The phrase "turn in the direction of" is correct and usable in written English.
For example, you might say, "The driver began to turn in the direction of the airport."
"It will turn in the direction of success.
The United States could turn in the direction of Europe, where many Jews feel fearful and threatened.
"You Can Have Your Moment" (Winter & Winter), the follow-up, takes a screeching turn in the direction of groove.
There are people who never learned to take their foot off the brake and turn in the direction of a skid, for example.
One is to measure the frame dragging, which would cause the gyros to turn in the direction of the Earth's rotation.
Only when a server dropped something to her right did she turn in the direction of the crashing noise, and then only briefly.
He turns in the direction of the leaf grinder, where your stepfather stands with his back turned.
Then the tide turned in the direction of Swinging London, and our film-makers have only sporadically gone north since.
Then he turned in the direction of the two figures who seemed to be eavesdropping on his call.
But Mr. Crockett turned in the direction of the officers with the gun in his hand, according to the police.
When a male sees a female's flash, the male turns in the direction of the female, even though the source is no longer visible.
