ElasticSearch provides a variety of mechanisms to boost the score of a document or term, such as:
The general idea is that you boost a document's score depending on the value of a field or fields. In your case, you may want to have a "popularity" field that is updated and used to boost the doc's value. It depends on how you implement your code internally.
This tutorial shows how to implement "Featured Results", which is a similar concept. They used the Constant Score query.