The ebb and flow of the tides / are / now understood.
I'll introduce some jargon. The ebb and flow is a compound subject that uses the coordinating conjunction and. Compound subjects joined by and are usually treated as plural and consequently need a plural verb:
John and Sarah are moving to Moscow this summer.
However, if the compound subject represents a single idea or a person, it is treated as a unit and a singular verb is used with it:
Ham and eggs is a popular breakfast dish.
"The ebb and flow (of something)" can clearly be treated as a single unit:
The ebb and flow of Iranian political fortunes has created opportunities and challenges for the development of Omani political and commercial interests in... (Google Books, "Oman, Culture and Diplomacy ", Jeremy Jones, Nicholas Peter Ridout - 2012)
And the same phrase has been sometimes treated as a combination of units in literature:
"This is particularly true when the ebb and flow of relationships between specific areas have to be examined." ("The First Western Greeks", David Ridgway, 1992)
"Though fashion's impact is not restricted to dress, the ebb and flow of clothing styles have historically been the most controversial of all the practices in virtually every cultural community." (Beverly Lemire, 2010)
"Up and down the historical route which leads from Baghdad to the heart of Persia the ebb and flow of battle were very marked in 1916." (Sir Percy Sykes, "A History of Persia")
However, these quotes, or some of them, could serve as examples of deviation from the predominant perception of "ebb and flow" as a single unit, or even slight errors. Wait for native speakers' opinions.
My guess is that it's up to the author. If they want to stress the wholeness of the subject, they might use a singular verb, or they might use a plural in order to stress the distinctness of "ebb" and "flow".