WordPress allows the addition of extra nav menus.
Add this to your child themes functions file:
register_nav_menus( array(
'secondary_menu' => 'My Second Menu'
) );
Add this to your header.php file or the file where you want to display your extra nav menu.
<nav id="site-navigation" class="main-navigation" role="navigation">
<?php wp_nav_menu( array( 'theme_location' => 'secondary', 'menu_class' => 'nav-menu' ) ); ?>
</nav><!-- #site-navigation -->
Change the menu_class in the code to match your existing themes nav menu or you may need to add extra CSS to style it.
Resources:
http://codex.wordpress.org/Function_Reference/register_nav_menus
http://codex.wordpress.org/Function_Reference/wp_nav_menu