Grammatical role of “the hell”?

I’m wondering exactly which grammatical role the word hell takes on in expressions such as

Get the hell out of here

the hell in this case seems to modify the phrasal verb to get out (get out of here quickly may have a similar meaning depending on the context), so I would classify it as an adverb, even though hell itself is a noun. I suspect that the reason for using the hell is that there is no other way of forming an adverb out of hell in an obvious and easily understandable way.

Is the hell simply an adverbial phrase (in addition to being an expletive)? If so, is there a name for creating adverbial phrases from nouns in this way?

(Originally, I was interested in the analogous expression involving f*ck.)

Solution 1:

I'm not so sure it modifies the verb. When you say what the hell is wrong with you?, it sounds more like it modifies what. But perhaps it is better to say the phrase is a disjunct that modifies the whole sentence or clause: it expresses the attitude of the speaker towards the clause as a whole, I would be inclined to think.

Solution 2:

The hell is, I believe, just a phrasal exclamation, used as an intensifier. It is used in "get the hell out of here" as a mock-adverb, but it can be a mock-adjective ("What the hell is this?") or mock-noun ("The hell you say!")

Solution 3:

The adverbial group "the hell" is simply an intensifier often used after question words as in - What the hell are you doing here? expressing strong annoyance. It can be used in imperatives as in your example with the same function.