Running the attached Mongo shell script with perfmon shows mongod's Private Bytes grow at 4.8 MB/s. The gap in the middle is when the test finished the first time. When it was then restarted, memory kept climbing.

Interestingly enough, if the test collection is dropped at the end of the test, then when the script is launched again, memory stays at the same level for a while. I didn't have the time to look closer into further behavior. If the collection is left alone and the script is restarted, memory keeps climbing.

I see the same behavior in the application.

Make sure to restart mongod when running it for the first time - it appears that it uses existing memory for a while and it is not as easy to spot the leak.