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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)

- James C Mcwilliams, Juan M Restrepo
- 1999

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)

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)

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 M Restrepo, Monte Carlo, Monte Carlo
- 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 eeective action provides an appropriate cost function to determine most probable (or optimal) histories for nonlinear dynamics with strong noise. In such strong-coupling problems, a nonperturbative technique is required to calculate the eeective action. We have proposed a Rayleigh-Ritz variational approximation, which employs simple moment-closures or… (More)

From algal suspensions to magma upwellings, one finds jets which exhibit complex symmetry-breaking instabilities as they are decelerated by their surroundings. We consider here a model system--a saline jet descending through a salinity gradient--which produces dynamics unlike those of standard momentum jets or plumes. The jet coils like a corkscrew within a… (More)

- Nusret Balci, Anna L Mazzucato, Juan M Restrepo, George R Sell, Cahn-Hilliard
- 2010

We propose a variant of the Bred Vector (BV) algorithm, orginally introduced by Z. Toth and E. Kalnay (Bulletin of the American Mete-outputs to changes in initial conditions for weather forecasting. The new algorithm, which we call the Ensemble Bred Vector or EBV, is based on collective dynamics in an essential way. As such, it features distinctive… (More)

For a self-adjoint linear operator with discrete spectrum or a Hermitian matrix the " extreme " eigenvalues define the boundaries of clusters in the spectrum of real eigenvalues. The outer extreme ones are the largest and the smallest eigenvalues. If there are extended intervals in the spectrum in which no eigenvalues are present, the eigenvalues bounding… (More)

- Douglas A Kurtze, Juan M Restrepo
- 2000

We consider a box model of the thermohaline circulation with mixed boundary conditions in which advective processes are incorporated via an explicit time delay mechanism. The pipes which connect the subtropical and subpolar boxes have a nite volume and do not interact with the atmosphere or with the rest of the ocean except for channeling uxes between the… (More)