Is it possible to send notifications to my Portal users?

Issue

Is there a way to send an alert so that a group of users, at a site or organization level, receive a notification in the Portal?

Currently, there is no way to configure OOTB alerts to appear in user notifications.
The way users are notified about alerts and announcements is via email only.
To display it on the interface, the Announcements and Alerts widgets can be used.