By "alert log", do you mean the ASE errorlog?
If the errorlog is deleted, ASE will automatically create a new errorlog file
the next time ASE is booted. You can manually cause ASE to start a new
errorlog file using the sp_errorlog stored procedure. See sp_errorlog
in the ASE Reference Manual.
It isn't quite the same thing as generating a false error message, but
you can cause some genuine errors that aren't normally sent to the
errorlog to get output to the errorlog using
sp_altermessage <msgnumber>, "with_log", true.
As an example:
sp_altermessage 207, "with_log", true
go
select no_such_column from sysobjects
go