Macos – OS X Terminal.app: how to start a new tab in the same directory as the current tab

Daniel's solution somehow opens a new Window – also, the exec command statement does not work as expected. One has to write text instead.

Also, you have to use

launch session "Default Session" 

in order to get a new tab.

The following does what you asked for:

tell application "iTerm"
    make new terminal
    tell the current terminal
        activate current session
        launch session "Default Session"
        tell the last session
            write text "cd ~/Downloads; clear; pwd"
        end tell
    end tell
end tell

The alternate screen is a concept that goes way back.

From the xterm man page:

In VT102 mode, there are escape sequences to activate and deactivate an alternate screen buffer, which is the same size as the display area of the window. When activated, the current screen is saved and replaced with the alternate screen. Saving of lines scrolled off the top of the window is disabled until the normal screen is restored. The termcap(5) entry for xterm allows the visual editor vi(1) to switch to the alternate screen for editing and to restore the screen on exit. A popup menu entry makes it simple to switch between the normal and alternate screens for cut and paste.