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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 9 (1997), S. 2023-2031 
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A low-dimensional model, using the proper orthogonal, or Karhunen–Loève decomposition, has been remarkably successful in representing the behavior of the wall region of a turbulent boundary layer. We briefly summarize this work. We may hope for similar success in other flows in which coherent structures play an important role, in particular flows with density fluctuations. We sketch an approach to such a decomposition for flows with density fluctuations, suggesting various alternatives which weigh the available information differently. In such a low-dimensional model, obtaining the empirical eigenfunctions poses a problem, since they can usually be determined only from extensive measurements or direct numerical simulations. However, recent work with energy method stability theory (modified by use of an anisotropic eddy viscosity and feedback to the mean profile) has been remarkably successful in predicting the form of the empirical eigenfunctions in the isothermal boundary layer. We present here preliminary results for sheared Rayleigh–Bénard convection; these results do not include anisotropic eddy viscosities and feedback, and do not predict directly the form of the POD eigenfunctions; however, a very satisfactory comparison can be made with the second order moments obtained from a DNS. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical and computational fluid dynamics 9 (1997), S. 269-280 
    ISSN: 1432-2250
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Physics
    Notes: Abstract. We study numerical solutions of the reduced-gravity shallow-water equation on a beta plane, subjected to a sinusoidally varying wind forcing leading to the formation of a double gyre circulation. As expected the dynamics of the numerical solutions are highly dependent on the grid resolution and the given numerical algorithm. In particular, the statistics of the solutions are critically dependent on the scheme's ability to resolve the Rossby deformation radius. We present a method, applicable to any finite-difference scheme, which effectively increases the spatial resolution of the given algorithm without changing its temporal stability or memory requirements. This enslaving method makes use of properties of the governing equations in the absence of time derivatives to reduce the overall truncation error. By examining statistical measures of stochastic solutions at resolutions near the Rossby radius, we show that the enslaved schemes are capable of reproducing statistics of standard schemes computed at twice the resolution.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 12 (1996), S. 13-40 
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: We show how the accuracy of a given finite difference scheme approximating a dissipative nonlinear PDE may be improved. The numerical solutions are decomposed into two parts that may be interpreted as approximating the large and small scales of the true solutions. By enslaving the small scales in terms of the larger ones, we derive a new difference scheme that is, in general, more accurate than the original scheme. The new scheme is also more computationally efficient, provided that the time derivatives of the problem are not too large. © 1996 John Wiley & Sons, Inc.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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  • 4
    Publication Date: 2022-05-25
    Description: Author Posting. © The Oceanography Society, 2016. This article is posted here by permission of The Oceanography Society for personal use, not for redistribution. The definitive version was published in Oceanography 29, no. 3 (2016): 96–107, doi:10.5670/oceanog.2016.74.
    Description: The 2010 Deepwater Horizon (DWH) oil spill in the Gulf of Mexico resulted in the collection of a vast amount of situ and remotely sensed data that can be used to determine the spatiotemporal extent of the oil spill and test advances in oil spill models, verifying their utility for future operational use. This article summarizes observations of hydrocarbon dispersion collected at the surface and at depth and our current understanding of the factors that affect the dispersion, as well as our improved ability to model and predict oil and gas transport. As a direct result of studying the area where oil and gas spread during the DWH oil spill, our forecasting capabilities have been greatly enhanced. State-of-the-art oil spill models now include the ability to simulate the rise of a buoyant plume of oil from sources at the seabed to the surface. A number of efforts have focused on improving our understanding of the influences of the near-surface oceanic layer and the atmospheric boundary layer on oil spill dispersion, including the effects of waves. In the future, oil spill modeling routines will likely be included in Earth system modeling environments, which will link physical models (hydrodynamic, surface wave, and atmospheric) with marine sediment and biogeochemical components.
    Description: This research was made possible by a grant from BP/The Gulf of Mexico Research Initiative to the CARTHE and Deep-C Consortia, and by contract M12PC00003 from the Bureau of Ocean Energy Management (BOEM).
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 5
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2005. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Bulletin of the American Meteorological Society 86 (2005): 1733-1737, doi:10.1175/BAMS-86-12-1733.
    Description: A group of junior faculty members and UCAR junior scientists convened in Boulder, CO on June 16-18, 2003 for discussion on future scientific directions. This report summarizes the goals and products of one of the three foci selected for special consideration: predictability. About 15 people, representing physical, mathematical, and biological sciences, were present for round-table discussions. The discussion sought common interpretation of the predictability problem, points of generalization, identification of major hurdles, and potential approaches to their solution. The diverse background of the participants generated a wide-ranging discussion. The participants addressed predictability generally, while supplying specific examples from their own areas of expertise. Recurring themes included the relationship between models and initial conditions, the importance of definitions and the choice of a norm for evaluation, and generalization across systems and disciplines. The group explored potential avenues for generalization through interdisciplinary networking. Short- and long-range challenges were identified related to probabilistic state estimation, verifying predictions and understanding error, and dealing with nonlinearity. In this essay we expand on these themes and challenges, and describe possible future research objectives.
    Repository Name: Woods Hole Open Access Server
    Type: Article
    Format: 68385 bytes
    Format: application/pdf
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