  It has been recently argued that near-integrable nonautonomous
one-degree-of-freedom Hamiltonian systems are constrained by KAM theory even
when the time-dependent (nonintegrable) part of the Hamiltonian is given in the
form of a superposition of time-periodic functions with incommensurate
frequencies. Furthermore, such systems are constrained by one fewer integral of
motion than is required to render the system completely integrable. As a
consequence, the phase space in systems of this type is expected to be
partitioned into nonintersecting regular and chaotic regions. In this note we
provide numerical evidence of the existence of such a characteristic mixed
phase space structure. This is done by considering the problem of acoustic ray
dynamics in deep ocean environments, which is naturally described as a
nonautonomous one-degree-of-freedom Hamiltonian system with a multiply periodic
Hamiltonian in the independent (time-like) variable. Also, we discuss the
implications of a mixed phase space for the dynamics of that geophysical system
and another one which describes Lagrangian motion in the ocean. The latter is
also naturally described as a nonautonomous one-degree-of-freedom Hamiltonian
system with a multiply time-periodic Hamiltonian.
