A bash script that writes all logs from running docker containers to files called <container_name>.log and compresses these into an archive

collect_containers_logs.sh

#!/bin/bash

set -xe

for name in $(docker ps --format "{{.Names}}"); do
  eval "docker logs \"$name\" 2> ${name}.log";
done

eval "env GZIP=-9 tar cvzf logs.tar.gz *.log"

On a Mac the compressing can be done using:
'tar -czf logs.tar.gz --options gzip:compression-level=9 *.log'