Lecture Notes for 550.695: Advanced Parameterization
Spring 2009


0. INTRODUCTION :

0. Overview


1. DYNAMICS :

1. (a)Classification

1. (b)Multiple Space/Time Scales

1. (c)Numerical Simulation


2. COARSE-GRAINED DYNAMICS:

2. (a)Spatial Coarse-Graining/Low-Pass Filtering

2. (b)Formal Closure

2. (c)Systematic Closure

2. (d)Systems with No Scale-Separation


3. ENSEMBLES & PROBABILITY:

3. (a)Rationale for a Probabilistic Approach

3. (b)Basic Probability Theory

3. (c)Direct Ensemble Methods

3. (d)Forward Equations


4. MOMENT CLOSURE :

4. (a)Rayleigh-Ritz Variational Method

4. (b)Equation-Free Implementation of Closure

4. (c)General Moment Closure


SPECIAL LECTURE #1: COUNTERFEITING TURBULENCE.

I. (a) Slides

I. (b)Codes


SPECIAL LECTURE #2: TIME-CORRELATIONS AND FLUCTUATION HISTORIES.

I. (a) Slides

I. (b)Code , Part I; Code , Part II;


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Last modified January 17, 2009 by Greg Eyink.