There are no scopes in SP 2013 ( we now have “Result sources” instead), so no more search scope dropdown !!!! 😦
but don’t worry, there is a way to have them back.
1) to test this out please create a basic search center
2) go to the result page by writing test for exemple and then hitting search and then edit the page
3) Edit the “Search Results” web part and click change query
4)Edit the query to match your scope.
5)For example, we added a “Path” variable to only search in this site
This page will be your new drop down menu selection. The above image shows a search that will only return items that match what is typed in the Search Box + sp2013-dev:14455/* in their URL.
6) Edit the page, and edit your search box web part, then Select “Turn on drop-down” and “Use this site’s Search Settings” in the web part menu, and hit apply.
8)Ensure the drop-down and use parent settings are applied, and then add a new link.
9)Fill out the title and URL (the URL is the link to your Search Result page), and click OK.
i added another link named active documents
10) Save your new Search Settings, and test out Search 2013 with the familiar drop-down menu