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Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and(More)
The formation of smng and potentially singular fronts in a two-dimensional quasi-geostrophic active scalar is studied here through the symbiotic interaction of mathematical theory and numerical experiments. This active scalar represents the temperature evolving on the two dimensional boundary of a rapidly rotating half space with small Rosshy and Ekman(More)
The single-point probability distribution function ͑PDF͒ for a passive scalar with an imposed mean gradient is studied here. Elementary models are introduced involving advection diffusion of a passive scalar by a velocity field consisting of a deterministic or random shear flow with a transverse time-periodic transverse sweep. Despite the simplicity of(More)
general area of geophysical fluid mechanics is truly interdisciplinary. Ideas from statistical physics are now being applied in novel ways to inhomogeneous complex systems such as atmospheres and oceans. In this book, the basic ideas of geophysics, probability theory, information theory, nonlinear dynamics, and equilibrium statistical mechanics are(More)
Recent observational analysis reveals the central role of three multicloud types, congestus, stratiform, and deep convective cumulus clouds, in the dynamics of large-scale convectively coupled Kelvin waves, westward propagating two-day waves, and the Madden–Julian oscillation. A systematic model convective pa-rameterization highlighting the dynamic role of(More)
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 fashion. These models have an explicitly solvable weak turbulence theory which is developed here, with Kolmogorov-type wave number spectra exhibiting interesting(More)
The filtering skill for turbulent signals from nature is often limited by model errors created by utilizing an imperfect model for filtering. Updating the parameters in the imperfect model through stochastic parameter estimation is one way to increase filtering skill and model performance. Here a suite of stringent test models for filtering with stochastic(More)
It is well-known that the envelope of the Madden-Julian oscillation (MJO) consists of smaller scale con-vective systems, including mesoscale convective systems (MCS), tropical cyclones, and synoptic scale waves called " convectively coupled equatorial waves " (CCW). In fact, recent results suggest that the fundamental mechanisms of the MJO involve(More)