Discrimination of coherent features in turbulent boundary layers by the entropy method
Abstract
Entropy in information theory is defined as the expected or mean value of the measure of the amount of selfinformation contained in the ith point of a distribution series x sub i, based on its probability of occurrence p(x sub i). If p(x sub i) is the probability of the ith state of the system in probability space, then the entropy, E(X) =  sigma p(x sub i) logp (x sub i), is a measure of the disorder in the system. Based on this concept, a method was devised which sought to minimize the entropy in a time series in order to construct the signature of the most coherent motions. The constrained minimization was performed using a Lagrange multiplier approach which resulted in the solution of a simultaneous set of nonlinear coupled equations to obtain the coherent time series. The application of the method to spacetime data taken by a rake of sensors in the nearwall region of a turbulent boundary layer was presented. The results yielded coherent velocity motions made up of locally decelerated or accelerated fluid having a streamwise scale of approximately 100 nu/u(tau), which is in qualitative agreement with the results from other less objective discrimination methods.
 Publication:

AIAA, Aerospace Sciences Meeting
 Pub Date:
 January 1984
 Bibcode:
 1984aiaa.meetX....C
 Keywords:

 Discriminant Analysis (Statistics);
 Entropy (Statistics);
 Maximum Entropy Method;
 Numerical Flow Visualization;
 Turbulent Boundary Layer;
 Coherence;
 Minimum Entropy Method;
 Probability Theory;
 Time Series Analysis;
 Fluid Mechanics and Heat Transfer