From his book, Exposition of the Holy Gospel According to Saint Luke with Fragments on the Prophecy of Isaias:

“‘[H]eaven was opened, the Holy Spirit descended in bodily shape like a dove’ (Luke 3:21-22). Why like a dove? For the grace of the washing requires simplicity, so that we may be ‘innocent like doves’ (Matt. 10:16). The grace of the washing requires peace, as in an earlier image the dove brought to the ark that which alone was inviolable by the flood (Gen. 8:10-11)…In that branch, in that ark, was the image of peace and of the church. In the midst of the floods of the world the Holy Spirit brings its fruitful peace to its church.

David too taught [about] the sacrament of baptism…with the Spirit of prophecy, [saying,] ‘Who will give me wings like a dove?’…

Because the Father did not wear a body,…the Father wished to prove to us that he is present in the Son, saying, ‘You are my beloved Son. In you I am well pleased’ (Luke 3:22). If you wish to learn that the Son is always present with the Father, read the voice of the Son saying, ‘If I go up into heaven, you are there. If I go down into the grace, you are present there’ (Ps. 139:8).”

Ambrose (ca. 333-397 AD) was the bishop of Milan, as well as Augustine’s teacher. He is most well known for his defense of the Holy Spirit as a divine part of the Trinity.