Here is my two cents... hopefully it helps. Usually a left or right
or local nav, as i've seen it, supports your global nav, not
replicates it. By having two navs that do the same thing you are just
filling that page up with noise that disrupts the user. The global nav
(which you have on top) should remain as constant as possible and the
support nav could change depending on which main navigation you are
in. Basically you make a selection with the global nav and you dive
even deeper with a support nav.
Usually support navs are useful if you have a deep taxonomy that
can't be surfaced in the global nav or if you have long (horizontal)
taxonomy with many similar pieces of content that are on the same
level. With these horizontal taxonomies you could use the support nav
as a filter (sort of like a tag list idea).