1. The young man, jogging every morning, is very strong.
2. My old car, breaking down every other week, won’t last much longer.
‘jogging every morning’ and ‘breaking down every other week’ are not (adverbial) clauses*. They are alternatives to relative clauses.
*In traditional grammar, a clause has its own subject and a finite verb (= full verb/a verb having tense). A clause can be defined as a grammatical unit operating at a level lower than a sentence but higher than a phrase.
Alternatives to relative clauses
Sometimes, instead of a complete relative clause, we use shorter phrases in order to describe the subject in the main clause or to provide more information. These are like simplified forms of relative clauses.
In your examples,’ jogging’ and’ breaking (down )’ appear in their present participle form without a relative pronoun.
3. Here is another question:
My old car, breaking down every other week, won’t last much longer.
How do we interprete this sentence when we see it?
(a) Because it breaks down every other week, my old car won’t last much longer.
This is an adverbial clause of reason, that answers the question: Why do you think it won’t last much longer?
In your sentence, ’breaking down every other week’ is just additional information about your car, and not necessarily the cause of its final breakdown.
(b)My old car, which breaks down every other week, won’t last much longer.
This is a real relative clause and means the same as its alternative (breaking down….). It’s a question of style.