I have several similar links that trigger different navigation divs to appear. I am trying to find a way in JQuery to determine which of the links was clicked and then trig
Andreas' suggestion is sound - the rel attribute is quite useful for this type of thing, and is the right way to go if you have control over the elements.
As for your original method, that ought to work as well (the added regex overhead notwithstanding). Just remember that match will return an array or null. If you forgo the null check, you'd use something like:
var nav_id = $(this).attr('id').match(/\d+/)[0];
One more tip: specifying the element type in your jQuery selector is good practice for speeding up load times. eg: $('a#nav1') vs $('#nav1'), $('a.expander') vs $('.expander')