The phrase "an unrelenting stream" is correct and usable in written English.
It can be used to describe a continuous and persistent flow of something, such as information, emotions, or physical objects.
Example: "The storm unleashed an unrelenting stream of rain that flooded the streets."
Alternatives: "a constant flow" or "an incessant stream".
"And we've also endured an unrelenting stream of disasters this year — from the earthquake in Haiti to the wildfires in Russia.
Call it the Marley Industrial Complex: an unrelenting stream of companies and commodities branded by a certain late, great Jamaican reggae singer.
"Rathlin has been the target of an unrelenting stream of misinformation, unfounded allegations about our objectives, scare-mongering and defamatory reputational damage.
The protest left the campus divided, with petitions springing up to oppose the demands and an unrelenting stream of articles and social-media posts published in both campus and national media.
With this sweltering desert city enduring one of the largest tumbles in housing prices for any urban area since the Depression, there is an unrelenting stream of foreclosures to choose from.
And with an unrelenting stream of hard-line rhetoric and enforcement in the news, as well as a swell of citizenship drives and advocacy, there are no signs the trend is abating.
Some investors hail Gyricon's birth as a welcome respite from the unrelenting stream of bad news that has flowed from Xerox lately.
Located in west Baghdad, the bloodiest half of the Iraqi capital, Yarmouk has coped for three years with an unrelenting daily stream of wounded, dying and dead.
Indeed, he reacted to the unrelenting stream of slander and congressional malfeasance with unflappable calm and an air of faintly amused detachment.
This unrelenting stream of bad news and broken faith has reshaped the public consciousness just as members of Congress head home.
