  The von Karman-Howarth equation implies an infinity of invariants
corresponding to an infinity of different asymptotic behaviours of the double
and triple velocity correlation functions at infinite separations. Given an
asymptotic behaviour at infinity for which the Birkhoff-Saffman invariant is
not infinite, there are either none, or only one or only two finite invariants.
If there are two, one of them is the Loitsyansky invariant and the decay of
large eddies cannot be self-similar. We examine the consequences of this
infinity of invariants on a particular family of exact solutions of the von
Karman-Howarth equation.
