Eddy Structure Identification pp 145-195 | Cite as

# Stochastic Estimation of the Structure of Turbulent Fields

## Abstract

The stochastic estimation method educes structure by approximating an average field in terms of event data that are given. The estimated fields satisfy the continuity equation, and they possess the correct scales of length and/or time. The fundamental concepts of general stochastic estimation and the specific application of this technique to the estimation of conditional averages are discussed. Linear stochastic estimation of random fields and of their conditional averages is developed as the principal tool, and its accuracy is demonstrated. The linear stochastic estimate is expressible in terms of second order correlation functions between the given event data and the quantity being estimated. This establishes a simple link between conditional averages, the coherent structure that they represent and correlation functions. The related problems of selecting events and interpreting the estimates that result from a given set of events are explored by considering events of increasing complexity: single-point vectors, two-point vectors, local deformation tensors, multi-point vectors, space-time vectors, and space-wave-number events. General kinematic and statistical properties are derived, and stochastically estimated structures from various types of turbulent flows are described and related to the underlying coherent structures.

## Keywords

Wall Shear Stress Shear Layer Coherent Structure Vortex Ring Proper Orthogonal Decomposition## Preview

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