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- Jerry L. Bona, William R. McKinney, Juan M. Restrepo
- J. Nonlinear Science
- 2000

Investigated here are interesting aspects of the solitary-wave solutions of the generalized Regularized Long-Wave equation u t + u x + (u p) x ? u xxt = 0: For p > 5, the equation has both stable and unstable solitary-wave solutions, according to the theory of Souganidis and Strauss. Using a high-order accurate numerical scheme for the approximation of… (More)

Oceanic surface gravity waves have a mean Lagrangian motion, the Stokes drift. The dynamics of wind-driven, basin-scale oceanic currents in the presence of Stokes drift are modified by the addition of so-called vortex forces and wave-induced material advection, as well by wave-averaged effects in the surface boundary conditions for the dynamic pressure, sea… (More)

- Juan M. Restrepo, Gary K. Leaf, Andreas Griewank
- SIAM J. Scientific Computing
- 1998

An application of Pontryagin's Maximum Principle, data assimilation is used to blend possibly incomplete or nonuniformly distributed spatio-temporal observational data into geo-physical models. Used extensively in engineering control theory applications, data assimilation has relatively recently been introduced into meteorological forecasting,… (More)

- Pierre FJ Lermusiaux, Bani K. Mallick, +14 authors Karen Willcox
- 2011

Description: This workshop will assess the current state-of-the-art and identify needs and opportunities for future research at the intersection of large-scale inverse problems and uncertainty quantification. It will bring together and cross-fertilize the perspectives of researchers in the areas of inverse problems and data assimilation, statistics,… (More)

- Jerry L. Bona, John P. Albert, Juan M. Restrepo
- SIAM Journal of Applied Mathematics
- 1999

Considered here is a model equation put forward by Benjamin that governs approximately the evolution of waves on the interface of a two-uid system in which surface tension eeects cannot be ignored. Our principal focus is the traveling-wave solutions called solitary waves, and three aspects will be investigated. A constructive proof of the existence of these… (More)

- Juan Mario Restrepo, Gary K Leafy
- 1997

Inner products of wavelets and their derivatives are presently known as connection coeecients. The numerical calculation of inner products of periodized Daubechies wavelets and their derivatives is reviewed, with the aim at providing potential users of the publicly-available numerical scheme, details of its operation. The numerical scheme for the… (More)

- Juan M. Restrepo
- 2007

Described here is a path integral, sampling-based approach for data assimilation, of sequential data and evolutionary models. Since it makes no assumptions on linearity in the dynamics, or on Gaussianity in the statistics, it permits consideration of very general estimation problems. The method can be used for such tasks as computing a smoother solution,… (More)

The relative merits of the wavelet-Galerkin solution of hyperbolic partial diieren-tial equations, typical of geophysical problems, are quantitatively and qualitatively compared to traditional nite diierence and Fourier-pseudo-spectral methods. The wavelet-Galerkin solution presented here is found to be a viable alternative to the two conventional… (More)

We present a theory for the interactions of waves and currents which results from depth-averaging the wave-driven circulation model proposed by McWilliams and Restrepo. This circulation model couples the gravity wave eld to oceanic scale ows. It speciically identiies the the drift velocity due to the gravity waves as the primary eeect of waves on the… (More)

This paper presents and evaluates the numerical solution of a coupled system of equations that arises in a model for the formation and evolution of three-dimensional longshore sand ridges. The model is based on the interaction between surrcial or internal weakly nonlinear shallow-water waves, having weak spanwise spatial dependence, and the deformable… (More)