I am running a container on a VM. My container is writing logs by default to /var/lib/docker/containers/CONTAINER_ID/CONTAINER_ID-json.log file until the disk is full.
Docker 1.8 has been released with a log rotation option. Adding:
--log-opt max-size=50m
when the container is launched does the trick. You can learn more at: https://docs.docker.com/engine/admin/logging/overview/