"a rush of wind" is a correct and usable phrase in written English.
You can use it to describe a sudden gust of wind that has an impact on a scene. For example: "The branches of the trees swayed with a rush of wind that swept through the valley."
A rush of wind came from each one, producing a symphony of flatulence.
One waits for a rush of wind to sway a flap of rear curtain to see a patch of blue Sound.
All around, however, was a scene of devastation, with the remnants of dozens of half-million-dollar homes that went up in a rush of wind and flame on Sunday morning still smoldering 24 hours later.
As we whizzed around Millennium's corners, I felt a rush of wind into my palms.
And the memory of Jeff stayed as a rush of wind went past me.
At about 9 30 p.m. there was a knock on the church door, and in came a group, all but one of them men, letting in a rush of frigid wind.
A quiet rush of wind filled the cave, perhaps from a thousand miles away.
The air resistance as the plane rushed so close to the ground created a constant rush of wind.
In "The Gust of Wind" a rush of dark clouds is indicated with fairly conventional brushwork, but the earth itself is nothing but jagged outcroppings of paint slightly differentiated by color into lake, rock and tree.
Try WeatherAction's: "Flare blasts shock waves in Solar wind heralding [possible extreme] weather…" Exciting, no? Piers creates long-range weather forecasts by analysing how the solar wind – a rush of particles from the sun – affects the Gulf Stream.
In another sign of solar quiescence, scientists reported last month that the solar wind, a rush of charged particles continually spewed from the Sun at a million miles an hour, had diminished to its lowest level in 50 years.
