The medieval depiction of the whale was somewhat fanciful; the illustration is taken from Gesner’s De Avibus et Piscibus, 1560. If a naturalistic depiction is desired, it must be specified as a “natural whale”, or more explicitly, e.g., a “sperm whale”. The whale is naiant by default.
In Society armory, there is also the “narwhal” or “narwhale”, a cetacean with a long unicorn-like “horn” (actually its tooth). It’s generally depicted as found in nature. The illustration shows a narwhal haurient. For related charges, see dolphin.
The Baron of Smoking Rocks bears: Argent, a whale haurient embowed sable within a laurel wreath vert.
André of Stormhold bears: Argent, a whale naiant azure.
Arinbjorn Talverri bears: Or, a narwhal haurient purpure.