Child 2” as menu items. Also, if I am on “Child 3”, I should see “Child 3” and “Child 4” as menu items. I don’t want “Parent 1” or “Parent 2” to be displayed at all in the menu.

The child pages can be main blog, categories, pages, etc.

Is there a simple way I can pull this out using a wp_nav_menu?

Thanks!