Ulmo, the outer Ocean, and Greek Mythology

Reading Megan Fontenot's recent post on Ulmo in her 'Exploring the Peoples of Middle-earth' series at Tor.com reminded me of a connection I'd recently noticed between this Vala and Greek Mythology. 

But mostly Ulmo speaks to those who dwell in Middle-earth with voices that are heard only as the music of water. For all seas, lakes, rivers, fountains and springs are in his government; so that the Elves say that the spirit of Ulmo runs in all the veins of the world. Thus news comes to Ulmo, even in the deeps, of all the needs and griefs of Arda, which otherwise would be hidden from Manwë.  

Silmarillion, p. 27

and

But Ulmo was alone, and he abode not in Valinor, nor ever came thither unless there were need for a great council; he dwelt from the beginning of Arda in the Outer Ocean, and still he dwells there. Thence he governs the flowing of all waters, and the ebbing, the courses of an rivers and the replenishment of Springs, the distilling of all dews and rain in every land beneath the sky. In the deep places he gives thought to music great and terrible; and the echo of that music runs through all the veins of the world in sorrow and in joy; for it joyful is the fountain that rises in the sun, its springs are in the wells of sorrow unfathomed at the foundations of the Earth. 

Silmarillion, p. 40

On p. 30 of Dr. Marie-Claire Beaulieu's fine book, The Sea in the Greek Imagination, she writes:

The sea also mediates between the different parts of the world due to its connection with a broader hydrological network. All ground water -- that is, not surface runoff -- radiates from the outer Ocean inward into the rivers and springs and then flows outward in to the sea [Plato, Phaedo 111c-112d]. In fact, according to Hesiod Theogony 337-62, the most important daughter of Oceanus is Styx, the river of the Underworld, and all the other rivers of the world are her sisters. Thus the hydrological network connects all the parts of the world, from the invisible world of the gods and the dead beyond the Ocean, to the Underworld, to the surface of the earth. The sea holds the middle position in this network as it receives the water that flows from the rivers and springs of the earth and brings it back to the outer Ocean.

Tolkien clearly knew the Phaedo from university*, if not before, and it would be strange if he had not read the Theogony at some point in school or out, in translation if not in the original. Dr Beaulieu discusses this aspect of the sea in greater length than I can quote here, but many of those texts, too, would have been familiar to Tolkien. The presence of such a 'hydrological network' in both Tolkien and Greek Myth and the general role of the sea as connecting the different worlds strongly suggests the influence of the myths he had read on the myths he was writing, though of course Tolkien re-imagines it by adding the echo of the music to the waters of the world, as well as Ulmo's ability to gather news by means of them.

 *Scull and Hammond, The J.R.R. Tolkien Companion and Guide, vol 1. Chronology, p. 44 (2017).