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"drift towards" is correct and usable in written English.
You can use it to express the gradual movement towards a goal or destination, or even an idea in a figurative sense. For example, "This year has seen a drift towards more progressive views in the media."
Exact(60)
Once formed, they drift towards the equator.
Could well drift towards Oscars in 2015.
He promises to reverse the country's drift towards international isolation.
But the drift towards federalism is a powerful force.
Mr Putin has already seen Central Asia drift towards China.
Or will we drift towards an election with the certain victor facing serious charges?
Leaviss wears a worried frown when he talks about the City's drift towards old excesses.
Recent developments have led to heightened concern at the fund about the drift towards economic nationalism.
Both he and Bryan are working on novels, though Finnegan will drift towards political journalism.
For some, the supermarket came to symbolise an unwanted drift towards mass commercialisation of their neighbourhood.
The film shows a dreamy drift towards pathos, which is valid enough as an emotional register.
Write better and faster with AI suggestions while staying true to your unique style.
Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com