For inbuilt Java (OpenJDK 1.8.0_242)

Install the prerequisites for Web Adaptor from the command line
sudo apt install openjdk-8-jre-headless

Manual Install of Tomcat 9.0.19 (Support has said it only works with a listed version of tomcat, hence the manual tomcat install)
Add the native APR Tomcat Libraries (for production systems) - https://askubuntu.com/questions/59836/do-i-need-to-act-on-tomcat6-apr-based-apache-tomcat-native-library-not-found
sudo apt-get install libtcnative-1
cd /opt
sudo tar -zxvf /home/<install username>/Enterprise_Install_Files/apache-tomcat-9.0.19.tar.gz
sudo ln -s apache-tomcat-9.0.19 tomcat
sudo chown -R <install username>:<install username> apache-tomcat-9.0.19

Adjust the tomcat-users.xml to add the user to the admin interface
cd $HOME/Enterprise_Install_Files
cp tomcat-users.xml /opt/tomcat/conf

Adjust the server.xml file to use port 80 and 443 as the default ports and the path to the /opt/tomcat/conf for the keystore below
sudo cp server.xml /opt/tomcat/conf
create the keystore for a self signed certificate for SSL
sudo keytool -genkey -alias tomcat -keyalg RSA -keystore /opt/tomcat/conf/localhost-rsa.jks
 https://tomcat.apache.org/tomcat-9.0-doc/ssl-howto.html
use the following options

Setup Tomcat to run as a non root user using authbind
sudo apt install authbind
sudo touch /etc/authbind/byport/80
sudo touch /etc/authbind/byport/443
sudo chmod 500 /etc/authbind/byport/80
sudo chmod 500 /etc/authbind/byport/443
sudo chown <install username> /etc/authbind/byport/80
sudo chown <install username> /etc/authbind/byport/443
edit /opt/tomcat/bin/startup.sh and shutdown.sh to add in authbind --deep
exec authbind --deep "$PRGDIR"/"$EXECUTABLE" start "$@"
make sure that the /opt/tomcat dir and everything underneath it is owned by the user running tomcat
sudo chown -R <install username>:<install username> /opt/tomcat/
edit the /etc/systemd/system/tomcat.service file to make sure it lists the user to run tomcat as

After modifying the file reload it
sudo systemctl daemon-reload
 
Install web adaptor
tar -zxvf  ArcGIS_Web_Adaptor_Java_Linux_1081_175313.tar.gz
cd WebAdaptor
./Setup -m silent -l yes -d /
deploy the arcgis.war file via the tomcat manager or by copying the file to /opt/tomcat/webapps directory
sudo cp /arcgis/webadaptor10.8.1/java/arcgis.war /opt/tomcat/webapps/server.war
sudo cp /arcgis/webadaptor10.8.1/java/arcgis.war /opt/tomcat/webapps/portal.war

To check the deployment navigate to /opt/tomcat/webapps and make sure that it has unpacked the war file to a server and portal directory.  Can also use the tomcat webmanager page to deploy and check that it was deployed

If ArcGIS Enterprise had already been deployed, then re-configure the web adaptor make sure that all of the arcgis services have been started first
./configurewebadaptor.sh -m server -w https://<fqhn server>/server/webadaptor -g https://<fqhn server>:6443 -u <ags admin username> -p <ags admin pwd> -a true
./configurewebadaptor.sh -m portal -w https://<fqhn server>/portal/webadaptor -g https://<fqhn server>:7443 -u <ags admin username> -p <ags admin pwd> -a true

We now need to start tomcat so that some dirs get created and also test to make sure it is working. Do it as the non-root user so that files don't get created at the root user
/opt/tomcat/bin/startup.sh
test by going to a web browser and navigating to https://<ip-address> and http://<ip-address>
Steps to allow access to the manager page (optional)
sudo cp manager.xml /opt/tomcat/conf/Catalina/localhost
The manager page can be use to deploy and verify the webadaptor war files or copied to the relevant dirs as per the Esri doco

Manually create systemctl script for stating & stopping the tomcat service - https://www.digitalocean.com/community/tutorials/install-tomcat-9-ubuntu-1804
sudo cp tomcat9.service /etc/systemd/system
sudo systemctl enable tomcat9.service
sudo /opt/tomcat/bin/shutdown.sh
sudo systemctl start tomcat9.service