Time-Dependent Probability Density Functions and Attractor Structure in Self-Organised Shear Flows

Probability distribution function for self-organization of shear flows

The Baroclinic Adjustment of Time-Dependent Shear Flows

Motivated by the fact that time-dependent currents are ubiquitous in the ocean, this work studies the twolayer Phillipsmodel on the beta plane with baroclinic shear flows that are steady, periodic, or aperiodic in time to understand their nonlinear evolution better. When a linearly unstable basic state is slightly perturbed, the primary wave grows exponentially until nonlinear advection adjusts...

Eulerian Mapping Closure Approach for Probability Density Function of Concentration in Shear Flows

The Eulerian mapping closure approach is developed for uncertainty propagation in computational uid mechanics. The approach is used to study the Probability Density Function (PDF) for the concentration of species advected by a random shear ow. An analytical argument shows that uctuation of the concentration eld at one point in space is non-Gaussian and exhibits stretched exponential form. An Eu...

Perturbation Growth and Structure in Time-Dependent Flows

Asymptotic linear stability of time-dependent flows is examined by extending to nonautonomous systems methods of nonnormal analysis that were recently developed for studying the stability of autonomous systems. In the case of either an autonomous or a nonautonomous operator, singular value decomposition (SVD) analysis of the propagator leads to identification of a complete set of optimal pertur...

Visualizing Climate Variability with Time-Dependent Probability Density Functions, Detecting It Using Information Theory

A framework is presented for visualizing and detecting climate variability and change based on time-dependent probability density functions (PDFs). The PDFs show how the distribution of values in the sample window changes over time and show more detail than do timeseries of windowed moments. A set of information-theoretic statistics based on the Shannon entropy and the Kullback-Leibler divergen...