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Entropy 2013, 15(1), 53-79; doi:10.3390/e15010053
Article

Ordered Regions within a Nonlinear Time Series Solution of a Lorenz Form of the Townsend Equations for a Boundary-Layer Flow

Received: 21 August 2012 / Revised: 12 December 2012 / Accepted: 20 December 2012 / Published: 24 December 2012
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Abstract

A modified form of the Townsend equations for the fluctuating velocity wave vectors is applied to a laminar three-dimensional boundary-layer flow. These equations are cast into a Lorenz-type system of equations. The initial system of Lorenz equations yields the generation of masked output signals containing internal ordered regions. The self-synchronizing property of the Lorenz system of equations is then exploited by considering the initial Lorenz system as a transmitter system providing chaotic masked information signals to a series of identical Lorenz receiver systems. The output signal from each successive receiver system indicates the growing recovery of ordered regions in the chaotic output signal. Finally, the three-dimensional graph of the output velocity wave vector signal from the fourth receiver system and the spectral entropy rates for the output axial velocity wave vector indicate the presence of ordered regions which are characterized as axially-directed spiral vortices.
Keywords: normal shock waves; boundary-layer flows; internal flow instabilities; spectral entropy rates; ordered regions; synchronized chaotic flow normal shock waves; boundary-layer flows; internal flow instabilities; spectral entropy rates; ordered regions; synchronized chaotic flow
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Isaacson, L.K. Ordered Regions within a Nonlinear Time Series Solution of a Lorenz Form of the Townsend Equations for a Boundary-Layer Flow. Entropy 2013, 15, 53-79.

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