Theophylact of Ohrid

The Holy Spirit descended upon Jesus so that we might learn from this that upon us also, when we are baptized, the Spirit comes. For the Lord had no need of the Spirit, but He does all things for our sake and Himself becomes the firstborn in all things (Col. 1:18) that we were to receive afterward, so as to be the firstborn among many brethren. The Spirit descended in bodily form, like a dove, so that we might learn that we need to be meek and pure. …

Commentary on Luke ↗

Clement of Alexandria

God here assumed the "likeness" not of a man, but "of a dove," because He wished, by a new apparition of the Spirit in the likeness of a dove, to declare His simplicity and majesty.

From the Catena on Luke, Edited by Corderius ↗

Bede

And a voice came from heaven: You are my beloved Son, in you I am well pleased. Rightly John is second to none among those born of women, to whom Christ showed himself to be baptized, the invisible Spirit appeared to be seen, and the Father commended his Son from heaven. For it was not revealed to the Son himself what he already knew well, but it was shown to John or to the others who were present, what they might know. …

On the Gospel of Luke ↗

Bonaventure

Again, to designate the person of the Holy Spirit, it is added: The Holy Spirit descended in bodily form like a dove upon him; John 1: "Upon whom you shall see the Spirit descending and remaining, he it is who baptizes." — Now he descended in the form of a dove by reason of signification, because, as Chrysostom says, "this bird above all others is the greatest cultivator of charity." Hence he appeared to Christ in a complete animal, but to the disciples in tongues, to signify that in Christ he was present according to every manner of …

Commentary on Luke, Chapter 3 ↗