Question

Which part of the sentence is an adverbial dependent clause? when they arrived at the beach who had never seen the ocean before by the size of the foaming waves that rolled gracefully toward the shore

Answer 1

 When they arrived at the beach should be the adverbial dependent clause 

the subordinated conjunction is When and answer to the question :
who had never seen the ocean before by the size of..........

The answer is when they arrived at the beach

Answer 2

The part of the sentence that is an adverbial dependent clause is the following one: "When they arrived at the beach".  Dependent clauses are a group of words that contain a subject and a verb yet they do not represent a complete thought so they can't stand alone.

Adverb dependent clauses modify verbs and are introduced by subordinating conjunctions. In this case, the subordinating conjunction introducing the dependent clause is "when".