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When a whale dives it leaves behind a so called 'footprint'. The water seems to be calmer or the surface is at least more smooth an shows less wrinkles.

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Image source

I read some text which were talking about a 'wake of the diving whale' but I wanted to understand it from a fluid dynamic (two-phase) point of view, so I thought asking here might be a good idea.

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The whale creates a vortex ring with its tail, which moves upwards and creates an oval patch of outward current on the surface: short surface waves can't propagate (well) against the current, and that's why the patch is smoother than the ocean around it.

Source: The flow induced by a mock whale : origin of flukeprint formation.

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