Turner: On the crest of a wave J M W Turner is beloved not just in his home country as the supreme English water colourist but internationally as one of the true giants of art. We like him here for the extraordinary way in which he pictured the sea and the scenery suffused with light and mist and mood. Abroad, they admire him most for the way that he pushed painting, in oil as in watercolour, to the extreme edges of representation to the point where it became virtually abstract. You can see that point and Turner's constant experiments with effect in a glorious show of some 80 of his works at the new Turner Contemporary gallery in Margate, built on the spot where Turner came every year to stay in the boarding house run by his mistress, Mrs Booth. Opened last year, it's a space, designed by David Chipperfield Architects, full of light and height. Both are needed for Turner's later work, where space and light themselves become the subject of his art. So far, Turner Contemporary, a group founded 10 years ago, has concentrated almost exclusively on modern art from here and abroad. This is its first exhibition of its namesake and one, fittingly perhaps, which has been curated not by themselves but by the directors of the Bucerius Kunst Forum in Hamburg and the Muzeum Narodowe in Krakow in Poland, where it has already been shown before arriving here. All to the good, one might say. The temptation of a home-grown exhibition would have been to concentrate on Turner's work done in Margate and the north Kent Coast, which he loved. But, while this show does include half-a-dozen of his local views, including some brilliant studies of the skies and clouds viewed from the harbour, the curators this time have ignored place and gone for what makes Turner incomparable as an artist: his determination to capture nature itself in all its moods and energy. Its title, Turner and the Elements, says it all. Turner, so the thesis goes, lived at a time when science was breaking down all the old divisions of nature - in this case the four classical elements of fire, water, earth and air - and replacing them with a nature far more fluid and dynamic. Turner was the artistic expression of it. That may well be a somewhat over-didactic view of a man so resolutely down to earth and taciturn as Turner, an old grouch if ever there was one and mean to boot, if the recollections of his mistress are anything to go by. Turner knew and was friends with scientists of his day and he was certainly interested in theory, particularly of colour. But it is hard to see him driven by the theories of science. What he set out to do, from his early days of embracing the romantic theories of the "sublime" in nature, was to depict sensation - the sensations experienced at sunrise and sunlight, in storm and dead calm, in rain and mist. The division of the works into the four elements proves, however, a surprisingly effective way of witnessing his ambition as he develops and pushes his skills. You start with "earth" and the classic watercolour views of mountain and gorges, in which the artist expresses the sublime in the majesty of nature. But as his art progresses, the outlines are blurred and the forms dissolve into each other in the fluidity of the watercolour and the confidence of the brush. With "fire" it is the same. The paintings start with the depiction of the event, the eruption of Mount Vesuvius, the burning of the House of Commons. But by the end it is the colour and energy of the fire itself that obsesses the artist, while with "water" and "air" the progression from observation to pure sensation is even more complete. Move on into the room of "fusion," when Turner abandons all divisions between components, and you are taken into works so far ahead of their time that you have to look twice at the dating to believe them. In watercolours such as Colour Beginning of 1820 and the The Rainbow of the same period or Mont Saint Michel of 1827, you are privy to a mind that is attempting (and succeeding) to find a means for painting to express the essence not the appearance of nature. Of course, these are colour sketches, the workings of a mind experimenting with technique, not the finished products. There is always a danger with Turner in reflecting backwards a modern vision of a man whose aims were often more conventional and backward looking. But if you doubt Turner's intentions, a final section shows this extraordinary artist translating what he was experimenting with watercolour into the much less malleable medium of oil. Paintings such as Stormy Sea with Dolphins of 1835-40 (spot the dolphins if you can), Shade and Darkness - the Evening of the Deluge from 1843 and Snow Storm - Steam-Boat off a Harbour's Mouth of 1842 are just stunning in the clear light of the Turner Contemporary building. They have titles. Turner has even added "the author was in this Storm on the Night the Ariel left Harwich" to his snow storm scene. They have subjects. But in the end they are beyond that. They are as near as you can get to abstraction without going the full hog. No wonder the American abstract expressionist, Mark Rothko, revered him and donated nine of his Four Seasons paintings to the Tate to hang near the Turners. This show isn't the whole of Turner. He remained until the end a supreme master of the atmospheric watercolour view, as a current show of Turner and his Contemporaries at the Abbot Hall Art Gallery in Cumbria amply illustrates. Defining him through the four elements also leaves out the element that intrigued him most, which was light itself. For that we will have to await the National Gallery's exhibition of his works alongside his great hero, Claude Lorrain, in March. But then there is probably no show that can properly encompass Turner's genius. He is one of those very rare people in any discipline: a true global Titan. As with Shakespeare, you simply gasp not just at the vaulting ambition of the man but the fact that he found the means to express it. There are more than enough works here to gasp at while you glance out of the windows at the view that so inspired him. Turner and the Elements, Turner Contemporary, Margate (0 1843 233000; turnercontemporary.org) to 13 May