The angling of the horizon in Turner's painting The Slave Ship has been emulated in motion pictures, where it's called a Dutch angle. The Seaghbough Says blog in this eloquent post about Turner explains: "Turner's use of just such an angular distortion increases the viewer's discomfort and further enhances the nightmarish qualities of the painting."
The Grey Havens set from the Lord of the Rings was inspired by Turner paintings.
A New York Press article about Max Payne states that the visual aspects of the movie rates association with Turner.
Turner's paintings have inspired such filmmakers as Stan Brakhage, Jordan Belson, and Pawel Pawlikowski. This Josh Carr post quotes Fred Camper, an expert on Brakhage’s films, as he explains that Brakhage: "Discovers metaphors for landscapes in the patterns of reflection and diffraction: rivers, volcanoes, and mountains are suggested by images so delicate they’re worthy of J.M.W. Turner. The film is simultaneously a vision of the world’s creation and an inner landscape of spatial and light effects organized almost as if light were music."
And finally, a publication of the Jane Austen Society of North America, article by Lydia Martin, compares specific Turner paintings: "The same blue tones are used for the second proposal scene, but the ray of sunshine which pierces the fog brings to mind J. M. W. Turner’s aesthetics (Norham Castle, Sunrise, c. 1844; S. Giorgio Maggiore: Early Morning, 1819; The Fighting Temeraire Tugged to her Last Berth to be Broken Up, 1838)."
More posts about looking at the influence of Fine Art on Motion Picture design:
Part 1: Edward Hopper
Part 2: Andrew Wyeth
Part 3: Thomas Gainsborough and Antoine Watteau
Part 4: Michelangelo Caravaggio