What is his purpose and why does Steinbeck put Noah in The Grapes of Wrath?

Functionally and superficially, Noah has several roles. We
can also look at his character thematically. 

Functionally,
Noah is the eldest son and so should hold a certain position of authority in the family.
He does not fulfill the role assigned to this position however as he is tempermentally
incapable of doing so. He is just not a leader. In this way, Tom becomes the leader of
his generation, having overcome this formal
obstacle. 

(Formal obstacles and arbitrary hurdles often
seem to get between Tom and his goals. Overcoming them is part of his development and
part of what makes him the protagonist of the
novel.) 

Superficially, Noah's presence brings the family
number up to twelve (Ma, Pa, Uncle John, Noah, Tom, Rose of Sharon, Connie, Al,
Winfield, Ruthie, Granpa, Granma). This has a Biblical resonance when considered
alongside the presence of the preacher,
Casy. 

Thematically, Noah is an example of how the family
breaks up under stress as well as under more overtly physical
demands.

When
[Tom] tells her about Noah, Ma feels the “family’s fallin’
apart.”

Death and despair
reduce the family to eight by the time the Joads leave their first camp in California.
Noah represents some of this despair, saying that he is "sad" and has to stay by the
river.