In his older years Joseph Mallord William Turner was not wanting for problems with his health.

He was suffering from cataracts, diabetes, alcoholism and the effects of lead toxicity due to the paints he'd been using down all the years. So in some ways the wonder of the current Tate Britain show Late Turner: Painting Set Free is the sprawling size of it. Painting follows painting. Watercolour follows sketchbook. A protean outpouring of art that no ailment could stem. That scene in Mike Leigh's film Mr Turner in which Timothy Spall as the artist drags himself from his deathbed to sketch the corpse of drowned woman comes back to you as you leave this exhibition. Turner sketched and painted whatever the circumstances. Until he couldn't.

The question asked here is what did he paint in those final years. The exhibition's subtitle, Painting Set Free, is an allusion to the idea that emerged in the 1960s that Turner in his smeary swirls of paint was in some manner a forerunner to the abstract expressionist artists who emerged in America after the Second World War. But that, some art critics have pointed out, a dangerous idea. Many of the paintings it depends upon were unfinished. Who knows how Turner would have added to them?

Still, what we have here does lend itself to an abstract reading if you want to find it. There's a small painting of Turner's bedroom on one of his trips to Venice, circa 1840, which if you squint your eye is an abstract arrangement of colour. Only the tower of St Marks through the window gives any sense of place.

And yet none of his work is bloodless or academic. His visions of shipwrecks and sea monsters, of steam trains and burning buildings are elemental. Turner painted scenes from the Bible, from myths and from history and - in paintings such as Rain, Steam and Speed with its vision of a train powering across a viaduct - the latest technological developments. But what you take away from them is a vision of light and weather. Of the very world in flux. Vortices of paint swirl and pulse across the canvas. You can see that in his watercolours, as the Vaughan Bequest in Edinburgh will once again prove next month. But it is At it's most apparent in the huge oil paintings that cover the walls of Tate Britain.

The elemental in Turner has its downside. He shows no great interest or facility for painting people. His cherubs in the painting Glaucus & Scylla look like limp gingerbread men. But it is no great loss. Turner is so often about scale. He revels in the immensity of sky and water as in his 1840 painting Sun Setting Over a Lake. Even in his cityscapes and mountain landscapes so often their forms are obscured - liquified? - by cloud and rain. So often in Turner we learn that nothing is solid, all is change. That's not abstract. That's a truth.

Late Turner: Painting Set Free continues at Tate Britain until January 25.