This paper gives a brief overview of some configurations in which high-frequency wave propagation modelled by Helmholtz equation gives rise to solutions that vary rapidly across thin layers. The configurations are grouped according to their mathematical structure and tractability and one of them concerns a famous open problem of mathematical physics.

Since the June 1995 ICES Symposium on Fisheries and Plankton Acoustics in Aberdeen (MacLennan and Holliday, 1996) the use of acoustics for studying zooplankton has seen important advances. Acoustical monitoring of small-scale zooplankton distributions can now be done at intervals of a fraction of a minute. Resolution at vertical spatial scales of tens of centimeters is now easily achieved with commercially available sensors. Multiple-frequency echo-ranging sensors (TAPS™) have been deployed in an up-looking mode on the bottom, and on moorings looking up, down and horizontally. Real-time telemetry provides data on plankton distributions at ranges up to tens of meters from the sensors for periods of weeks to months. These sensors allow one to estimate total zooplankton biomass and the size-abundance spectrum of the animals in the water column at different depths and times. When a profiling CTD and multi-spectral optical sensors were used to define the physical environment and phytoplankton distributions near an acoustical zooplankton profiler, bold relationships were observed between measured spatial and temporal patterns. New methods in zooplankton acoustics are illustrated with data collected from these sensors while monitoring thin, sub-meter thick layers of plankton and diel migrations of benthopelagic crustaceans.