The wave solutions discovered by Rossby are of fundamental importance
for atmospheric dynamics. The nonlinear interactions between these waves
determine the primary characteristics of the energy spectrum. These
interactions take place between triplets of waves known as “resonant
triads” and, for a small amplitude, they are described by the
three-wave equations. These same equations also govern the dynamics of a
simple mechanical system, the elastic pendulum or swinging spring.
This equivalence allows us to deduce properties, not otherwise evident,
of resonant triads from the behavior of the mechanical system. In
particular, the characteristic stepwise precession of the swing plane,
so obvious from observation of the physical spring pendulum, is also
found for the Rossby triads. This phenomenon has not been previously
noted and is an example of the insight coming from the mathematical
equivalence of the two systems. The implications of the precession for
predictability of atmospheric motions are considered. The pattern of
breakdown of unstable Rossby waves is very sensitive to unobservable
details of the perturbations, making accurate prediction very
difficult.