Responsive sidebar sub-navigation

We're working on a new, responsive version of a large website and need to support the main navigation and sub-navigation that changes based on the department. Below is a mockup of how we are approaching this.

Main navigation goes under the hamburger menu while the local sidebar menu becomes a toggle at the top of the page. Is there a better approach? Are there any major pitfalls to this approach?

We are also trying to decide on the label for the submenu toggle. If, for example, this is for a university website and the department is "Financial Aid," should the label just be "Financial Aid" or "Financial Aid Links" or something more generic like "Additional Navigation"? If it just says "Financial Aid," is it still clear that the toggle is sub-navigation? Thanks for any input.