As of the date of this post, Google Drive does ***not*** support searching within a specific folder. However, the new Docs, Sheets, and Slides home screens do have a way to let you do this via the *File Picker* search interface:

 - Go to: https://docs.google.com
 
 - Click the File Picker folder icon on the right side of screen.
 
 - Navigate to the specific folder that you want to search.

 - Now put your query term in the file picker's search box and hit 'Enter'
 (Or click the 'Search for all items containing ')

Your search results will only come from the folder you selected.

Note: you can still filter by file type in the *File Picker* search bar by clicking the drop down arrow.