It feels like as if the English translation should be ' the cat is purring/purrs' then the Danish version would be 'katten spinder' . In this case the cat is making this characteristic humming sound when in relaxed state instead of physically moving around one point.

Is rundt needed in the absence of an object? I only ask because "han drejer flasken" was a previous solution.

I don't think purring is it possible meaning here, is it? Turning makes sense and, I even thought of the German expression "spinnen", which suggests that "The cat is crazy" is another possible answer. But purring?