{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:36:33Z","timestamp":1760243793820,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2011,1,31]],"date-time":"2011-01-31T00:00:00Z","timestamp":1296432000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>This paper presents the results of a study of the prediction of the entropy growth within an internal free shear layer of an ideal gas flow downstream of a sudden expansion of the flow area. The objective of the study is exploratory in nature by invoking concepts from information theory to connect the deterministic prediction of the spectral entropy growth within the shear layer to the experimentally inferred increase in entropy across the flow region. The deterministic prediction of the spectral entropy increase along the shear layer is brought into agreement with the experimentally inferred increase in entropy through the ad hoc inclusion of the activation spectral entropy. The values for this activation spectral entropy are directly related to the area ratios across the expansion region and have a specific numerical value for each area ratio.<\/jats:p>","DOI":"10.3390\/e13020402","type":"journal-article","created":{"date-parts":[[2011,1,31]],"date-time":"2011-01-31T11:44:06Z","timestamp":1296474246000},"page":"402-421","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Deterministic Prediction of the Entropy Increase in a Sudden Expansion"],"prefix":"10.3390","volume":"13","author":[{"given":"LaVar King","family":"Isaacson","sequence":"first","affiliation":[{"name":"Professor Emeritus of Mechanical Engineering, University of Utah, 2067 Browning Avenue, Salt Lake City, UT 84108, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2011,1,31]]},"reference":[{"key":"ref_1","unstructured":"Gosman, A.D., Pun, W.M., Runchal, A.K., Spalding, D.B., and Wolfshtein, M. (1969). Heat and Mass Transfer in Recirculating Flows, Academic."},{"key":"ref_2","unstructured":"Patankar, S.V. (1980). Numerical Heat Transfer and Fluid Flow, Hemisphere."},{"key":"ref_3","unstructured":"Pantankar, S.V. (1991). Computation of Conduction and Duct Flow Heat Transfer, Innovative Research."},{"key":"ref_4","unstructured":"Hirsch, C. (2007). Numerical Computation of Internal and External Flows: Fundamentals of Computational Fluid Dynamics, Butterworth-Heinemann."},{"key":"ref_5","first-page":"234","article-title":"Numerical prediction of entropy generation in separated flows","volume":"4","year":"2005","journal-title":"Entropy"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"38","DOI":"10.3390\/e7010038","article-title":"Numerical study on local entropy generation in compressible flow through a suddenly expanding pipe","volume":"7","author":"Yapici","year":"2005","journal-title":"Entropy"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1103\/PhysRev.108.171","article-title":"Information theory and statistical mechanics. II","volume":"108","author":"Jaynes","year":"1957","journal-title":"Phys. Rev."},{"key":"ref_8","unstructured":"Barclay, L.P. (1972). Pressure losses in dump combustors, unpublished work."},{"key":"ref_9","unstructured":"Oates, G.C. (1988). Aerothermodynamics of Gas Turbines and Rocket Propulsion, AIAA."},{"key":"ref_10","unstructured":"Landau, L.D., and Lifshitz, E.M. (1958). Quantum Mechanics: Non-Relativistic Theory, Pergamon Press, Ltd."},{"key":"ref_11","unstructured":"Townsend, A.A. (1976). The Structure of Turbulent Shear Flow: Second Edition, Cambridge University Press."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1063\/1.867010","article-title":"Chaotic behavior of interacting elliptical instability modes","volume":"31","author":"Hellberg","year":"1988","journal-title":"Phys. Fluid."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1515\/jnet.1993.18.3.256","article-title":"A deterministic prediction of ordered structures in an internal free shear layer","volume":"18","author":"Isaacson","year":"1993","journal-title":"J. Non-Equilib. Thermodyn."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1016\/0375-9601(92)90745-8","article-title":"Continuous control of chaos by self-controlling feedback","volume":"170","author":"Pyragas","year":"1990","journal-title":"Phys. Lett. A"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/0375-9601(93)90640-L","article-title":"Predictable chaos in slightly perturbed unpredictable chaotic systems","volume":"181","author":"Pyragas","year":"1993","journal-title":"Phys. Lett. A"},{"key":"ref_16","unstructured":"Glasstone, S., Laidler, K.J., and Eyring, H. (1941). The Theory of Rate Processes, McGraw-Hill Book Company, Inc."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1017\/S0022112067000941","article-title":"On finite amplitude oscillation in laminar mixing layers","volume":"29","author":"Stuart","year":"1967","journal-title":"J. Fluid Mech."},{"key":"ref_18","unstructured":"Kirchoff, R.H. (1985). Potential Flows: Computer Graphics Solutions, Marcell Dekker, Inc."},{"key":"ref_19","unstructured":"Press, W., Teukilsky, S.A., Vetterling, W.T., and Flannery, B.P. (1992). Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press. [2nd ed.]."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Golyandina, N., Nekrutkin, V., and Zhiglijavsky, A. (2001). Analysis of Time Series Structure: SSA and Related Techniques, CRC Press LLC.","DOI":"10.1201\/9781420035841"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.ijforecast.2008.09.007","article-title":"Forecasting European industrial production with singular spectrum analysis","volume":"25","author":"Hassani","year":"2009","journal-title":"Int. J. Forecast."},{"key":"ref_22","unstructured":"Press, W., Teukilsky, S.A., Vetterling, W.T., and Flannery, B.P. (1992). Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press. [2nd ed.]."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Kantz, H., and Schreiber, T. (2004). Nonlinear Time Series Analysis, Cambridge University Press. [2nd ed.].","DOI":"10.1017\/CBO9780511755798"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Maindonald, J., and Braun, W.J. (2010). Data Analysis and Graphics Using R: An Example-Based Approach, Cambridge University Press. [3rd ed.].","DOI":"10.1017\/CBO9781139194648"},{"key":"ref_25","unstructured":"Press, W., Teukilsky, S.A., Vetterling, W.T., and Flannery, B.P. (1992). Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press. [2nd ed.]."},{"key":"ref_26","unstructured":"Chen, C.H. (1982). Digital Waveform Processing and Recognition, CRC Press, Inc."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2053","DOI":"10.1088\/0305-4470\/12\/11\/017","article-title":"A spectral entropy method for distinguishing regular and irregular motion for Hamiltonian systems","volume":"12","author":"Powell","year":"1979","journal-title":"J. Phys. Math. Gen."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2591","DOI":"10.1103\/PhysRevA.28.2591","article-title":"Estimation of the Kolmogorov entropy from a chaotic signal","volume":"28","author":"Grassberger","year":"1983","journal-title":"Phys. Rev. A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1872","DOI":"10.1103\/PhysRevA.31.1872","article-title":"Computing the Kolmogorov entropy from time signals of dissipative and conservative dynamical systems","volume":"31","author":"Cohen","year":"1985","journal-title":"Phys. Rev. A"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1016\/0167-2789(95)00041-2","article-title":"Generalized redundancies for time series analysis","volume":"84","author":"Prichard","year":"1995","journal-title":"Phys. Nonlinear Phenom."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Lynch, S. (2004). Dynamical Systems with Applications Using MATLAB, Birkhauser.","DOI":"10.1007\/978-0-8176-8156-2"},{"key":"ref_32","unstructured":"Tribus, M. (1961). Thermostatics and Thermodynamics: An Introduction to Energy, Information and States of Matter, with Engineering Applications, D. Van Nostrand Company, Inc."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Mathieu, J., and Scott, J. (2000). An Introduction to Turbulent Flow, Cambridge University Press.","DOI":"10.1017\/CBO9781316529850"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Sagaut, P., and Cambon, C. (2008). Homogeneous Turbulence Dynamics, Cambridge University Press.","DOI":"10.1017\/CBO9780511546099"},{"key":"ref_35","unstructured":"Saad, M.A. (1985). Compressible Fluid Flow, Prentice-Hall, Inc."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/13\/2\/402\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:55:07Z","timestamp":1760219707000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/13\/2\/402"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,1,31]]},"references-count":35,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2011,2]]}},"alternative-id":["e13020402"],"URL":"https:\/\/doi.org\/10.3390\/e13020402","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2011,1,31]]}}}