Is yours an automatic? If so, the whirring sound could be the
electronic motor mounts.  There is a tech bulletin describing
troubleshooting and repair: a symptom when they are failing  is a
whirring or buzzing sound lasting several seconds after shutting off
the engine.

Repair is to replace with new, re-designed motor mounts which is
covered under 3/36 warranty only (not 60K warranty).

They "soften" at low RPM to control engine vibration, and then firm up
as RPM increases above 2K or so to more tightly couple the engine to
the drive train. I guess that when they fail completely they will stay
in whatever state they're in when the failure occurs.

I couldn't fix mine right away when the buzzing started, so I
disconnected them.... just idle up the engine to 2500RPM or so (to
firm them up) with tranny in drive and trusted person on brake pedal,
then disconnect the one electrical lead to each mount.

They are now in firm all the time.  At first I figured I'd buy
replacements and do the change over on a spare weekend,  but the
difference in vibration is so minor it just isn't worth it!  Also, the
firmer drive train is appreciated as there's noticeably more snap
pulling away from a stop.

BuddyWh  

It is the active motor mounts.  They make noise when you turn the engine
off.  Not all the time but they do make a whir or a buzz.  If the engine
shakes when you drive the car you might want to replace them.  It is
usually the back one against the firewall that goes first.  If the
engine is not causing vibration when you drive the car I would wait...
This was a Technical Service Bulletin when the car came out but you like
me did not know until the warranty went out...

The funny noise are the motor mounts.  They are electronically
controlled.  If you are not getting engine vibration you should be fine.
 My 2000 Maxima has made the noise on and off since day one.