A Turbulence Closure Based On The
Maximum Entropy Method
Author(s)
R. W. Derksen
Abstract
The fundamental problem of turbulence is that of closing the infinite sequence of
equations that result from the application of Reynolds averaging to the governing
relations for momentum, heat and mass transfer. These equations model the
moments of the turbulent probability density, PDF, such as the first, second,
third, and higher order moments, each equation depending on higher order
moments. The ability to relate the set of moments of order n to moments of n+1
would permit closure to a finite system of equations as we could truncate the
sequence of equations. The concept of the Shannon entropy allows us to model
the degree of uncertainty of a PDF. The Shannon entropy is related to the
concept of thermodynamic entropy. The maximum entropy method determines
the PDF that maximizes the entropy subject to a number of constraints. The most
usual method is to use a finite number of lower order moments. A maximum
entropy PDF is often used to approximate the shape of a PDF as the solution has
desirable features such as being positive definite. The maximum entropy method
is of great value as an approximation method in general. An examination of the
behavior of the moments generate from a maximum entropy for a single degree
of freedom fit to real, turbulent PDFs for velocity, skin-friction, and temperature
fluctuations have been carried out to examine the methods ability predictive
capability. In this examination experimentally determined data sets that
contained data for all moments up to the sixth order were compiled from the
literature. The maximum entropy method was applied using the first four
moments. The fifth and sixth moments computed from the maximum entropy
approximations were compared and found to compare very favorably with those
measured. The presentation will start with a review of the maximum entropy
method for a finite number of moments and a discussion of the computational
Keywords
turbulence closure, maximum entropy, turbulence modelling, turbulent PDF
Related Book
Other papers in this volume
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