* Supercharger whine: The supercharger's bearings might be worn or the belt tensioner is faulty. A slight whine for a few seconds after shutdown isn't unusual (due to residual energy), but if it's prolonged or loud, it's a problem.
* Cooling fan: The electric cooling fan might be continuing to run. This is often due to the cooling system still needing to cool down, but a faulty sensor or relay could cause it to run excessively.
* Fuel pump: Some fuel pumps run for a few seconds after engine shutoff to prime the system, but a persistent whirring or buzzing suggests a problem.
* Exhaust system leak: A leak in the exhaust system, particularly near the catalytic converter, could cause a hissing or rumbling sound that might be more noticeable after the engine's noise is gone.
* Power steering pump: While less likely, a faulty power steering pump could make a whining sound after the engine is turned off, especially if there's a leak.
* Alternator: Although less common, a failing alternator could sometimes produce a humming or whining sound even after the engine is off.
Importance: Ignoring these sounds can lead to more serious (and expensive) repairs. It's crucial to get your Buick Riviera checked by a mechanic as soon as possible to diagnose the cause. The sound you're hearing is a clear indication something isn't right. Don't continue to drive it until it's investigated.