Internal waves, which are waves formed between two layers of a stratified water column, are observed to propagate towards the coastline in most continental shelve regions. As these waves shoal, or are slowed by bottom friction, when entering into water depths of approximately one-half of the wave amplitude, their interaction with the bottom causes these waves to undergo transformations. Observations of across-shore transport and nutrient and plankton mixing suggest that nonlinear internal waves (NLIWs) play a critical role in the maintenance of some inner shelf benthic communities. However, the across-shore transport length scales, the dispersion rates and the fluxes of buoyancy, momentum and energy, and, thus, the potentially important influence of these waves on coastal circulation and ecosystems, have not yet been quantified. Oceanographers from Oregon State University and the University of North Carolina, with support from the Woods Hole Oceanographic Institute, will use a combined observational and numerical approach to quantify transport, dispersion, buoyancy and momentum fluxes, and flux divergences of shoaling NLIWs and determine their influence on the low-frequency circulation and density field in Massachusetts Bay. Their field observations will include deployments of a mooring array to quantify nonlinear internal wave fluxes, rapid shipboard surveys to study the evolution of individual waves from their generation point, through the region of shoaling, and to their demise near the coast, and dye injections and shipboard tracking to quantify scales of across-shore transport and rates of dispersion. In addition to field observations, a 'state-of-the-art', adaptive grid, nonhydrostatic, numerical model will be used to simulate nonlinear internal wave generation and evolution to compare the numerical output with the field observations and understand the detailed, three-dimensional evolution of these waves. Studying this process will provide an objective assessment of the significance of NLIWs relative to other physical processes in the coastal ocean. Understanding the mechanisms which transport and disperse water-borne materials (e.g., nutrients, pollutants, plankton) in the coastal ocean is a high priority objective for coastal physical oceanographic research and can have direct influence on environmental management.
The interior of the ocean can be idealized as a stack of layers of density increasing from the surface towards the bottom. Undisturbed, the layers are flat. When disturbed, waves, aptly called internal waves, are generated due to the restoring gravitational force. In coastal areas, the tide flowing over topographic reliefs displaces the layers vertically, resulting in the generation of waves that are tied to the tidal forcing. In many coastal areas, these internal waves can be quite large, displacing the density layers by amounts can be as large as 50% of the total depth. These waves affects the biology and geochemistry of the coastal ocean. For example, they can concentrate and move plankton in the direction of propagation, and can promote the resuspension of sediments, contaminants and cists from the sea-bed. In Massachusetts Bay this phenomenon can be readily observed during the summer months. Waves are generated by the tidal flow over Stellwagen Bank, on the eastern side of Massachusetts Bay, and propagate westward towards the coast. Due to the proximity of the Bank from the coastline, where the waves ultimately shoal and break, the area is an excellent natural laboratory to study these waves. In particular, we were interested in understanding how topographical variations along the direction perpendicular to the direction of propagation of the waves affect the evolution of the waves. The project was collaborative, with our group in charge of the numerical modeling component, while the OSU group conducted in situ observations, which are described elsewhere. The challenge in developing a model that can follow the evolution of these waves from generation to shoaling is that the waves have relatively small wavelengths, requiring fine numerical meshes covering a large horizontal domain. In addition, the vertical inertia of the fluid cannot be ignored, resulting in a very challenging numerical problem. Our approach consisted in developing a numerical model, the Stratified Ocean Model with Adaptive Refinement (SOMAR), which combines an efficient way to deploy scarce numerical resources, with a specialized numerical core that does not suffer from the characteristic slow down which standard model suffer from. This model allows for the first time the simulation of nonlinear waves in realistic coastal settings. The model was developed under the guidance of the PI by a graduate student and is available under the GPL license. While it is aimed specifically to simulate strongly baroclinic coastal phenomena, the numerical techniques developed in this project have attracted the interests of astrophysicists interested in simulation the evolution of stellar accretion disks.
