The easiest way is to unmount and re-mount. If you choose the usual eject, then some OSes will actually turn off the device and it cannot be re-mounted without disconnecting.
On Linux, I use pmount and pumount to connect & disconnect the media.
On MacOS, I usually use `diskutil eject /Volumes/<name>`, though that has the same problem. You can also unmount and remount, using this:
diskutil unmount /Volumes/<name>
then to find it again:
diskutil list | grep Volume
and then remount with:
diskutil mount <id, from last column>
EDIT: For MacOS You can also use the graphical "Disk Utility" program, right click on the drive and choose "unmount", then "remount" -- NOT eject.
...
for Windows, well, you're on your own.
