1. She stood at the bus station, waiting for his mother. (waiting for his mother here functions as a concomitant adverbial.)
***** NOT A TEACHER *****
Of course, I can
not answer the OP's question.
I have, however, found some information that has helped me to understand the matter a
little bit, and I am delighted to share it.
1. "Concomitant" = occurring concurrently; accompanying. (THE AMERICAN HERITAGE DICTIONARY OF THE ENGLISH LANGUAGE, 1969.)
2. "As an
adverb, a participal is sometimes used to limit a
verb (by denoting
concomitant acts)." [my emphases] (Rand McNally English Grammar, 1898, accessed through Google.)
a. "The mighty rocks come
bounding down."
b. "Now the bright star, day's harbinger / Comes
dancing from the East." (Milton)
3. Above all, another source helped me to advance a bit in understanding the term "concomitant adverbial."
a. "The phrase which mentions Elisha's seeing is a circumstantial clause, which in this form (where the verb is participial) is used in Hebrew to depict
concomitant rather than
sequential action; hence my preferred rendering '
While Elisha ....' " [my emphases] (PROPHECY AND DISCERNMENT by R.W.L. Moberly (2006), a Google result.
4. I may be totally wrong (as usual), but I have a sneaking suspicion that "concomitant adverbial" might be a more elegant term for what some textbooks call an adverbial element indicating
accompanying circumstances.
a. "He
rambled on foot through France,
playing a flute for a supper and a bed."
b. ""Then he
went to Leyden, still
pretending to study medicine.
[my emphases] (Walter Kay Smart, ENGLISH REVIEW GRAMMAR, copyright 1940 - 1968.)