"prevailing tradition" is correct and can be used in written English.
You can use it when referring to a custom or idea that is widely accepted or practiced within a particular group or society. For example, "The prevailing tradition at the university is for freshmen to wear green caps on their first day of classes."
Throughout the 3rd century the prevailing tradition in the African church had regarded the church as a body of the elect.
As for efforts whose ambitions have not yet been set, the prevailing tradition in large-scale activism has for decades been that good ideas about tactics and strategy are heeded and implemented no matter from whom they originate.
Although reacting, especially in his early papers, primarily against the prevailing tradition of 19th-century British idealism, Moore criticized Berkeley's esse est percipi doctrine while at the same time rejecting Kant's transcendental idealism.
In her book, Mistress of the Elgin Marbles, Susan Nagel tells the story of the life and imploding marriage of this spirited young woman who, against the prevailing traditions of her time, insisted on playing an active role in shaping her own life.
Although Autrecourt was no skeptic — on the contrary, he attacked the "Academics" or ancient Skeptics — his philosophical stance challenges the prevailing Aristotelian tradition.
Until relatively recently, the prevailing scientific tradition was to not include women in clinical trials.
Given the variability of socio-demographic and cultural contexts, differentials in perception of vulnerability or risk for newborns, and prevailing customs, traditions and beliefs within communities, it is critically important to understand community-specific patterns and determinants of population-level neonatal care seeking practices, especially for preterm newborns.
Each country has its own unique legal and medical traditions, prevailing social, economic, and cultural conditions, and constitutional principles that no model law can fully address.
The recitatives are in the French style, but the arias are fluent and strong in the prevailing Italian tradition.
Mr. Girard's vivid, "untasteful" blues, magentas, yellows and reds broke with the prevailing polite tradition of deadened ochres and turquoises popular in interior design.
There is therefore, contrary to the prevailing religious tradition, no survival after death, no reincarnation, and no punishment in Hades.
