The smoke, is a specific area of smoke, defined by the 'the'. It is not a generic idea of smoke or an insignificant whisp of smoke that doesn't deserve the indefinite article, being so brief in its passing.
It is, in the example 'the smoke from the burning field' (implied).
It is smoke that is important enough to become an entity of its own, important enough to acquire a 'the' that makes it a significant player in the sentence, having the importance of an 'it', because it is not 'generic'.
If it was a mere concept of 'smoke', or was a short-lived momentary puff of smoke, then it wouldn't have been around long enough to have earned the indefinite article: 'the'.
If it was a generic bit of smoke, that could be located anywhere, it won't deserve a 'the' either. But if the smoke has cachet - a style of its own, a particular location or way of swirling evocatively, or does something – makes an action of its own – then it may acquire a 'the' of its own.
It acquires 'the' if we already know of it and/or spoke of it – 'the red smoke over there', 'the foggy patch just before Shoreditch', because then it is not generic.
Generic uses – without 'the':
smoke swirled in the hollow
red smoke puffed around our ankles, as we danced the tango
the motorway was thick with smoke
Specific uses – with 'the':
the smoke in the hollow swirled spookily, as it had the other day
the red smoke swirling round our ankles stained our socks pink
the smoke at junction 4 of the M6 motorway caused delays