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The Navier-Stokes equations remain a great mystery in mathematical physics. The equations govern fluid motion, and their complexity exists in the fact that although the governing equations are the same throughout scales of space and time spanning several orders of magnitude, the resulting behavior can be surprisingly different at each scale. Although otherwise intractable, the solution of the Navier-Stokes equations is amenable to large-scale numerical computation. Because of the multitude of scales involved in the Navier-Stokes equations, the need to better resolve these scales in numerical modeling through the use of high-performance computers will continue forever or until an analytical solution is found.
Adaptive Mesh Refinement (AMR) is emerging as the method of choice for multi-scale computational fluid mechanics. As the name implies, AMR methods are able to adapt computational resources to resolve interesting flow features in a particular system… and what better system to apply the method to than the world's oceans? With so many interesting features on a variety of scales, such as surface waves, internal waves, Kelvin waves, mesoscale eddies, and oceanic gyres, it's sometimes hard to choose one in particular. With AMR you don't have to tailor your simulation around a particular scale or feature.
I am working to develop a block-structured AMR non-hydrostatic ocean model. While applicable to many oceanic phenomena, the model will be applied to simulation of internal wave generation and propagation.
"Maximum annually recurring wave heights in Hawai‘i." Vitousek, S. and Fletcher, C.H.. Pacific Science, vol. 62, no. 4: 541-553. 2008.
"Frequency and Duration of Coinciding High Surf and Tides
along the North Shore of Oahu, Hawaii, 1981--2007" Caldwell, P., Vitousek, S., Aucan, J., Journal of Coastal Research. In Press. 2009.
"A practical approach to mapping extreme wave inundation: consequences of sea-level rise and coastal erosion." Vitousek, S., Fletcher, C.H. and Barbee, M. Proceedings: Solution to Coastal Disaster 2008, Oahu, Hawaii, April 13-16, p. 85-96. 2008.
"Model Scenarios of Shoreline Change at Kaanapali Beach, Maui, Hawaii: Seasonal and Extreme Events", S. Vitousek, C.H. Fletcher, M. Merrifield, G. Pawlak, C. Storlazzi. ASCE Coastal Sediments 2007 Conference Proceedings, v. 2, p. 1227-1240. 2007.
"Natural and Anthropogenic Controls on Beach Morphology from Analysis of Terrestrial Scanning Laser Time Series Data, Waimea Bay, Oahu." Brooks, B A. Becker, J. Merrifield, M. Foster, J. Ericksen, T. Hilmer, T. Vitousek, S. Eos Trans. AGU, 89(53). 2008. Fall Meet. Suppl., Abstract G52A-05.
"Coral Reefs of the U.S.A." Fletcher, C.H., Bochicchio, C., Conger, C.L., Engels, M., Feirstein, E.J., Grossman, Grigg, R., E.E., Harney, J.N., Rooney, J.J., Sherman, C.E., Vitousek, S., Rubin, K., Murray-Wallace, C.V. (2008) Geology of Hawaii Reefs. Chapter 11, Springer, p. 435-488.
"Modeling alongshore propagating tides and currents around West Maui, Hawaii and implications for transport using Delft3D", S. Vitousek, C.H. Fletcher, and C. Storlazzi. POSTER. AGU Fall meeting Dec, 2006. OC11C-1524.
"Crystallization Damage from Ice and Salt", S. Vitousek, J.J. Valenza II, and G.W. Scherer, presented at the 107th Annual Meeting of the American Ceramic Society, Cements Division, Baltimore, MD, April 10-13, 2005
"Expansion of hardened cement paste in saline solutions", J.J. Valenza II, S. Vitousek, and G.W. Scherer, pp. 207-212 in Creep, Shrinkage and Durability of Concrete and Concrete Structures, ed. G.Pijaudier-Cabot, B. Gerard, P. Acker (Hermes, London, 2005).
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