Meaning of "the waft of"

Now he was beginning to have the waft of an old man who hadn't bathed for several days.

The meaning of the sentence is absolutely clear to me, since the second part of the sentence explains the meaning.

But I have only a rough perception what the exact meaning of a waft of is.
I found this explanation of waft:

To cause to go gently and smoothly through the air or over water.

And to waft means:

to move, or make something move, gently through the air

But at this point I stuck and I fail to figure out the exact meaning. It sounds like it means the smell itself in an foul-smelling way, but then it would be rather uncouth.

Am I headed in the right direction or has a waft of a deeper meaning?

Solution 1:

The basic meaning of the verb "waft" is to "move through the air" (or over water). What (often) "moves through the air"? A smell. That is why when used as a noun, a "waft" refers to the associated smell.

Solution 2:

Waft can be a noun or a verb. In your example sentence, it is used as a noun referring to a smell that moves through the air.