So I assume you are trying to do the drop down with jQuery and not CSS ? (perhaps then, it might be best if this post was moved)
Just to get you started on a solution tho: your script is not targeting the right selectors.
$(‘ul.nav [data-toggle=dropdown]’) would target a <UL class="nav"> that has decent element ( any descendant element) with the attribute data-toggle with the value dropdown… so with your actual markup- this selects none.
also you aretageting an element with an ID of ‘menu’ earlier in your script, but this element does not exist in your markup sample… but I will assume that element wraps around <nav id="navbar">, but w/o that wrapper the script won’t select anything either