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Peter Diamessis

105 Hollister Hall
255-1719
pjd38@cornell.edu

Research

Our research focuses on the investigation of basic fluid flow processes in the natural environment through numerical simulation. The environmental flows of interest occur at scales of 1 km or less in the open/coastal ocean and in lakes. Such flows are governed by extremely complex dynamics over a broad range of scales characterized by wave propagation, highly energetic localized events (intermittent turbulent bursts, sharp fronts, critical layers etc.) and interactions with solid boundaries. Computational process modeling isolates the salient features of the flow of interest and seeks to replicate, as accurately as possible, the fundamental underlying mechanisms at high spatiotemporal resolution and a tractable computational cost.

 

We employ spectral/spectral multidomain schemes (based on Fourier, Legendre and Chebyshev orthogonal polynomials) in the discretization of the governing equations. The combination of spectral discretization with the spatial adaptivity of the multidomain approach permits the reproduction of localized finescale flow features (such as instabilities and turbulence) with very high (spectral) accuracy. In addition, the domain decomposition philosophy inherent in the above numerical methodologies makes them ideal candidates for efficient implementation on distributed memory computers (e.g. Linux clusters). Until lately however, the non-dissipative character of spectral multidomain schemes prohibited their application to the inherently under-resolved simulations of high Reynolds number flows due to inevitable and catastrophic numerical instabilities. Through the development and implementation of a spectral multidomain penalty method model, we successfully addressed this issue for the case of flows in domains with one non-periodic direction. Our objective is to extend multidomain penalty techniques to increasingly complex domain geometries. We ultimately aim to provide  the capability for non-hydrostatic simulations of flow phenomena near coastlines, irregular bathymetries and closed basins with high accuracy, adaptivity and parallelism.

 

The specific flow processes we investigate share the common feature of ambient stable density stratification. We are particularly interested in the interplay between turbulence and internal gravity waves near or away from benthic/lateral boundaries. Example flows include stratified turbulent wakes, the boundary layers induced by propagating internal solitary wave (ISW) packets in lakes or the coastal ocean, the shoaling of ISW and the absorption of internal wave packets by critical layers. The objective is to characterize the coherent structure of the turbulent and internal wave components of these flows and to quantify the associated transport, dissipation and mixing. We are also interested in studying the interaction between hydrodynamics and biology in environmental stratified flows, e.g. the formation of thin layers of nutrients due to ISW-induced resuspension in coastal regions. The insight gained by our physical investigations facilitates the development of parameterizations used in larger, regional-scale simulations.

 

Finally, we firmly believe that our computational studies clearly benefit through feedback with more experimentally, observationally or theoretically oriented colleagues. On one hand, the realism of numerical simulations can be greatly enhanced through information on initial/boundary conditions and forcing from all three of the above orientations. On the other, computation can complement shortcomings of the laboratory/field arising from spatiotemporally incomplete data and can transcend the parameter limitations of theoretical models. We are thus strong proponents of regular interactions with Fluid Dynamicists, Applied Mathematicians, Computer Scientists, Environmental Engineers, a Physical Oceanographers/Limnologists and Marine Biologists.