You can switch to the alternate screen using this command:
$ tput smcup
And back with:
$ tput rmcup
These commands just output the appropriate escape sequences for your terminal. If it is an XTERM they will be equivalent to the (more known but less elegant or portable):
$ echo -e "\e[?1049h"
And:
$ echo -e "\e[?1049l"
For more terminal control commands see man 5 terminfo
.