Yeah, Tulane University does provide scholarships based on merit. Here are some of them:

Deans’ Honor Scholarship (DHS)
Total Worth: Full Tuition
Eligibility: Full Tuition
Separate application needed: Yes
Application deadline: December 5

Paul Tulane Award
Total Worth: Full Tuition
Eligibility: Full Tuition
Separate application needed: Yes
Application deadline: December 5

Stamps Scholarship
Total Worth: Full Tuition
Eligibility: Full Tuition
Separate application needed: Yes
Application deadline: December 5

Tulane University provides aids at an average of 45405 per student meeting 97% of students need. 100% of students with need receive financial aid at an average of 32464 need-based grant. They also provide other scholarships including Athletic Scholarship and ROTC Scholarship.