A family of one-dimensional nonlinear dispersive wave equations is introduced as a model for assessing the validity of weak turbulence theory for random waves in an unambiguous and transparent… (More)

A complete self-contained treatment of the stability and convergence properties of conservation-form, monotone difference approximations to scalar conservation laws in several space variables is… (More)

A natural class of appropriate viscosity matrices for strictly hyperbolic systems of conservation laws in one space dimension, II, + f(u), =0, u E R”, is studied. These matrices are admissible in the… (More)

Several different ways of constructing optimal bases for efficient dynamical modeling are compared: empirical orthogonal functions (EOFs), optimal persistence patterns (OPPs), and principal… (More)

There has been a recent burst of activity in the atmosphere/ocean sciences community in utilizing stable linear Langevin stochastic models for the unresolved degree of freedom in stochastic climate… (More)

In dynamical systems with intrinsic chaos, many degrees of freedom, and many conserved quantities, a fundamental issue is the statistical relevance of suitable subsets of these conserved quantities… (More)

The first mathematically rigorous equilibrium statistical theory for three-dimensional vortex filaments is developed here in the context of the simplified asymptotic equations for nearly parallel… (More)

In an earlier paper the authors introduced a new version of the vortex method for three-dimensional, incompressible flows and proved that it converges to arbitrarily high order accuracy, provided we… (More)

The nature of predictability is examined in a numerical model relevant to the midlatitude atmosphere and oceans. The approach followed is novel and uses new theoretical tools from information theory,… (More)

Tropical cyclogenesis is studied in the context of idealized three-dimensional Boussinesq dynamics with perhaps the simplest possible model for bulk cloud physics. With low-altitude input of water… (More)