結論

ボリュームを共有して擬似的に行う。

kubanetesみたいに、一つのホストに複数プロセスを共存させるやり方はできなさそう。

version: '3'

services:
  tomcat:
    image: tomcat:alpine
    container_name: "tomcat"
    volumes:
      - logs:/usr/local/tomcat/logs
    ports:
      - "8080:8080"
  localhost_logger:
    image: busybox
    volumes:
      - logs:/logs
    stop_signal: SIGKILL
    command: ["/bin/sh", "-c", "
                  while [ ! -e /logs/localhost.*.log ]; 
                  do 
                    echo \"Waiting for localhost to become available\"; 
                    sleep 2; 
                  done; 
                  tail -f /logs/localhost.*.log"]

  access_logger:
    image: busybox
    volumes:
      - logs:/logs
    stop_signal: SIGKILL
    command: ["/bin/sh", "-c", "
                  while [ ! -e /logs/localhost_access_log.*.txt ]; 
                  do 
                    echo \"Waiting for localhost_access_log to become available\"; 
                    sleep 2; 
                  done; 
                  tail -f /logs/localhost_access_log.*.txt"]
volumes:
  logs:

Docker Tips & Tricks - NCR Edinburgh - Medium