  Geophysical fluids such as the ocean and atmosphere can be stratified: their
density depends on the depth. As a consequence, they can host internal gravity
waves that propagate in the bulk of the fluid, far from the surface. These
waves can transport energy and momentum over large distances, thereby affecting
large-scale circulation patterns, as well as the transport of heat, sediments,
nutrients and pollutants in the ocean. When the density stratification is not
uniform, internal waves can exhibit wave phenomena such as resonances,
tunneling, and frequency-dependent transmissions. Spatially periodic density
profiles formed by thermohaline staircases are commonly found in stratified
fluids ranging from the Arctic Ocean to giant planet interiors, and can produce
extended regions with periodically stratified fluid. Here, we report on the
experimental observation of band gaps for internal gravity waves, ranges of
frequencies over which the wave propagation is prohibited in the presence of a
periodic stratification. We show the existence of surface states controlled by
boundary conditions and discuss their topological origin. Our results suggest
that energy transport can be profoundly affected by the presence of periodic
stratifications in geophysical fluids ranging from Earth's oceans to gas
giants.
